DEPARTMENT OF INDUSTRIAL ENGINEERING & MANAGEMENT · 2016-02-27 · Motivation Theories, Communication – Meaning and Importance – Coordination, Meaning and importance ... Compare

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(ACADEMIC YEAR 2011-12)

VV SSEEMM EESSTTEERR Name : _____________________________________________ USN : _____________________________________________ Semester & Section : _____________________________________________

The Mission

“The mission of our institutions is to provide

world class education in our chosen fields and

prepare people of character, caliber and vision

to build the future world”

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06IM51-MANAGEMENT AND ENTREPRENEURSHIP

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MANAGEMENT AND ENTREPRENEURSHIP

Sub Code:06IM51 IA Marks: 25 Hrs / Week: 5 Hrs Exam: 3 Hrs Total Hrs: 62 Marks: 100

MANAGEMENT PART – A

UNIT – I MANAGEMENT: Introduction - meaning – nature and characteristics of Management, scope and Functional Areas of Management, management science, art of profession – Management & Administration – roles of management, Levels of Management, Development of Management Thought – early management approaches – Modern management approaches. 06 Hrs UNIT – II PLANNING: Nature, Importance and purpose of planning process – objectives - Types of plans(meaning only) – Decision making – Importance of Planning - Steps in planning and planning premises – Hierarchy of plans. 07 Hrs UNIT – III ORGANIZING AND STAFFING: Nature and purpose of Organization, Principles of Organizations, Types of Organizations – Departmentation. Centralization vs. Decentralization of Authority and responsibility, Span of Control, MBO and MBE (meaning only) Nature and importance of Staffing, Process of selection and recruitment (In brief). 07 Hrs UNIT – IV DIRECTING & CONTROLLING: Meaning and nature of directing – Leadership styles, Motivation Theories, Communication – Meaning and Importance – Coordination, Meaning and importance and techniques of co-ordination. Meaning and steps in controlling – Essentials of a sound control system – Methods of establishing control (in brief). 08 Hrs

PART - B UNIT – V ENTREPRENEURSHIP: Meaning of Entrepreneur; Evolution of the concept, Function of an Entrepreneur, Types of Entrepreneur, Intrapreneur – An emerging class. Concept of Entrepreneurship – evolution of entrepreneurship, development of entrepreneurship; stages in entrepreneurial process; Role of entrepreneurs in economic development; entrepreneurship in India; entrepreneurship – its barriers. 06 Hrs UNIT – VI SMALL SCALE INDUSTRIES: Definition; Characteristics; Need and rationale; Objectives; Scope; role of SSI in Economic Development. Advantages of SSI Steps to start and SSI – Government policy towards SSI; Different Policies of SSI; Government Support for SSI during 5 year plans. Impact of Liberalization, Privatization, Globalization on SSI Effect of WTO/GATT Supporting Agencies of Government for SSI, Meaning, Nature of support; Objectives; Functions; Types of Help; Ancillary Industry and Tiny Industry (Definition Only). 07 Hrs UNIT - 7 INSTITUTIONAL SUPPORT: Different Schemes; TECKSOK; KIADB; KSSIDC; KSIMC; DIC Single Window Agency; SISI; NSIC; SIDBI; KSFC. 07 Hrs

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UNIT - 8 PREPARATION OF PROJECT: Meaning of Project; Project Identification; Project Selection; Project Report; Need and Significance of Report; Contents; Formulation; Guidelines by Planning Commission for Project report; Network Analysis; Errors of Project Report; Project Appraisal. Identification of business opportunities: Market Feasibility Study; Technical Feasibility Study; Financial Feasibility Study & Social Feasibility Study. 07 Hrs TEXT BOOKS: 1. Principles of Management – P.C.Tripathi, P.N.Reddy – Tata McGraw Hill, 2. Dynamics of Entrepreneurial Development & Management – Vasant Desai – Himalaya Publishing House 3. Entrepreneurship Development – Poornima.M.Charantimath – Small Business Enterprises – Pearson Education – 2006 (2 & 4). REFERENCE BOOKS: 1. Management Fundamentals – Concepts, Application, Skill Development – Robers Lusier – Thomson – 2. Entrepreneurship Development – S.S.Khanka – S.Chand & Co. 3. Management – Stephen Robbins – Pearson Education/PHI – 17th Edition, 2003.

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LESSON PLAN

Sub Code: 06IM51 I.A. Marks: 25 Hours / Week: 05 Total Hours: 62 Subject: Management & Entrepreneurship Sem:V

Hour Topics to be covered

1. Introduction - meaning – nature and characteristics of Management

2. Scope and Functional Areas of Management

3. Management science, art of profession 4. Management & Administration 5. Roles of management, Levels of Management 6. Revision/quiz/surprise test 7. Development of Management Thought 8. Early management approaches – Modern management approaches 9. Nature, Importance and purpose of planning process 10. Objectives - Types of plans (meaning only) 11. Decision making 12. Revision/quiz/surprise test 13. Importance of Planning 14. Steps in planning and planning premises 15. Hierarchy of plans 16. Nature and purpose of Organization 17. Principles of Organizations 18. Revision/quiz/surprise test 19. Types of Organizations

20. Departmentation. Centralization vs. Decentralization of Authority and responsibility

21. Span of Control - MBO and MBE (meaning only) Nature and importance of Staffing

22. Process of selection and recruitment (In brief). 23. Meaning and nature of directing – Leadership styles 24. Revision/quiz/surprise test 25. Motivation Theories 26. Communication – Meaning and Importance – Coordination 27. Meaning and importance and techniques of co-ordination 28. Meaning and steps in controlling 29. Essentials of a sound control system 30. Revision/quiz/surprise test 31. Methods of establishing control (in brief). 32. Meaning of Entrepreneur; Evolution of the concept,.,; 33. Function of an Entrepreneur, Types of Entrepreneur 34. Intrapreneur – An emerging class

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35. Concept of Entrepreneurship – evolution of entrepreneurship 36. Revision/quiz/surprise test

37. Development of entrepreneurship; stages in entrepreneurial process; Role of entrepreneurs in economic development

38. Entrepreneurship in India; entrepreneurship – its barriers. 39. Definition; Characteristics; Need and rationale; Objectives; Scope;., 40. Role of SSI in Economic Development.

41. Advantages of SSI Steps to start and SSI – Government policy towards SSI; Different Policies of SSI;

42. Revision/quiz/surprise test 43. Government Support for SSI during 5 year plans

44. Impact of Liberalization, Privatization, Globalization on SSI Effect of WTO/GATT Supporting Agencies of Government for SSI

45. Meaning, Nature of support; Objectives; Functions; Types of Help; Ancillary Industry and Tiny Industry (Definition Only).

46. Different Schemes; TECKSOK 47. KIADB; KSSIDC 48. Revision/quiz/surprise test 49. KSIMC; DIC Single Window Agency 50. SISI 51. NSIC 52. SIDBI 53. KSFC 54. Revision/quiz/surprise test 55. Meaning of Project; Project Identification 56. Project Selection; Project Report; Need and Significance of Report 57. Contents; Formulation; Guidelines by Planning Commission for Project report 58. Network Analysis; Errors of Project Report; Project Appraisal. 59. Identification of business opportunities: 60. Market Feasibility Study; Technical Feasibility Study; 61. Financial Feasibility Study & Social Feasibility Study. 62. Revision/quiz/surprise test

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QUESTION BANK 1. Define ‘Management’. What are its crucial elements? 2. What does the ‘Management Process’ mean? 3. What are the 5 major functions of management? Would you attach different levels of

importance to these functions at various levels of management? 4. Is planning the most important function of management? If so, why? 5. Discuss the importance of management in the present world. 6. Discuss the different approaches/ system models in management. 7. What are some of the social issues a management is expected to be involved with? 8. Discuss a few approaches to meeting social responsibilities. 9. What are ‘Ethics’? Elaborate on some of the pressure points for an ethical management. 10. Discuss the evolution of management techniques. 11. Write in detail on Taylor’s 5 principles of management. 12. Write a short note on Gilbreth’s contribution to management. 13. Explain some of the reasons for planning. Are there ‘good’ plans and ‘bad’ plans? 14. Describe the characteristics of good planning. 15. Briefly discuss the steps in the process of formal planning. 16. Resistance to change is considered as a major problem in implementing innovative plans.

What are the causes for resistance and how can they be rectified? 17. Differentiate between the different types of strategies employed in organizational planning. 18. Explain in detail the concept of ‘policies, procedures and rules’. 19. Differentiate between qualitative decision-making and quantitative decision-making. Under

what circumstances is each type more suitable? 20. Explain the qualitative decision-making step-by-step. 21. Differentiate between programmed and non-programmed decisions. 22. What are the advantages of group decision-making? 23. What guidelines would you prescribe to dilute the disadvantages of group decision-making? 24. Differentiate between the different approaches to group decision-making. 25. List and justify the specific characteristics of a group leader. Should this leader be assigned

to the group or be elected by the group? 26. List a few guidelines to make decision-making more effective. 27. What are some of the common errors committed in decision-making and how can these

errors be avoided? 28. What are the 10 principles of an organization? 29. Explain the benefits of an efficiently structured organization. 30. Differentiate between authority and responsibility. Can one be exercised without the other? 31. Explain in detail the process of delegation. 32. What are the factors involved in determining the optimum span of management? 33. Discuss centralization – decentralization issue with its pros and cons. 34. What is MBO? Does it help or hinder effective operation? 35. Discuss the advantages and disadvantages of MBO. Can the disadvantages be eliminated? 36. What type of managerial behaviour would result in the failure of MBO program? 37. Describe the various steps involved in the staffing process. 38. Define a. Job analysis b. job description and c. job specification. 39. Discuss the pros and cons of various recruiting sources. 40. How important is the process of interview for the candidate as well as for the management?

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41. What important advice would you give a candidate to be selected in an interview? 42. What are the various steps required in the process of actual selection of the candidate for the

job? 43. What incentives as well as motivators can the management use to retain the work force and

build up a sense of belonging among the workers? 44. Explain the need for training and retraining the work force. 45. Explain the steps involved in any effective training programme. 46. What do we mean by ‘human relations’? What part does our upbringing play in developing

these ‘human relations’? 47. What are the different theories of leadership? Which theory seems to justify the leadership

of a democratic country like India? 48. Under what circumstances are the following leaderships acceptable and why?

a. Autocratic leadership b. Participative leadership c. Free-reign leadership

49. Describe and explain some of the personal characteristics of successful leaders. Which of these characteristics are most important and why?

50. Differentiate between trait theory and behaviour theory of leadership. 51. “Leaders are born, not made”. Comment on it. 52. Why do different human beings behave differently under similar circumstances? Does

individual behaviour subscribe to ‘cause-effect’ phenomenon? 53. In explaining behaviour, differentiate between inherited and learnt factors. 54. Compare and contrast the Maslow and Herzberg motivational models. 55. What steps can the management take to satisfy social, esteem and self-actualization needs of

the employees? 56. What do we mean by ‘job-enrichment’? 57. What are the effects of job enrichment programs? 58. Explain the basic meaning and necessity for control. 59. What are the characteristics of an effective control system? 60. Describe the different methods of comparing the actual results with expected results for the

purpose of evaluating the effectiveness of control system. 61. What are the various types of managerial controls? 62. Is ‘self-control’ the best control, thus eliminating the necessity of all other type of controls? 63. What are some of the symptoms of inadequate control? Are all these symptoms traceable to

certain well-defined causes? Explain. 64. Define Entrepreneurship. 65. Describe how entrepreneurship evolved from the economic theory. 66. Explain entrepreneurship and the characteristics of entrepreneurs. 67. How do entrepreneurs differ from people not interested in new ventures? 68. Discuss small business as a dimension of entrepreneurship. 69. Describe the concept of corporate entrepreneurship. 70. Describe the risks a manager might assume when championing a new corporate innovation. 71. Explain how entrepreneurship has influences economic development and productivity in

recent years with an Indian case study. 72. Distinguish between franchisor and franchisee.

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73. ‘Luck of Persistence?’ Which of these do you think plays a role in entrepreneurship? Discuss.

74. Explain the process of creativity. 75. Describe how innovation is important as a dimension of entrepreneurship. 76. Distinguish between creativity and innovation. 77. How is innovation different from invention? 78. Describe 3 key roles and 7 conditions important for technological innovation. 79. Identify major changes that create opportunity for entrepreneurs. 80. Explain the concepts of ‘windows’ and ‘corridors’ for new ventures. 81. Describe how economic and legal changes can occur to create new opportunities for

industries. 82. Explain how opportunities arise from social, cultural and demographic changes. 83. Discuss popular myths of entrepreneurship and why they are more fantasy than fact. 84. Describe the main factors that lead to success for new ventures. 85. Describe the environment of small business and how it is changing. 86. Identify the most common causes for small business failure. 87. Explain the important success factors for small business enterprises. 88. Describe corporate entrepreneurship. 89. Discuss the major approaches to corporate entrepreneurship. 90. Describe emerging ways corporations are encouraging entrepreneurship. 91. Describe local markets, competition and types of products or services that constitute the

small business environment. 92. Describe external factors that can threaten small business. 93. Discuss the concept of a planning paradigm for new ventures. 94. Discuss the concept of using a model for planning new ventures. 95. Discuss the four-stage growth model of entrepreneurship. 96. Define the growth continuum and contrast new venture activities at the polar extremes.

What is a ‘comfort zone’ in the continuum? 97. Discuss the fundamentals of a good feasibility plan. 98. Explain the major components of a good feasibility plan. 99. Explain how a feasibility plan is used and why it is important to entrepreneurs. 100. Explain how sales forecast influences marketing and financial plans. 101. Explore the planning responsibilities and ways in which entrepreneurs can get assistance. 102. Explain why planning benefits an entrepreneur and why the planning process can, by itself,

be helpful to the entrepreneur.

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06IM52-SIMULATION MODELING & ANALYSIS

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SIMULATION MODELING AND ANALYSIS

Sub Code: 06IM52 IA Marks: 25 Hrs/week: 05 Exam Hours:03 Total Lecture Hrs: 62 Exam Marks: 100 1. Introduction to Simulation : Simulation, advantages, disadvantages areas of application.

System environment, components of a system, types of models, steps in simulation study. 6 Hours

2. Simulation Examples: Simulation of Queuing systems, Simulation of Inventory System, Other Simulation examples 6 Hours

3. General Principles: Concepts in discrete events simulation, event-scheduling time advance algorithm, simulation using event scheduling. 6 Hours

4. Random Numbers: Properties, Generation methods, Tests for random number- frequency test, Run test, Autocorrelation test, and Gap test, Poker Test. 6 Hours

5. Random Variate Generation: Inverse transform technique - Exponential, Uniform, Weibull, Triangular distributions. Direct transformation for normal and log normal distribution, convolution methods – Erlang distributions, acceptance-rejection techniques – Poisson distribution, Gamma Distribution. 7 Hours

6. Analysis of Simulation Data: Input Modeling: Data Collection, Identification and distribution with data, parameter estimation, goodness of fit tests, Selection of input models without data, Multivariate and time series analysis. Verification & validation of model : Model building, verification, calibration and validation of models. 7 Hours

7. Output analysis: Stochastic nature of output data, Measures of Performance and their estimation, Output analysis of terminating simulation, output analysis of steady state simulations. 7 Hours

8. Optimization Via Simulation : Meaning, difficulty, Robust Heuristics, Random Search Applications: Simulation of manufacturing and Material handling Systems, Simulation of

Computer systems, Simulation of Plant Layout, Simulation of Project Management. Simulation Software: Selection of Simulation Software, simulation Packages, experiment and

Statistical Analysis tools, Trends in Simulation Software 7 Hours Text Books: 1. Discrete Event System Simulation – Jerry Banks, John S Carson, II, Berry L Nelson, PHI

Publications (EEE), ISBN-81-203-1130-3. 2. Systems Simulation with Digital Computer – Narsingh Deo; PHI Publication (EEE), ISBN –0-

87692-028-8 3. Simulation Modelling & Analysis – Averill M Law, W David Kelton; McGraw Hill

International Editions– Industrial Engineering Series, ISBN-0-07-100803-9

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LESSON PLAN Sub Code: 06IM52 I.A. Marks: 25 Hours / Week: 04 Total Hours: 62 Subject: Simulation Modeling & Analysis Sem:V

Hour. No Topics to be covered

1. Introduction to simulation, Simulation, advantages, Disadvantages, Areas of

application. 2. System environment, Components of a system 3. Types of models, steps in simulation study 4. Simulation Of Queuing Systems 5. Simulation Of Queuing Systems 6. Revision/quiz/surprise test 7. Simulation Of Inventory Systems 8. Simulation Of Inventory Systems 9. Simulation Of Other Systems 10. Concepts in discrete – events simulation, event scheduling. 11. Time advance algorithm 12. Simulation using event scheduling 13. Revision/quiz/surprise test 14. Properties, Generation methods 15. Test for Random numbers 16. Run tests 17. Autocorrelation Tests 18. Gap test , Poker Test 19. Poker Test 20. Revision/quiz/surprise test 21. Inverse Transform Technique 22. Direct Transformation for normal distribution 23. Convolution methods, Acceptance – Rejection Techniques 24. MODEL Test 25. Statistical models in simulation concepts 26. Useful statistical models 27. Revision/quiz/surprise test 28. Discrete / Continuous distributions 29. Poisson Process 30. Empirical Distributions 31. Input modeling: Data collection, Identification 32. Parameter estimation 33. Goodness of fit tests 34. Revision/quiz/surprise test 35. Selection of input models without data 36. Multivariate and time series analysis 37. Verification

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38. Calibration and Validation of Models 39. Output analysis, Stochastic nature of output data 40. Estimation replication of runs 41. Revision/quiz/surprise test 42. Output analysis of terminating simulation 43. Output analysis of steady state simulations 44. Meaning difficulty 45. Heuristics, Random Search 46. Simulation Of Manufacturing System 47. Simulation Of Material Handing System 48. Revision/quiz/surprise test 49. Simulation Of Computer System 50. Simulation Of Plant Layout System 51. Simulation of Project management 52. Selection of Simulation software 53. Simulation packages 54. Experiments and statistical Analysis tool 55. Revision/quiz/surprise test 56. Experiments and statistical Analysis tool 57. Trend in Simulation Software 58. Model Questions Solving 59. Problems using Arena Package 60. Problems using Arena Package 61. Exercises 62. Exercises

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QUESTION BANK

01 Name several entities, attributes, activities, events & state variables for the following

systems: � A Small Appliance Repair Shop � A Cafeteria � A Grocery Store � A Laundromat � A Fast – Food Restaurant � A Hospital Emergency Room � A Taxicab Company With 10 Taxis � An Automobile Assembly Line

02 Consider the simulation process shown in the figure No. 1 � Reduce the steps by at least two combine similar activities. Give your rationale. � Increase the steps by at least two by separating current steps or enlarging on

existing steps. Give your rationale Problem Formulation

Setting of objectives & overall performance

Data Collection Model Conceptualization

Model Translation

Verified?

Experimental Design

Documentation & reporting

Implementation

1

2

3 4

5

6

NO NO

YES

YES YES

NO

7

8

9

10 11

Verified?

Production runs & analysis

More Runs?

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03 A simulation of a major traffic intersection is to be conducted with the objective of improving the current traffic flow. Provide three iterations, in increasing order of complexity, of steps 1 & 2 in the simulation process of fig No 1

04 In what way & at what steps might a personal computer be used to support the simulation process of fig No. 1

05 A simulation is to be conducted of cooking a spaghetti dinner to determine what time a person should start in order to have the meal on the table by 7:00P.M. Read a recipe for preparing a spaghetti dinner (or ask a friend or relative etc, for the recipe). As best you can, trace what you understand to be needed in the data collection phase of the simulation process of figure 1.3 in order to perform a simulation in which the model includes each step in recipe, What are the events, activities, and state variables in this system?

06 A small grocery store has only one checkout counter. Customers arrive at this checkout counter. Customers arrive at this checkout counter at random from1 to 8 minutes apart. Each possible value of inter arrival time has the same probability of occurrence, as shown below.

Distribution of time between arrivals Time between

arrivals Probability

1 0.125 2 0.125 3 0.125 4 0.125 5 0.125 6 0.125 7 0.125 8 0.125

Service –Time Distribution

Service Times Probability

1 0.10 2 0.20 3 0.30 4 0.25 5 0.10 6 0.05

07 In the above example, let the arrival distribution be uniformly distributed between 1 and 10 minutes. Develop the simulation table and the analysis for 20 customers. What is the effect of changing the arrival time distribution? In example 1, let the service distribution be changed to the following.

Service Time in minutes 1 2 3 4 5 6

Probability 0.05 0.10 0.20 0.35 0.25 0.10

Develop the simulation table and the analysis for 20 customers. What is the effect of

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changing the service time distribution? Consider the following continuously operating job shop. Inter arrival times of jobs are distributed as follows:

Time between Arrivals (Hours)

Probability

0 0.23 1 0.37 2 0.28 3 0.12

08 Processing times for jobs are normally distributed with mean 50 minutes and standard deviation 8 minutes. Construct a simulation table, and perform a simulation for 10 new customers. Assume that when the simulation begins there is one job being processed (Scheduled to be completed in 25 minutes) and there is one job with a 50 minute processing time in the queue.

a. What was the average time in the queue for the 10 new jobs? b. What was the average processing time of the 10 new jobs? c. What was the maximum time in the system for the 10 new jobs?

09 Six dump trucks are used to haul the coal from a small mine to the railroad. Each truck is loaded by one of the two loaders. After loading, the truck immediately moves to the scale to be weighed as soon as possible. Both the loaders and scale have first come first served waiting line for trucks. Travel time from loader to the scale is considered negligible. After being weighed, a truck begins a travel time (during which time the truck unloads), and then afterward returns to the loader queue. The distribution of of loading time, weighing time and travel time are given in tables. The purpose of the simulation is to estimate the loader and scale utilizations Traveling

Queue

Loader

Queue Queue

Loading

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10 In the dump truck problem, it is desired to estimate mean response time and the proportion of response times, which are greater than 30 minutes. A response time for a truck begins when that truck arrives at the loader queue, and ends when the truck finishes weighing. Add the model components and the cumulative statistics needed to estimate these two measures of system performance. Simulate for 8 Hours. � Rework the above example using the following data:

Loading Times 10 5 10 10 5 10 5 Weigh Times 12 16 12 12 16 12 12 Travel Times 40 60 40 80 100 40

� Consider a drive in restaurant where carhops take orders and bring food to the car.

Cars arrive in the manner shown in the table. There are two carhops Able and Baker. Able is better able to do the job, and works somewhat faster than the Baker. The distribution of service times is given below

Interarrival Distribution of cars

Time between Arrivals Probability

a. 0.25 b. 0.40 c. 0.20 d. 0.15

11 A production process manufactures alternators for outboard engines used in recreational boating. ON the average, 1% of the alternators will not perform up to the required standards when tested at the engine assembly plant. When a shipment of 100 alternators is received at the plant they are tested and if more than two are non-conforming, the shipment is returned to the alternator manufacturer. What is the probability of returning a shipment?

12 Lead-time demands for condenser unit is Poisson distributed with mean of 6 units. Prepare a table for the inventory manager which will indicate the order level to achieve protection o the following levels: 50%, 80%, 90%,95%,97%,,97.5%,99%,99.5%and 99.9%.

13 A random variable X which has PMF given by p (x) = 1/ (n+1) over the range Rx = {0,1,2…n} is said t have a discrete uniform distribution.

� Find the mean and variance of this distribution. � If Rx = {a, a+1, a+2, …b}, determine the mean and variance of X

14 An aircraft has dual hydraulic systems. The aircraft switches to the standby system automatically if the first system fails. If both the systems have failed the plane will crash. Assume that the life of a hydraulic system is exponentially distributed with a mean of 2000 air hours. � If the hydraulic systems are inspected every 2500 hours, what is the probability that an

aircraft will crash before that time? � What danger would there be in moving the inspection point to 3000 hrs?

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15 A random variable X is beta distributed if its pdf is given by

otherwise

xxx

xFa

,0

,10!!

)1()1()( <<•

−++=βα

βα β

Show that the beta distribution becomes the uniform distribution over the unit interval when α = β = 0

16 Lead-time is gamma distributed in 100’s of units with a parameter of 3 and a scale parameter of 1. What is the lead-time exceeds 2 (hundred) units during an upcoming cycle?

17 Lifetime of the asynchronous adapter card for a PC, in months, denoted by the random variable X, is gamma distributed with β = 4 and = 4 and θ = 1/16. What is the probability that the card will last for at l4east 2 years?

18 Many states have license tags, which have the following format: letter letter number, the letters indicate the weight of the automobile, but the numbers are at random, ranging from 100 to 999. � What is the probability that the next two tage seen (at random) will have number of

500 or higher? � What is the probability that the sum of the next two tage seen (at random) will have a

total of 1000 or higher? 19 Let X be a random variable that is normally distributed with a mean of 10 and a variance

of 4. Find the values a and b such that P(a < X < b ) = 0.90 and [ µ - a ] =[ µ - b] 20 Given the following distributions: Normal (10.4), Triangular (4,10,16 ), Uniform (4,16)

Find the probability that 6 < X < 8 for each of the distributions 21 Three shafts are made and assembled in a linkage. L The length of each shaft, in each

shaft, in centime5ters. Is distributed as follows: Shaft 1 : N (60,0,09) Shaft 2 : N (40,0,05) Shaft 3 : N (50,0,11) � What is the distribution of the linkage? � What is the operability that the linkage will be longer than 150.2 centimeters? � The tolerance limits for the assembly are (149.83,150.21). What proportion of

assemblies are within the tolerance limits? 22 The circumference of battery posts in a nickel cadmium battery are Weibull distributed

with ν = 3.25 centimeters, β = 1/3, and α 0.005 centimeters. � Determine the probability that a battery post chosen at random will have a

circumference larger than 3.40 centimeters. � If battery posts are larger than 3.50 centimeters, they will not go through the hole

provided; if thy are smaller than 3.30 centimeters, the clamp will not tighten sufficiently. What proportion of posts will have to be scrapped for one of these reasons?

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23 A postal letter carrier has a route consisting of five segments with the time in minutes to complete each segment being normally distributed with mean and variance as shown

Tennyson Place N (38,16) Windsor Parkway N (99,29) Knob Hill Apartments N (85,25) Evergreen Drive N (73,20) Chastain Shopping Center N (52,12)

In addition to the above times, the letter carrier must organize the mail at the central office, which requires a time that is distributed by N (90,25). The drive to the starting point of the route requires a time that is distributed N (10,4). The return from the route requires a time that is distributed N (15,4). The letter carrier then performs administrative tasks with a time that is distributed N (30,9).

� What is the expected length of the letter carrier’s workday? � Overtime occurs after eight hours of work on a given day. What is the probability that

the letter carrier works overtime of any given day? � What is the probability that the letter carrier works overtime on two or more days in a

six-day week? � What is the probability that the route will be completed within ±24 minutes of eight

hours on any given day? 24 High temperature in Biloxi, Mississippi on July 21, denoted by the random variable

X, has the following probability density function where X is in degrees F. 2(x - 85) , 85 ≤ x ≤ 92 f (x) = 119 2(102 –x ), 92 < x ≤ 102 170 0, otherwise � What is the variance of the temperature, V ( X ) ? � What is the median temperature? � What is the modal temperature?

25 The time to failure of Easting home light bulbs is Weibull distributed with V = 1.8 x103 hours, β = ½ and α =1/3 x103 hours.

a. What fraction of bulbs is expected to last longer that the mean lifetime? b. What is the median lifetime of alight bulb?

26 Lead time demand is gamma distributed in 100’s of units with a shape parameter of 2 and a scale parameter of ¼ . What is the probability that the lead-time exceeds 4 (Hundred) units during an upcoming cycle?

27 A tool crib has exponential Interarrival and service times, and serves a very large group of mechanics. The mean time between arrivals is4 minutes. It takes 3 minutes on the average for a tool crib attendant to service a mechanic. The attendant is paid $ 10 per our and the mechanic is paid $ 15 per hour. Would it be advisable to have a second tool rib attendant?

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28 A two- runway (one runway for landing, one runway for taking off) airport is being designed for propeller-driven aircraft. The time to land an airplane is known to be exponentially distributed with a mean of 1-1/2 minutes. If airplane arrivals are assumed to occur at random, what arrival rate can be tolerated if the average wait in the sky is not to exceed 3 minutes?

29 The Port of Trop can service only one ship at a time. However, there is mooring space for three more ships. Trop is a favorite port of call, but if no mooring space is available, the ships have to go to the Port of Poop. An average of seven ships arrive each week. According to Poisson process. The port of Trop has the capacity to handle an average of eight ships a week, with service times exponentially distributed. What is the expected number of ships waiting or in service at the Port of Trop?

30 Given the following information for a finite calling population problem with exponentially distributed runtimes and service times: K = 10

1/µ = 15 1/λ = 82 C = 2

Compute Lq, and Wq. Determine the value of λ such Lq = L/2 31 Suppose that Figure 7.8 represents the number in system for a last-in-first-out (LIFO)

single-server system. Customers are not preempted (i.e. kicked out of service) but upon service completion the most recent arrival next begins service. For this LIFO system apportion the total area under L (t) to each individual customer, as was done in Figure 7.10 for the FIFO system. Using the figure, show that Equations (7.13), (7,11), (7.12) hold for the single-server LIFO system

32 Consider a M /G / 1 queue with the following type of service distribution. Customers request one of two types of service in the proportions p and 1 – p. Type I service is exponentially distributed at rate µi, I = 1,2 Let Xi denote a type I service time and X an arbitrary service time. Then E(Xi) = 1/µi ,V(X i) = 1/ µi

2 and X1 with probability p X = X2 with probability (1 – p)

The random variable X is said to have a hyper exponential distribution with parameters (µ1,µ2,p).

� Show that E (x) = p/µ1 + (1 –p) /µ2 and E (X2) = 2p /µ12 + 2(1-p) /µ2

2. � Use V (X) = E (X2) – [E (X)] 2 to show V (X) = 2p / µ1

2 + 2(1 – P) /µ22 –[p/µ1+ (1

– P) / µ2] 2.

33 A fleet of 10 trucks supplies a small lumberyard. One overhead crane is available to unload the long logs from the trucks. It takes an average of 1 hour to unload a truck. After unloading, a truck takes an average of 3 hours to get the next load of logs and return to the lumberyard

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34 A tool crib with one attendant serves a group of 10 mechanics. Mechanics work for an exponentially distributed amount of time with mean 20 minutes, then go to the crib to request a special tool. Service times by the attendant arte exponentially distributed with a mean of 3 minutes. If the attendant is paid $ 6 per hour and the mechanic is paid $ 10 per hour, would it be advisable to have a second attendant?

35 A small copy shop has a self-service copier. Currently there is room for only 4 people to line up for the machine (including the person using the machine); when there are more than 4 people, then the additional people must line up outside the shop. The owners would like to avoid having people line up outside the shop as much as possible. For that reason they are thinking about adding a second self-service copier. Self-service customers have been observed to arrive at a rate of 24 per hour, and they use the machine 2 minutes, on average Assess the impact of adding another copier. Carefully state any assumptions or approximations you make.

36 A self-service car wash has 4 washing stalls. When they are in a stall, customers may choose among three options: rinse only; wash and rinse; and wash, rinse and wax. Each option has a fixed time to complete; rinse only (3 minutes); wash and rinse (7 minutes); and wash, rinse and wax (12minutes). The owners have observed that 20% of customers rinse only; 70% wash and rinse; and 10% wash, rinse and wax. There are no scheduled appointments, and customers arrive at a rate of about 34 cars per hour. There is only room for 3 cars to wait in the parking lot, so currently many customers are lost, The owners what to know how much more business they will do if they add another stall. Adding a stall will take away one space in the parking lot. Develop a queuing model of the system. Estimate the rate at which customers will be lost in the current and proposed system. Carefully state any assumptions or approximations you make

37 Use the linear congruential method to generate a sequence of three two-digit random integers. Let X0 = 27, a = 8, c = 47, and m = 100. Do we encounter a problem in the previous exercise if X0 = 0?

38 The sequence of number 0.54, 0.73, 0.98, 0.11, and 0.68, has been generated. Use the Kolmogorov-Smirnov test with α =0.05 to determine if the hypothesis that the numbers are uniformly distributed on the interval [0,1] can be rejected

39 Consider the following sequence of 120 digits

1 3 7 4 8 6 2 5 1 6 4 4 3 3 4 2 1 5 8 7 0 7 6 2 6 0 5 7 8 0 1 1 2 6 7 6 3 7 5 9 0 8 8 2 6 7 8 1 3 5 3 8 4 0 9 0 3 0 9 2 2 3 6 5 6 0 0 1 3 4 4 6 9 9 8 5 6 0 1 7 5 6 7 9 4 9 3 1 8 3 3 6 6 7 8 2 3 5 9 6 6 7 0 3 1 0 2 4 2 0 6 4 0 3 9 3 6 8 1 5

Test whether these digits can be assumed to be independent based on the frequency with which gaps occur. Use α = 0.05.

40 Develop the poker test for: i. Four-digit number ii. Five-digit number 41 A sequence of 1000 four-digit number had been generated and an analysis indicates the

following combinations and frequencies.

Combination i Observed Frequency, Oi

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Four different digits 565 One pair 392

Two pairs 17 Three like digits 24 Four like digits 2

1000 Based on the poker test, test whether these numbers are independent. Use α = 0.05

42 Determine whether the linear congruential generators shown below can achieve a maximum period. Also, state restrictions on X0 to obtain this period. a. The mixed congruential method with

A = 2,814, 749, 767, 109 C = 59, 482, 661, 568, 307 M = 248

b. The multiplicative congruential generator with A= 69,069 C = 0 M = 232

c. The mixed congruential generator with a = 4951 c = 247 m = 256

d. The Multiplicative congruential generator with a = 6507 c = 0 m = 1024

43 Use the mixed congruential method to generate a sequence of three two-digit random numbers with X0 = 37, a = 7, c = 29 and m = 100.

44 Use the mixed congruential method to generate a sequence of three two-digit random integers between 0 and 24 with X0 = 13, a = 9 and c = 35.

45 Write a computer program that will generate four-digit random numbers using the multiplicative congruential method. Allow the user to input values of X0, a, c and m.

46 If X 0 = 3579 in Exercise 17 (c ), generate the first random number in the sequence. Compute the random number to four-place accuracy.

47 Investigate the random number generator in a spreadsheet program on a computer to which you have access. In many spreadsheets, random numbers are generated by a function called RAND or @ RAND. � Check the user’s manual to see if it describes how the random numbers are generated. � Write macros to conduct each of the tests described in this chapter. Generate 100 sets

of random numbers, each set containing 100 random numbers. Perform each test on each set of random numbers. Draw conclusions

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48 Consider the multiplicative congruential generator under the following circumstances a. a = 11,m = 16, X0 = 7 b. a = 11,m = 16, X0 = 8 c. a = 7,m = 16, X0 = 7 d. a = 7,m = 16, X0 = 8

Generate enough values in each case to complete a cycle. What inferences can be drawn? Is maximum period achieved?

49 For 16-bit computer, L’ Ecuyer [1988] recommends combining three multiplicative generators with m1 = 32363,a1 = 157, m2 = 31727, a2 = 146, m3 = 31657 and a3 = 142. The period of this generator is approximately 8 x 1012 . Generate 5 random number with the combined generator using initial seeds Xi,0 = 100,300,500 for the individual generators I = 1,2,3.

49 Use the principles described in this chapter to develop your own linear congruential random number generator.

50 Use the principles described in this chapter to develop your own combined linear congruential random number generator.

51 Test the following sequence of numbers for uniformity and independence using procedures you learned in this chapter: 0.594,0.928,0.515,0.055,0.57,0.351,0.262,0.797,0.788,0.442,0.097,0.798,0.227,0.127, 0.474,0.852,0.007,0.182,0.929,0.852

52 Develop a random variate generator for a random variable X with the pdf e2x, - ∞ < x ≤ 0 f (x) = e-2x, 0 < x < ∞

53 Develop a generation scheme for the triangular distribution with pdf

½ ( x –2), 2≤ x ≤ 3 f (x) = ½ ( 2 – x/3), 3 < x ≤ 6 0, otherwise

Generate 10 values of the random variate, compute the sample mean, and compare it to the true mean of the distribution.

54 Develop a generator for a triangular distribution with range (1,10) and mode at x = 4. 55 Develop a generator for a triangular distribution with range (1,10) and a mean of 4 56 Given the following cdf for a continuous variable with range-3 to 4, develop a

generator for the variable. 0, x ≤ - 3

½ + x/6, - 3 < x ≤ 0 F (x) = ½ + x2 / 32, 0 < x ≤ 4 1, x > 4 Given the cdf F(x) = x4 /16 on 0 ≤ x ≤ 2, develop a generator for this distribution. Given the pdf f (x) = x2/9 on 0 ≤ x ≤ 3, develop a generator for this distribution. Develop a generator for a random variable whose pdf is

1/3, 0≤ x ≤ 2 f(x) = 1/24, 2< x ≤10

0, otherwise

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57 The cdf of a discrete random variable X is given by: F (x) = x (x+1) (2x+1)/ n (n+1) (2n+1), x = 1,2…..n When n = 4, generate three values of X using R1 = 0.83, R2 = 0.24, and R3 =0.57.

58 Times to failure for an automated production process have been found to be randomly distributed with a Weibull distribution with parameters β = 2 and α = 10. Derive equation (9.6) and then use it to generate five values from this Weibull distribution, using five random numbers taken from Table A.1.

59 A Machine is taken out of production if it fails, or after 5 hours, whichever comes first. By running similar machines until failure, it has been found that time to failure, X, has the Weibull distribution with α = 8, β = 0.75, and ν = 0 (refer to Sections 6.4 and 9.1.3.). Thus, the time until the machine is taken out of production can be represented as Y = min (x,5). Develop a step-by-step procedure for generating Y.

60 The time until a component is taken our of service is uniformly distributed on 0 to 8 hours. Two such independent components are put in series, and the whole system goes down when one of the components goes down. If Xi (I = 1,2) represents the component runtimes. Then Y = min (X1, X2) represents the system lifetime. Devise two distinct way to generate Y.

61 Develop a technique for generating a binomial random variable, X, using the convolution technique.

62 Develop an acceptance rejection technique for generating a geometric random variable, X, with parameter p on the range {0,1,2..}.

63 Write a computer routine to generate standard normal varieties by the exact method discuss3d in this chapter. Use it to generate 1000 values. Compare the true probability, φ (z), that a value lies in (-∞,z) to the actual observed relative frequency that values were≤ z, for z=-4,-3,--2,-1,0,1,2,3and 4.

64 Write a computer routine to generate gamma varieties with shape parameter β and scale parameter θ Generate 1000 values with β = 2.5 and θ = 0.2 and compare the true mean,1/θ = 5, to the sample mean.

65 Many spreadsheet, symbolic calculation and statistical analysis programs have built in routines for generating random variates form standard distributions. Try to find our what variate-generation methods are used in one of these packages by looking at the documentation. Should you trust a variate generator is the method is not documented?

66 Suppose that somehow we have available a source of exponentially distributed random variates with mean I. Write an algorithm to generate random variates with a triangular distribution by transforming the exponentially distributed random variates with a triangular distribution by transforming the exponentially distributed random variates.

67 Go to a major traffic intersection and determine the interarrival time distributions from each direction. Some arrivals want to go straight, some turn left, and some turn right. The interarrival time distribution varies during the day and by day of the week. Every now and then an accident occurs.

68 Go to grocery store and determine the interarrival and service distributions at the checkout counters. These distributions may vary by time of day and by day of week. Record, also, the number of service channels available at all times. (Make sure that the management gives permission to perform this study).

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69 Go to a cafeteria and collect data on the distributions of interarrival and service times. The distribution of interarrival times is probably different for each of the three daily meals and May also may during the meal; that is, the interarrival time distribution for 11:00A.M to 12:00 noon may be different than from 12:00 noon may be different than from 12:00 noon to 1:00p.m. Define service time as the time from when the customer reaches the point at which the first selection could be made until exiting from the cafeteria line. (Any reasonable modification of this definition is acceptable) The service-time distribution probably changes for each meal. Can times of the day or days of the week for either distribution be grouped due to homogeneity of the data? (Make sure that the management gives permission to perform this study.)

70 Draw the p.m.f of the Poisson distribution that results when the parameter α is equal to following:

(a) α = ½ (b) α = 1 (c) α = 2 (d) α = 4

71 On one figure draw the three Weibull pdf’s which result when ν = 0, α = ½ , and β = 1,2,and 4

72 The following data are randomly generated from a gamma distribution:

1.691 1.437 8.221 5.976 1.116 4.435 2.345 1.782 3.810 4.589 5.313 10.90 2.649 2.432 1.581 2.432 1.843 2.466 2.833 2.361

Determine the maximum likelihood estimators β and θ. 73 The following data are randomly generated from a Weibull distribution where ν = 0:

7.936 5.224 3.937 6.513 4.599 7.563 7.172 5.132 5.259 2.759 4.278 2.696 6.212 2.407 1.857 5.002 4.612 2.003 6.908

Determine the maximum likelihood estimators α and β

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74 The highway between Atlanta, Georgia, and Athens, Georgia, has a high incidence of accidents along its 100 kilometers. Public safety officers say that the occurrence of accidents along the highway is randomly (uniformly) distributed, but the news media say otherwise. The Georgia Department of Public Safety published records for the month of September. These records indicated the point at which 30 accidents involving an injury or death occurred, as follows (the data points represent the distance from the city limits of Atlanta):

88.3 40.7 36.3 27.3 36.8 91.7 67.3 7.0 45.2 23.3 98.8 90.1 17.2 23.7 97.4 32.4 87.8 69.8 62.6 99.7 20.6 73.1 21.6 6.0 45.3 76.6 73.2 27.3 87.6 87.2

Use the Kolmogorov- Smirnov test to determine whether the distribution of location of accidents is uniformly distributed for the month of September.

75 Show that the Kolomogorov-Smirnov test statistic for Example 10.17 is D = 0.1054 76 Records pertaining to the monthly number of job related injuries at an underground coal

mine were being studied by a federal agency. The values for the past 100 months were as follows:

INJURIES PER MONTHS FREQUENCY OF OCCURRENCE 0 35 1 40 2 13 3 6 4 4 5 1 6 1

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77 2. The time required for 50 different employees to compute and record the number of hours worked during the week was measured with the following result in minute:

Employee Time (Minutes) Employee Time (Minutes) 1 1.88 26 0.04 2 0.54 27 1.49 3 1.90 28 0.66 4 0.15 29 2.03 5 0.02 30 1.00 6 2.81 31 0.39 7 1.50 32 0.34 8 0.53 33 0.01 9 2.62 34 0.10 10 2.67 35 1.10 11 3.53 36 0.24 12 0.53 37 0.26 13 1.80 38 0.45 14 0.79 39 0.17 15 0.21 40 4.29 16 0.80 41 0.80 17 0.26 42 5.50 18 0.63 43 4.91 19 0.36 44 0.35 20 2.03 45 0.36 21 1.42 46 0.90 22 1.28 47 1.03 23 0.82 48 1.73 24 2.16 49 0.38 25 0.05 50 0.48

Use the chi-square test (as in Example10.14) to test the hypothesis that these service times are exponentially distributed. Let the number of class intervals be k =6. Use a level of significance of α = 0.05

MVJCE 28

78 Student wiser Beer Company is trying to determine the distribution of the breaking strength of their glass bottles. Fifty bottles are selected at random and tested for breaking strength, with the following results (in pounds per square inch):

218.95 232.75 212.80 231.10 215.95 237.55 235.45 228.25 218.65 212.80 230.35 228.55 216.10 229.75 229.00 199.75 225.10 208.15 213.85 205.45 219.40 208.15 198.40 238.60 219.55 243.10 198.40 224.95 212.20 222.90 218.80 203.20 223.45 213.40 206.05 229.30 239.20 201.25 216.85 207.25 204.85 219.85 226.15 230.35 211.45 227.95 229.30 225.25 201.25 216.10

� Use the chi-square test with equiprobable intervals to test these breaking strengths for normality at a level of significance of α = 0.05.

� The manufacturer of the bottles says the breaking strengths are normally distributed with µ = 200 and σ = 15. Test the manufacturer’s claim at a level of significance of α =0.05.

79 The Cross Towner is a bus that cuts a diagonal path from northeast Atlanta to southwest Atlanta. The bus operator, the bus runs Monday through Friday, maintains the time required to complete the route. The times of the last fifty 8:00 A.M. runs, in minutes, are as follows:

92.3 92.8 106.8 108.9 106.6 115.2 94.8 106.4 110.0 90.9 104.6 72.0 86.0 102.4 99.8 87.5 111.4 105.9 90.7 99.2 97.8 88.3 97.5 97.4 93.7 99.7 122.7 100.2 106.5 105.5 80.7 1079 103.2 116.4 101.7 84.4 101.9 99.1 102.2 102.5 111.7 101.5 95.1 92.8 88.5 74.4 98.9 111.9 96.5 95.9

How are these run times distributed? Develop and test a suitable model

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80 The time required for the transmission of a message (in minutes) is sampled electronically at a communications center. The last 50 values in the sample are as follows:

7.936 4.612 2.407 4.278 5.132 4.599 5.224 2.003 1.857 2.696 5.259 7.563 3.937 6.908 5.002 6.212 2.759 7.172 6.513 3.326 8.761 4.502 6.188 2.566 5.515 3.785 3.742 4.682 4.346 5.359 3.535 5.061 4.629 5.298 6.492 3.502 4.266 3.129 1.298 3.454 5.289 6.805 3.827 3.912 2.969 4.646 5.963 3.829 4.404 4.924

How are the transmission times distributed? Develop and test an appropriate model 81 Suppose that in Example 12,13 the simulation analyst decided to investigate the bias using

batch means over a batching interval of 2000 minutes. By definition, a batch mean for the interval [(j – 1) j (2000) is defined by: Yj = 1 / 2000 ∫ j (2000) (j – 1) 2000 Lq (t) dt � Show algebraically that such a batch mean can be obtained from two adjacent batch

means over the two halves of the interval. � Compute the seven averaged batch means for the intervals [0, 2000),[2000,4000),….for

the M /G /1 simulation. Use the data (Y,j) in Table 12.6 (ignoring Y.15 = 8.76). � Draw plots of the type in Figures 12.4 and 12.5. Does it still appear that deletion of the

data over [0,2000) (the first “new” batch mean) is sufficient to remove most of the point-estimator bias?

82 Simulate the dump truck problem in Example 3.5. At first make the run length TE = 40 hours. Make four independent replications. Computer a 90% confidence interval for mean cycle time, where a cycle time for a given truck is the time between its successive arrivals to the loader. Investigate the effect of different initial conditions (all trucks initially at the loader queue, versus all at the scale, versus all traveling, versus the trucks distributed throughout the system in some manner)

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83 Consider an (M.L) inventory system, in which the procurement quantity, Q, is defined by M – I if I < L Q = 0 if I ≥ L

Where I is the level of inventory on hand plus on order at the end of a month, M is the maximum inventory level. And L is the reorder point. Since M. L are under management control. The pair (M, L) is called the inventory policy. Under certain conditions, the analytical solution of such a model is possible, but the computational effort may be prohibitive. Use simulation to investigate an (M, L) inventory system with the following properties. The inventory status is checked at the end of each month. Backordering is allowed at a cost of $ 4 per item short per month. When an order arrives, it will first be used to relieve the backorder. The lead-time is given by a uniform distribution on the interval (0.25,1.25) months. Let the beginning inventory level stand at 50 units, with no orders outstanding. Let the holding cost be $ 1 per unit in inventory per month. Assume that the inventory position is reviewed each month. If an order is placed, its cost is $ 60 + $ 50Q,where $ 60 is the ordering cost and $5 is the cost of each item. L The time between demands is exponentially distributed with a mean of 1/15 month. The sizes of the demands follow the distribution:

Demand Probability 1 ½ 2 ¼ 3 1/8 4 1/8

� Make four independent replications, each of run length 100 months preceded by a 12-months initialization period, for the (M, L) = (50,30) policy. Estimate long-run mean monthly cost with a 90% confidence interval.

� Using the results of part (a), estimate the total number of replications needed to estimate mean monthly cost within $ 5.

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84 Consider the following inventory system: (a) Whenever the inventory level falls to or below 10 units, an order is placed. Only

one order can be outstanding at a time. (b) The size of each order is Q. Maintaining an inventory costs $0.50 per day per

item in inventory. Placing an order results is a fixed cost of $ 10.00 (c) Lead-time is distributed in accordance with a discrete uniform distribution

between zero and 5 days. (d) If a demand occurs during a period when the inventory level is zero, the sale is

lost at a cost of $2.00 per unit. (e) The number of customers each day is given by the following distribution:

Number of Customers per Day Probability 1 0.23 2 0.41 3 0.22 4 0.14

(f)The demand on the part of each customer is Poisson distributed with a mean of 3 units.

(g) For simplicity, assume that all demands occur at 12 noon and that all orders are planked immediately thereafter.

Assume further that orders are received at 5.00 p.m. or after the demand that occurred on that day. Consider the policy having Q = 20 Make five independent replications, each of length 100 days and compute a 90% confidence interval for long-run mean daily cost. Investigate the effect of initial inventory level and existence of an outstanding order on the estimate on mean daily cost. Begin with an initial inventory of Q + 10, and no outstanding orders.

85 A store selling Mother’s Day cards must decide 6 months in advance on the number of cards to stock. Reordering is not allowed. Cards cost $ 0.25 and sell for $ 0.60 any cards not sold by Mother’s Day go on sale for $0.20 for 2 weeks. However, sales of the remaining cards in probabilistic in nature according to the following distribution:

32% of the time, all cards remaining gets sold. 40% of the time, 80% of all cards remaining is sold. 28% of the times, 60% of all cards remaining are sold.

Any cards left after 2 weeks are sold for $0.30. The card shop owner is not sure how many cards can be sold, but thinks it is somewhere (i.e. uniformly distributed) between 200 and 400. Suppose that the card shop owner decides to order 300 cards. Estimate the expected total profit with an error of at most $5.00

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86 A very large mining operation has decided to control the inventory of high-pressure piping by a periodic review, order up to M policy, where M is a target level. The annual demand for this piping is normally distributed with a mean of 600 and a variance of 800 this demand occurs family uniformly over the year. The lead-time for resupply is Erlang distributed of order k = 2 with a mean of 2 months. The cost of each unit is $ 400 . The inventory carrying charge, as a proportion of item cost on an annual basis, is expected to fluctuate normally about a mean of 0.25 (simple interest) with a standard deviation of 0.01. The cost of making a review and placing an order is $200, and the cost of making a review and placing an order is $200, and the cost of a backorder is estimated to be $ 100 per unit backordered. Suppose that the inventory level is reviewed every 2 months, and let M = 337. (a) Make five independent replications, each of run length 100 months, to estimate long run

mean monthly cost by means of a 90% confidence interval. (b) Investigate the effects of initial conditions. Determine an appropriate number of monthly

observations to delete to reduce initializations to a negligible level. 87 3. Jobs enter a job shop in random fashion according to a Poisson process at overall rate 2

every 8-hour day. The jobs are of four types. They flow from workstation to work station in a fixed order depending on type. As shown below. The proportions of each type are also shown.

Type Flow through Stations Proportion 1 1,2,3,4 0.4 2 1,3,4 0.3 3 2,4,3 0.2 4 1,4 0.1

Processing times per job at each station depend on type, but all times are (approximately) normally distributed with mean and s.d. (in hours) as follows: At Small-town U. there is one graphics workstation for student use located across campus from the computer center. At 2:00 A.M. one night six students arrive at the workstation to complete an assignment. A student uses the workstation for 10± 8 minutes, then leaves to go to the computer center to pick up graphics output. There is a 25% chance that the run will be OK and the student will go to sleep. If it is not OK, the student returns to the workstation and waits until it becomes free. The roundtrip from workstation to computer center and back takes 30 ± 5 minutes. The computer becomes inaccessible at 5:00 A.M Estimate the probability, P. that at least five of the six students will finish their assignment in the 3 hour period. First make R = replications and compute a 95% confidence interval for p. Next determine the number of replications needed to estimate p within ± .02 and make these replications. Recompute the 95% confidence interval for p. Four workers are evenly spaced along a conveyor belt. Items needing processing arrive according to a Poisson process at rate 2 per minute. Processing time is exponentially distributed with a mean of 1.6 minutes. If a worker becomes idle, then he or she takes the first item to come by on the conveyor. If a worker is busy when an item comes by, that item moves down the conveyor to the next worker, taking 20 seconds between two successive workers. When worker finishes processing an item, the item leaves the system. If an item passes by the last worker, it is recalculated on a loop conveyor and will return to the first worker after 5 minutes.

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89 Reconsider the dump truck problem of Example 3.5, which was also analyzed in Example 13.3. As business expands, the company buys new trucks, making the total number of trucks now equal to 16. The company desires to have a sufficient number of loaders and scales so that the average number of trucks waiting at the loader queue plus the average number at the weigh queue is no more that three. Investigate the following combinations on number of loaders and number of scales:

Number of Scales Number of Loaders 2 3 4

1 - - - 2 - - -

The loaders being considered are the “slow” loaders in Example 13.3. Loading time, weighing time, and travel time for each truck are as previously defined in Example 13.3. Use common random numbers to the greatest extent possible when comparing alternative systems designs, The goal is to find the smallest number of loaders and scales to meet the company’s objective of an average total queue length of no more than three trucks. In your solution, take into account the initialization conditions, run length and number of replications needed to achieve a reasonable likelihood of valid conclusions.

90 In Exercise 12.6, consider the following alternative (M,L) policies:

L

Low High 30 40

Low 50 M

High 100

(50,30) (50,40)

(100,30) (100,40) Investigate the relative costs of these policies using suitable modifications of the simulation model developed in Exercise 12.6 Compare the four system designs on the basis of long-run mean monthly cost. First make four replications of each (M, L) policy, using common random numbers to the greatest extent possible. Each replication should have a 12-month initialization phase followed by a 100-month data collection phase. Compute confidence intervals having an overall confidence level of 90% for mean monthly cost for each policy. Then estimate the additional replications needed to achieve confidence intervals, which do not overlap. Draw conclusions as to which is the best policy.

91 In Exercise 12.9, investigate the effect of the order quantity on long-run mean daily cost. Since each order arrives on a pallet on a delivery truck, the permissible order quantities, Q, are multiples of 10 (i.e., Q may equal 10, or 20, or30,). In Exercise 12.9, the policy Q= 10 was investigated. � First, investigate the two policies Q= 10 and Q = 50. Use the run lengths, and so on,

suggested in Exercise 12.9. On the basis of these runs, decide whether the optimal Q, say Q*, is between 10 and 50, or greater than 50. (The cost curve as a function of Q should have what kind of shape?).

� Based on the results in part (a), suggest two additional values for Q and simulate the two polices. Draw conclusions. Include an analysis of the strength of your conclusions.

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92 A clerk in the admissions office at Small State University processors requests for admissions materials. The time to process requests depends on the program of interest (e.g., industrial engineering, management science, computer science, etc.) and the level of the program (Bachelors, Masters, Ph.D.). Suppose that the processing time is well modeled as normally distributed with mean 7 minutes and standard deviation 2 minutes. At the be inning of the day it takes the clerk some time to get set to begin working on requests; suppose that this time is well modeled as exponentially distributed with mean 20 minutes. The admissions office typically receives between 40 and 60 requests per day. Let x be the number of applications received on a day, and let Y be the time required to process them (including the set-up time.). Fit a metamodel for E (Y/x) by making n replications at the design points x = 40,50,60. Notice that in this case we know that the correct model is E (Y/x) = β0 + β1x = 20 + 7x (why?). Begin with n =2 replications at each design point and estimate β0 and B1. Gradually increase the number of replications and observe how many are required for the estimates to be close to the true values.

93 Riches and Associates retain its cash reserves primarily in the form of certificates of deposit (CDs), which earn interest at an annual rate of 8%. Periodically, however, withdrawals must beamed from these CDs in order to pay suppliers, etc, these cash outflows are made through a checking account that earns no interest. The need for cash cannot be predicted with certainty, Transfers from CDs to checking can be made instantaneously, but the is a “substantial penalty” for early withdrawal from CDs. Therefore, it may make sense for R&A to make use of the overdraft protection on their checking account, which charges interest at a rate of $0.00033 per dollar per day (i.e., 12% per year) for overdrafts. R&A likes simple policies in which they transfer a fixed amount, a fixed number of times, per year. Currently they make 6 transfers per year of $ 18,250 each time. Your job is to find a policy that reduces their long-run cost per day. Based on historical patterns, demands for cash arrive a rate of about 1 per day, with the arrivals being well modeled as a Poisson process. The amount of cash needed to satisfy each demands is reasonably represented by a log normally distributed random variable with mean $300 and standard deviation $ 150. The penalty for early withdrawal is different for different CDs. It averages $ 150 for each withdra2al (regardless of size), but the actual penalty can be modeled as uniformly distributed random variable with range $ 100 to 200. Use cash level in checking to determine the length of the initialization phase. Make enough replications so that your confidence interval for the difference in long-run cost per day does not contain zero. Be sure to use correlated sampling in your experiment design.

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06IM53 – STATISTICS FOR ENGINEER’S

MVJCE 36

STATISTICS FOR ENGINEERS

Sub code: 06IM53 I A Marks: 25 Hours / Week: 5 Hrs Exam Hours: 3 Hrs Total Lecture Hrs: 62 Exam Marks: 100 1. The Role of Statistics in Engineering (Data Summary and presentation): Statistical

Thinking, collecting data, Statistical Modeling framework, measurement of central tendency and variance, Importance of Data summary and display, Tabular and graphical display. 06 hrs

2. Discrete Random variables and probability distributions: Discrete Random variables,

probability distributions and probability mass functions, Cumulative distribution functions, Mean and variance of a discrete random variable, discrete uniform distribution, binomial distribution, hyper geometric distribution, Poisson distribution, Applications. 07 hrs

3. Continuous Random variables and probability distributions: Continuous random variables,

Probability distributions and Probability density functions, cumulative distribution functions, Mean and variance of a continuous random variable, uniform distribution, Normal distribution, Normal approximation to binomial and Poisson distribution, Exponential distribution, Applications. 05 hrs

4. Estimation Theory: Statistical Inference, Random sampling, properties of Estimators, sampling

distribution, sampling distribution of means, variance and proportion, Introduction to confidence Intervals. 05 hrs

5. Statistical Inference for a single sample and two samples: Hypothesis testing, Inference on

the mean of a population (variance known and unknown), Inference on the variance of a normal population, Inference on a population proportions. 07 hrs

6. Statistical Inference for a single sample and two samples: Testing of goodness of fit,

Inference for a difference in means, variances known, Inference for a difference in means of two normal distributions. Variances unknown, Inference on the variances of two normal populations, Inference on two population proportions. 07 hrs

7. Simple Linear Regressions and Correlation: Simple Linear Regression, Properties of Least square Estimators and Estimation of variances, Common abuses of regression, prediction of new observations, assessing the adequacy of regression model, Transformations to straight line, Introduction to multiple regression ( no problems) Correlation. 06 hrs

8. Design of experiments: Strategy Of Experimentation completely randomized single factor

experiment, tests on individual treatment means, the random effects model. The randomized

MVJCE 37

complete block design, one way analysis of variance and two way analysis of variance. 06 hrs

Textbooks: 1. Applied statistics and probability for engineers- Douglas C Montgomery, George C Runner, 2nd

Edition John Wiley and sons ISBN-0-471-17027-5. 2. Statistics of Management, Richard I Levin, David S Rubin 6th Edition Prentice Hall India,

ISBN-81-203-0893-X. Reference Books: 1. Probability and Statistics in engineering, William W Hines, Douglas C Montgomery 2nd edition

John Wiley & Sons 2. Business Statistics for Management and Economics, Daniel, Terrell 6th Edition Houghton

Mifflin Company ISBN-0-395-62835-0 3. Probability & Statistics by Wall pole Mayer

MVJCE 38

LESSON PLAN

Sub Code: 06IM53 I.A. Marks: 25 Hours / Week: 05 Total Hours: 62 Subject:Statistics For Engineers Sem:V

Hour. No Topics to be covered

1. Statistical Thinking, uses of statistics, History. 2. Grouping & Displaying data, 3. Collecting data, Importance of data summary difference between sample and

populations, arranging data using the data array and Constructing frequency distributions problems.

4. Measures of central tendency Mean, Median, Mode, Geometric Mean and Harmonic Mean problems.

5. Tabular and graphical display Histogram, Problems. 6. Exercises 7. Frequency polygons, Frequency curves & Ogives Problems. 8. Exploratory data analysis Stem and Leaf Diagrams, Box Plots and Time sequence

plots. 9. Probability distributions Discrete Random variable Continuous Random variable

Probability mass functions. 10. Cumulative distribution functions Mean and variance of a discrete random

variable discrete uniform distribution. 11. Binomial distribution Cumulative distribution function Mean, variance Standard

deviation Problems 12. Exercises 13. Binomial distribution Cumulative distribution function Mean, variance Standard

deviation Problems 14. Binomial distribution Cumulative distribution function Mean, variance Standard

deviation Problems 15. Poisson distribution Mean, variance problems 16. Poisson distribution Mean, variance problems 17. Poisson distribution Mean, variance problems 18. Exercises 19. Hyper geometric distribution Mean, variance problems 20. Hyper geometric distribution Mean, variance problems 21. Mean and variance of continuous random variable, continuous uniform

Distribution. 22. Normal distribution Mean and variance, problems 23. Normal distribution problems 24. Exercises 25. Normal approximation to binomial and Poisson problems 26. Exponential distribution Erlang, Gamma distributions and Weibull distribution

and problems. 27. Statistical Inference Random sampling Properties of estimators

MVJCE 39

Hour. No Topics to be covered

28. Statistical Inference Random sampling Properties of estimators 29. Sampling distribution, sampling distribution of means 30. Exercises 31. Introduction to confidence Intervals 32. Confidence Intervals Problems 33. Hypothesis testing, null hypothesis, alternative hypothesis, significance level, 34. Type-I and Type-II Errors 35. Concept mean of a population variance known and unknown 36. Exercises 37. Inference on the mean of a population variance known and unknown 38. Inference on the variance of a normal population 39. Inference on the variance of a normal population problems 40. Inference on a population proportion 41. Testing for goodness of fit procedure and problems 42. Exercises 43. Testing for goodness of fit problems 44. Inference for a difference in means Variance known. Problems 45. Inference for a difference in means Variance known. Problems 46. Inference for a difference in means of two normal distributions. Problems 47. Concept of Linear Regression, Empirical models simple linear Regression

Properties of least square estimators. 48. Exercises 49. simple linear Regression, correlation coefficient problems 50. Linear Regression problems coefficient of correlation 51. Estimators and Estimation of variances Problems 52. Common abuses of Regression, Hypothesis tests in simple linear regression. 53. Prediction of new observations. 54. Exercises 55. Assessing the adequacy of regression model, Transformations to a Straight Line

Correlation. Problems 56. Concept of Multiple linear regression model, 57. Prediction of new observations, Measures of model adequacy. 58. Concept of design of experiments strategy of experimentation 59. Completely randomized single factor experiments. 60. Tests on Individual treatment means, the random effects model 61. The randomized complete block design, determining sample size in single factor

experiment. 62. Exercises

MVJCE 40

QUESTION BANK

01 Given below are the marks of 12 students in an examination, find the mean marks 68,82,94,105,120,122,127,130,133,140,141,145.

02 A firm purchased a certain type of items from four different manufactures. Manufacturer A supplied 50% of the items at a price of Rs 1.35 per item, B supplied 35% at a price of Rs 1.40, C’, 10%at Rs1.42 and D, 5%at Rs1.47. Find the mean price of the items.

03 The mean wage of 100 laborers in a factory, running two shifts of 60 and40 workers respectively, is Rs.38. the mean wage of 60 laborers working in one shifts isRs.40. Find the mean wage of 40, laborers working in the other shifts

04 Calculate the mean for the following data x 0 1 2 3 4 5 6 7 8 f 1 9 26 59 75 52 29 7 1

05 Find the mean for the following data in a test carrying 100 marks given to 88 students, 77 students get above 10 marks, 72 get above20, 65 get above 30, 55 get above 40, 43 get above 50, 28 get above 60, 16 get above70, 10 get above 80 and 8 get above 90. Find the mean marks

Class 0-10 10-30 30-50 50-60 60-90 90-100 Frequency 2 5 17 22 20 9

06 Enumerate on Stem and Leaf Diagrams. 07 Prepare a stem and leaf Diagram for the following data: 10, 33, 9, 8, 75, 12, 15, 85, 18,

22, 25, 27, 29, 33, 68 35, 38, 42, 47, 52, 45, 56, 51, 50, 62, 64, 68, 70, 71, 78, 80, 75, 82, 88, 90, 91, 93, , 98, 32, , 56, 75, 24, 38, 56, 67, 84.

08 Explain briefly on the uses of measures of central tendency 09 A student computed the mean and standard deviation for 100 items of an observation as

40 and 5.1 respectively. It was later discovered that he had wrongly copied down an item as 50 instead of 40. Calculate the mean and standard deviation

10 Define the terms i. Probability ii. Conditional probability 11 What do you understand by: i. Equal likely events, ii. Independent events, iii. Mutually

exclusive events, iv. Independent events, v. Dependent events 12 What is a Random experiment and sample space 13 State and prove Baye’s Theorem 14 Tickets are numbered from 1 to 100 they are well shuffled and a ticket is drawn at

random. What is the probability that the drawn ticket has: i. An even number, ii. A number 5 or multiple of 5, iii. Number which is greater than 75, iv. A number, which is a square.

15 An employer wishes to hire 4 people from a group of twenty applicants 12 men and 8 women all of whom are equally qualified to fill the position. If he selects the four at random, what is probability that: i. All four will be men, ii. At least one will be woman, iii. At least two will be woman.

16 A bag contains 17 counters marked with numbers 1 to 17. A counter is drawn and replaced a second drawing is then made what is the chance that the first number drawn is even and second is odd.

17 A man wants to marry a girl having qualities, white complexion, the probability of getting such a girl is 1 in 20, handsome dowry the probability of getting that is 1 in 50, westernized manners and etiquettes the probability here is 1 in 100. Find out the

MVJCE 41

probability of his getting married to such a girl when the possessions of three attributes are independent

18 The Probability that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9 respectively. Find the probability that in 20 years i. Both ii . Neither iii . At least one will be alive

19 A speaks truth in 60% cases and B in 70% cases. In what percentage of cases are they likely to contradict each other in stating the same fact

20 The probability that Mr. X passes mathematics is 2/3 the probability that he passes statistics is 4/9. If the probability of passing atleast one subject is 4/5, what is the probability that Mr X will pass both the subjects

21 If P (A)=0.6 P (B)=0.4 and P (A∩B)=0.3 Find 1. P (A∪B) 2. P (A∩B) 22 The digits 0,1,2,3,4 without repetition form a five-digit number. Find the probability that

number formed is divisible by 4 23 If A and B are independent events, prove that: )()(1)( BPAPBAP −=∪ 24 In a housing colony, 70% of the houses are well planned and 60% of the houses are well

planned and well built. Find the probability that a house that is well planned is also well built

25 A bag contains 2 white marbles and 4 red marbles and another bag contains 2 red marbles and 4 white marbles. If a marble is selected at random from one of the two bags, what is the probability that it is a white marble?

26 Two different digits are selected at random from the digits 1 to 9 i If the sum is odd, what is the probability that 2 is one of the digit selected ii . If 2 is one of the digits selected, what is probability that the sum is odd?

27 A picnic is arranged to be held on a particular day. The weather forecast says that there is 80% chance of rain on that day. If it rains the probability of good picnic is 0.3 and f it does not the probability is 0.9. What is the probability of good picnic?

28 The chances that doctor A will diagnose a disease X correctly are 60%. The chances that a patient will die by his treatment after correct diagnose is 40% and the chance of death by wrong diagnose is 70%. A patient of doctor A, who had disease X died, what is the chance that his disease was diagnosed correctly

29 A binary communication channel carries data as one of two types of signals denoted by 0 and 1. Due to noise, a transmitted 0 is received as 1with the probability 0.06 and a transmitted 1 is received as 0 with probability 0.09. The probability of transmitting 0 is 0.45. If a signal is sent find i. The probability that a 0 is received ii . The probability that a 1 was transmitted, given that 1 was received.

30 A ball is drawn from an Urn containing 3 white and 3 black balls. After the ball is drawn it is placed and another ball is drawn. This goes indefinitely, what is probability that of the first four balls drawn exactly 2 are white

31 Define discrete and continues random variables with an example. 32 Define Probability mass function and density function 33 Find the mean, variance and standard deviation for the following distribution

X i -5 -4 1 2 P(xi) ¼ 1/8 ½ 1/8

34 The following table gives the probability distribution of a random variable X. Find k and evaluates mean and standard deviation

MVJCE 42

X i 0 1 2 3 4 5 P(xi) K 5k 10 10k 5k k

35 If a random variable X has the probability density function

≤>

=−

00

02)(

2

x

xexf

x

Evaluate P(1<X<3) and P(X>0.5)

36 The length of time (in min.) that a certain lady speaks on the telephone is found to be a random variable with density function

≥

=−

whereelse0

0 x)(

5/ forAexp

x

Find the value of A

37 Find the probability that the number of minutes that she will speak on the phone: i. More than 10 minutes ii. Less than 5 minutes iii. Between 5 and 10 minutes

38 The probability density function p(x) of a continues random variable is given by p(x) = y0e

-|x| , -∞ <x<∞ . Prove that y0=1/2 and hence find mean and variance of the distribution. 39 Obtain the mean and variance of the binomial distribution 40 Let X be binomially distributed random variable based on 6 repetitions of an experiment.

If p = 0.3, evaluate the following probabilities 4)p(X and 4)ii)p(X 3)p(X ) >=≤i 41 The probability that a pen manufactured by a company will be defective is 0.1. If 12 such

pens are selected at random find the probability that i. Exactly 2 will be defective ii. At least 2 will be defective iii. None will be defective

42 Suppose 2% of the items produced by a machine are defective. Find the probability that there are 3 defective items in a sample of 100 items

43 The number of accidents in a year to auto-drivers in a city is a poisson variate with mean 3. Out of 1000 such drivers find approximate number of drivers with a) no accidents b) more than 3 accidents in a year

44 In a certain city the probability that rain occurs on a day during June is 5/8. Find the probability that there is a rain on June 5th and not earlier

45 The probability that the prediction of a sooth sayer will come true is 0.01. What is the probability that his 13th prediction is the first one to be true

46 A random variable X has a uniform distribution over (-α α) where α>0, Determine α in the following cases i ) P(X>1) ii) P(X<1/2) iii) p(|X|<1)=p(|X|>1).

47 Find the CDF for a uniform distribution in the interval (a b). 48 On a certain city transport route, buses ply every 30 min. between 6am and 10pm. If a

person reaches a bus stop on this route at a random time during this period, what is the probability that he will have to wait for at least 20 minutes

49 If X is uniformly distributed over the interval (-1 1), find the density function of Y=CosπX

50 Find the mean and standard deviation of exponential distribution 51 Find the CDF of an exponential distribution 52 The duration of a telephone conversation has been found to have exponential distribution

with mean 3 min. Find the probability that the conversation may last i. more than 1 min. ii. less than 3 min

53 In a certain town the duration of a shower is exponentially distributed with mean equal to

MVJCE 43

5 min. What is the probability that i ) a shower will last for at least 2 min. more given that it has already lasted for 5 min. ii) a shower will last for not more than 6 min. if it has already lasted for 3 min

54 For the following joint probability distribution of two random variables X and Y, find i ) marginal distribution of X and Y ii) Cov(X,Y) iii) ρ(X,Y)

X Y -4 2 7 1 1/8 1/4 1/8 5 ¼ 1/8 ½

55 The following table gives the joint distribution of two random variables X and Y. Find the probability of X given Y=0

X, Y -1 0 1 -1 0 0.2 0 0 0.1 0.2 0.1 1 0.1 0.2 0.1

56 For the distribution with the density function

<<<<−−

=wiseother

yxyxyxp

0

42,20)6)(8/1(),(

Evaluate i. p(x<1,y<3) ii . p(x+y<3) iii . p(x<1| y<3)

57 For the distribution defined by the density function

≥≥

=+−

wise0

0,0),(

)1(

other

yxxeyxp

yx

Evaluate E(y | x) and E(x | y).

58 The joint probability density function for a distribution is

≥≥

=−−

wise0

0,06),(

32

other

yxeyxp

yx

Verify that x and y are independent. 59 A firm purchased a certain type of items from four different manufactures. Manufacturer

A supplied 50% of the items at a price of Rs 1.35 per item, B supplied 35% at a price of Rs 1.40, C’, 10%at Rs1.42 and D, 5%at Rs1.47. Find the mean price of the items

60 The mean wage of 1oo laborers in a factory, running two shifts of 60 and40 workers respectively, is Rs.38. the mean wage of 60 laborers working in one shifts isRs.40. Find the mean wage of 40, laborers working in the other shifts

61 Fit a straight line by the method of least squares to each of the following data

X 0 1 3 6 8 Y 1 3 2 5 4

62 Fit an equation of the form y=abx to the given data

X 2 3 4 5 6 Y 9.3 15.3 33.1 65.2 127.4

63 Find the coefficient of correlation and the regression lines for the following data

X 1 2 3 4 5 6 7 8 9 10

MVJCE 44

Y 10 12 16 28 25 36 41 49 40 50 64 The correlation coefficient between two variables x and y is r = 0.6. If σx =1.5 σy = 2.00,

x= 10 and y = 20, find the regression of y on x and of x on y 65 For the data given in the following table, compute

i. Standard deviation of X ii. Standard deviation of Y iii. Co-variation of X and Y vi. The coefficient of correlation between X and Y X 1 3 4 6 8 9 11 14

Y 1 2 4 4 5 7 8 9 66 Psychological tests of intelligence and computational ability were applied to ten children.

Following is the record showing intelligence ratio (I.R) and ability ratio (A.R). Calculate the coefficient of correlation

I.R.(x) 105 104 102 101 100 99 98 96 95 94 A.R.(y) 101 103 100 98 95 96 104 97 97 96

67 Find the coefficient of correlation and regression lines for the following data X 1 2 3 4 5 6 7 8 9 10 Y 10 12 16 28 25 36 41 49 40 50

68 The following table indicates the test scores of ten sales person in an intelligence test and their weekly sales (in hundred units) Find the regression line of the sales on test scores and estimate the most probable weekly sale of the sales person whose test score is 85

Test scores 40 70 50 60 80 50 90 40 60 60 Sales 2.5 6.0 4.5 5.0 4.5 2.0 5.5 3.0 4.5 3.0

69 In a partially destroyed laboratory data, only the following regression equations were available: 7X-16Y+9=0,5Y-4X-3=0.Find the coefficient of correlation between X and Y.

70 A correlation coefficient based on a sample of size 27 was computed to be 0.40. Can we conclude at a significance level of 0.01 that the corresponding population correlation coefficient differs from 0?

71 A correlation coefficient based on a sample of space 35 was computed to be 0.50. Can we reject the hypothesis that the population correlation coefficient is ρ=0.70 at 0.05 significance level?

72 A correlation coefficient of 0.5 is found from a sample of size 19. Can we say that the population correlation coefficient is closed to 0.3 at 5% level of significance?

73 Find 99% confidence limits for correlation coefficient, which is computed to be 0.60 from a sample of size 28.

74 Find the probability that in 120 tosses of a fair coin i) between 40% and 60% will be heads, ii) 5/8 or more will be heads.

75 It has been found that 2% of the items produced by a certain machine are defective. What is the probability that in a sample of 400 items, i) 3% or more, ii) 2% or less will be defective?

76 A certain machine part manufactured by a company has a weight of 0.5 gm on the average with a standard deviation of 0.02gm. What is the probability that the mean weight in two lots, of 1000 such parts each, will differ by more than 0.02 gm.

77 An urn contains 60 red marbles and 40 white marbles. Two sets of 30 marbles each are

MVJCE 45

drawn with replacement from the urn and their colors are noted. What is the probability that the two sets differ by 8 or redder marbles.

78 A sample of 5 measurements of the diameter of a sphere were recorded as 6.33, 6.37,6.36,6.32,6.37 mm. Determine unbiased and efficient estimate of i) the true mean, and ii) the true variance.

79 For the frequency distribution given below, find the unbiased and efficient estimate for the mean and variance.

xi 60 61 62 63 64 65 66 67 68 f i 2 0 15 29 25 12 10 4 3

80 Suppose that 10, 12, 15, 16, 19 is a sample taken from a normal population with variance σ2 = 6.25, find the 95% of confidence interval for the mean µ.

81 If the measurement of a sample mean is recorded as 216.48 with a probable error of 0.272, find the 95% confidence limits for the measurement.

82 Suppose that the CPU service time of a job is normal variate with standard deviation 1.5 sec. Find the how large a sample is to be taken in order to assert with 99% confidence that the estimated mean service time is less than half a second of the true mean time.

83 In a sample of 200 items produced by a machine, 15 were found defective, while in a sample of 100 items produced by another machine, 12 were found defective. Find 99% and 99.74% confidence limits for the difference in proportions of defective items produced by the two machines.

84 In a hospital, 230 females and 270 males were born in a year. On the basis of this information, can the hypothesis that sexes are born in equal proportions be rejected?

85 The mean life time of sample of 150 bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours. Test the hypothesis that the mean lifetime of all bulbs produced by the company is 1590 hours at 0.01 and 0.05 levels of significance.

86 A sample of 100 electric bulbs produced by manufacturer A showed a mean lifetime of 1190 hours and a standard deviation of 90 hours. A sample of 75 bulbs produced by manufacturer B showed a mean lifetime of 1230 hours with a standard deviation of 120 hours. Is there a difference between the mean lifetimes of the two brands at a significance level of 0.05?

87 The mean lifetime of electric bulbs manufactured by a company has in the past been 1120 hours with a standard deviation of 125 hours. A sample of 8 bulbs chosen from supply of newly produced bulbs showed a mean lifetime of 1070 hours. Test the hypothesis that the mean lifetime has not changed, using a level of significance of 0.01.

88 The following table gives the marks of 10 students in two tests Test 1 67 24 57 55 63 54 56 68 33 43 Test 2 70 38 58 58 56 67 68 75 42 38

Can we conclude that there is a difference in the performance in the two tests at 0.5 level of significance?

89 For the data given in the following table, compute : i. Standard deviation of X, ii. Standard deviation of Y, iii. Co-variation of X and Y, and vi. The coefficient of correlation between X and Y.

X 1 3 4 6 8 9 11 14 Y 1 2 4 4 5 7 8 9

90 Psychological tests of intelligence and computational ability were applied to ten

MVJCE 46

children. Following is the record showing intelligence ratio (I.R) and ability ratio (A.R) . Calculate the coefficient of correlation

I.R.(x) 105 104 102 101 100 99 98 96 95 94 A.R.(y) 101 103 100 98 95 96 104 97 97 96

91 Find the coefficient of correlation and regression lines for the following data. X 1 2 3 4 5 6 7 8 9 10 Y 10 12 16 28 25 36 41 49 40 50

92 The following table indicates the test scores of ten sales person in an intelligence test and their weekly sales (in hundred units)

Test scores 40 70 50 60 80 50 90 40 60 60 Sales 2.5 6.0 4.5 5.0 4.5 2.0 5.5 3.0 4.5 3.0

Find the regression line of the sales on test scores and estimate the most probable weekly sale of the sales person whose test score is 85

93 In a partially destroyed laboratory data, only the following regression equations were available: 7X-16Y+9=0,5Y-4X-3=0.Find the coefficient of correlation between X and Y.

94 A correlation coefficient based on a sample of size 27 was computed to be 0.40. can we conclude at a significance level of 0.01 that the corresponding population correlation coefficient differs from 0?

95 A correlation coefficient based on a sample of space 35 was computed to be 0.50. Can we reject the hypothesis that the population correlation coefficient is ρ=0.70 at 0.05 significance level?

96 Define Random experiment, Sample space, Event and classical definition of probability with example each.

97 State axioms of Probability and prove the following

B)P(A-P(B)P(A)B)P(A iii)

0 )P( )

)(1A)P( )

∩+=∪=Φ

−=ii

APi

98 A box contains 75 good IC chips and 25 defective IC chips. If 12 IC chips are selected

at random, what is the probability at least one chip is defective. 99 A tea set has 4 sets of cups and saucers. Two of these sets are one color and the other

two sets are of different color. If the cups are placed at random on the saucers, what is the probability that the no cup is on a saucer of the same color?

100 In a factory turning out optical lenses, there is a small chance of 1/500 for any one lens to be defective. The lenses are supplied in packets of 10. Use Poisson distribution to calculate the approximate number of packets containing no defective, one defective, two defective, three defective lenses in a consignment of 20000 packets.

101 A systematic sample of 100 pages was taken from the concise oxford dictionary and the observed frequency distribution of foreign words per page was found to as follows:

No. of foreign words per page (X) 0 1 2 3 4 5 6 Frequency 48 27 12 7 4 1 1

Calculate the expected frequencies using poisson distribution also compute variance of fitted distribution.

102 Enumerate on the properties of normal distribution.

MVJCE 47

103 List the importance of normal distribution. 104 The per acre yield of a crop in a particular area is observed to follow a normal

distribution with mean 15 quintals and S.D of 5 quintals. Find i. The proportion of the area yielding at least 25 quintals ii. What extend of the land under the crop can yield between 10 and 20 quintals if the total land crop is 782 acres.

105 Find the probability that the number of heads lie in the range 185 and 220 when a fair coin is tossed 400 times.

106 In a competitive examination, 5000 students have appeared for a paper in statistics. Their average mark was 62 and S.D is 12. If there are 100 vacancies find the minimum marks that one should secure to get selected against a vacancy.

107 In a normal distribution 17% of the items are below 30 and 17% of the items are above 60. Find the mean and standard deviation.

108 Fit a normal curve to the following data. Class interval 5-9 10-14 15-19 20-24 25-29 Frequency 10 22 40 21 7

109 Fit a normal curve to the data given below Diameter in inches 7 8 9 10 11 12 13 14 15 Frequency 1 6 7 11 20 10 6 5 1

110 The wage distribution of the workers in a factory is normal with mean Rs. 400 and S.D is 50, If the wage of 40 workers be less than Rs 350, what is the total number of workers in the factory.

111 Write short notes on one-tailed tests and two tailed tests. 112 Write a note on Degree of freedom and students “t “ distribution. 113 Define unbiased estimator, efficient estimator. 114 Discuss F distribution and F-test.

MVJCE 48

06IM54 – INDUSTRIAL ENGINEERING

MVJCE 49

INDUSTRIAL ENGINEERING Sub Code: 06IM54 IA Marks: 25 Hrs/week: 05 Exam Hours:03 Total Lecture Hrs: 62 Exam Marks: 100 PART - A UNIT - 1 PRODUCTIVITY: Definition of productivity, individual enterprises, task of management Productivity of materials, land, building, machine and power. Measurement of productivity, factors affecting the productivity, productivity improvement programmes, wages and incentives (simple numerical problems) 7 Hours UNIT - 2 WORK STUDY: Definition, objective and scope of work study. Human factor in work study. Work study and management, work study and supervision, work study and worker. 6 Hours UNIT - 3 INTRODUCTION TO METHOD STUDY: Definition, objective and scope of method study, activity recording and exam aids. Charts to record moments in shop operation – process charts, flow process charts, travel chart and multiple activity charts.( With simple problems) 7 Hours UNIT - 4 MICRO AND MEMO MOTION STUDY: Charts to record moment at work place – principles of motion economy, classification of moments two handed process chart, SIMO chart, and micro motion study. Development,definition and installation of the improved method, brief concept about synthetic motion studies. 6 Hours

PART - B UNIT - 5 INTRODUCTION TO WORK MEASUREMENT: Definition, objective and benefit of work measurement. Work measurement techniques. Work sampling: need, confidence levels, sample size determinations, random observation, conducting study with the simple problems. 6 Hours UNIT - 6 TIME STUDY: Time Study, Definition, time study equipment, selection of job, steps in time study. Breaking jobs into elements, recording information. Rating & standard Rating, standard performance, scale of rating, factors of affecting rate of working, allowances and standard time determination. Predetermined motion time study – Method time measurement (MTM) 7 Hours UNIT - 7 ERGONOMICS: Introduction, areas of study under ergonomics, system approach to ergonomics model, man-machine system. Components of manmachine system and their functions – work capabilities of industrial worker, study of development of stress in human body and their consequences. computer based ergonomics 6 Hours UNIT - 8 DESIGN OF MAN-MACHINE SYSTEM: Fatigue in industrial workers. Quantitative qualitative representation and alphanumeric displays. Controls and their design criteria, control types, relation between controls and displays, layouts of panels and machines. Design of work places, influence of climate on human efficiency. Influence of noise, vibration and light. 7 Hours

MVJCE 50

TEXT BOOKS: 1. ILO, Introduction to work study - III Revised Edition, 1981 2. Motion and Time study - Ralph M Barnes; John Wiley, 8th Edition, 1985. 3. Engineered work Measurement - Wledon, ELBS , 1991 Marvin E. Mundel- Motion and Time study, PHI, 1st edition REFERENCES BOOKS: 1. Human Factors in Engineering Design - S Sanders and E J McCormick, 6th Edition, Mc Graw Hill 2. Work Study and Ergonomics - S Dalela and Sourabh, – Chand Publishers, 3rd edition. 3. Industrial Engineering Hand book Maynard

MVJCE 51

LESSON PLAN

Sub Code: 06IM54 I.A. Marks: 25 Hours / Week: 05 Total Hours: 2 Subject: Industrial Engineering Sem:V

Hour. No Topics to be covered

1. Introduction and definition of productivity, 2. Task of management and individual enterprises, techniques for productivity 3. Productivity of materials, land, building, machine and power 4. Factors affecting productivity and measurements of productivity

5. Introduction to wages objective, procedure and incentives and productivity improvement programmes

6. Revision/Quiz/Surprise Test. 7. Definition, and scope of work study 8. Human factor in the application of work study and roles in work study

9. Work study and management, worker and supervisor and its influence of working conditions

10. Introduction, definition, objectives, procedure and scope of method study 11. Selection of jobs, activity recording and exam aids 12. Different charts to record moments in shop operation and its explanation 13. Revision/Quiz/Surprise Test. 14. Process chart symbols and operation process chart with problems 15. Flow process chart of man type, material type and equipment type 16. Flow and handling of materials and developing a new layout 17. Handling of materials and making correct choice of handling equipment 18. Travel chart and multiple activity chart and its related problems 19. Principles and purpose of charts to record moment at work place. 20. Revision/Quiz/Surprise Test. 21. Classification of moments with two-handed process chart.

22. SIMO chart and micro motion study, movements and principles of motion economy

23. Development, definition and installation of improved methods

24. Brief concept about synthetic motion studies and classification of various movements

25. Use of films in method analysis and other recording techniques 26. Introduction, definition, purpose and objectives of work measurement 27. Revision/Quiz/Surprise Test. 28. Techniques and procedures of work measurement techniques 29. Basic concepts, definition and procedure of work sampling

30. Need, confidence levels, sample size determinations and random observations of work measurement

31. Conducting study with simple problems and errors and use of work sampling 32. Definition and forms of time study and time study equipment 33. Different selection of jobs and steps in time study.

MVJCE 52

34. Revision/Quiz/Surprise Test. 35. Breaking jobs into elements and recording information 36. Steps and classification of elements in time study 37. Determination of sample size and timing elements by stop watch 38. Standard performance, rating and standard rating 39. Various scales of rating and factors affecting rate of working 40. Allowances and standard time determination. 41. Revision/Quiz/Surprise Test. 42. Predetermined motion time study and method time measurement 43. Introduction and definition of ergonomics, and areas of study under ergonomics 44. System approach to various ergonomics model

45. Discussion of man-machine system and components of man-machine system and their functions

46. Various work capabilities of industrial worker 47. Study of development of stress in human body and their consequences 48. Revision/Quiz/Surprise Test. 49. A case study on ergonomics 50. Fatigue in Industrial workers. 51. Quantitative, qualitative representation and alphanumeric displays, 52. Controls and their design criteria 53. Control types and their forms 54. Relation between controls and displays 55. Revision/Quiz/Surprise Test. 56. Layouts of panels and machines 57. Design of work place and its layouts with specification 58. Influence of climate on human efficiency 59. Influence of Noise and its adverse effects on environment 60. Influence of Vibration & Light on employees in organization 61. Revision/Quiz/Surprise Test. 62. Revision/Quiz/Surprise Test.

MVJCE 53

QUESTION BANK

01 Productivity and mention the benefits of higher productivity 02 Explain the productivity of land, buildings, machines and manpower. 03 What are the factors contributing to productivity improvement? 04 Sketch and explain the various tasks of a manager 05 Determine how productivity can be improved by reducing work 06 Define Work Study and explain its basic procedure 07 What are the prerequisites of conducting work-study? 08 What are the roles of management and supervisor in work-study? 09 What are the factors affecting working conditions? 10 How does noise and vibration affect the working conditions? 11 What are the factors considered for the arrangement of working time in work place? 12 Define method study and its procedures 13 Explain the factors involved in the selection of job 14 With notations explain the various process chart symbols 15 What are the primary and secondary questions involved in method study? 16 Mention the various methods of determining space requirements 17 What is cross-chart? Where is it used? 18 Is handling of materials necessary? If so, why? 19 Explain the various handling equipments and their area of usage 20 Differentiate between flow process chart - man type and material type 21 Give the importance of travel chart and multiple activity chart 22 State and explain the principles of motion economy. 23 What are the various classification of movements 24 Define two handed process chart and points required for compiling THPC. 25 What is micro motion study, explain its importance 26 Sketch the various Therblig’s symbols, with its abbreviations. 27 How is any new improved method maintained in work-study? 28 What is work measurement and describe the various purpose involved. 29 What are the basic procedure and techniques of work measurement? 30 Define work sampling and explain its basic concepts. 31 What are the various procedure of work sampling 32 What are the various procedures for selecting random observation and describe the

methods for determining sample size. 33 Give an example for conducting work-sampling study. 34 What are the time study equipments and forms 35 How is a job and worker selected for time study 36 Explain the basic steps for conducting time study 37 What are the timing elements of stopwatch? 38 Explain the standard rating and standard performance of a qualified worker 39 How is the comparison of the observed rate of working done with the standard 40 What are the factors affecting the rate of working? 41 How is rating factors recorded? 42 How is a study summary sheet prepared?

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43 What are the numbers of elements and cycles to be considered in time study? 44 What are relaxation allowances and how is it calculated? 45 What are the various allowances considered in time study? 46 The observed time is recorded to be 15 minutes for a job done by a worker whose rating is

80. Following allowances are recommended by the management – i. Personal needs allowance - 5% of basic time ii. Basic fatigue allowance - 2% of basic time iii. Contingency work allowance - 1% of basic time vi. Contingency delay allowance - 2% of basic time

Determine basic time, work content and standard time for the job. 47 How is the standard time and cycle time determined in setting time standards? 48 How is interference allowance different from other allowances? 49 What are the concepts of restricted work and cycle time? 50 Explain the basic definitions pertaining to a man – machine system 51 What are the advantages and different forms of PTS systems? 52 List the applications of PTS system 53 How is a standard data developed? 54 How is PTS system used for developing standard data? 55 Explain the technical set-up and work specification of time standard. 56 List and explain the various uses of time standard. 57 Define ergonomics and discuss the factors of ergonomics. 58 Sketch and explain the three major functions of ergonomics. 59 What are the characteristics of man-machine system? 60 What are the various classification of man- machine systems? Explain. 61 Differentiate the various features between man and machine in ergonomics. 62 Explain the design of displays and controls. 63 What are the major factors considered for the designing of working environment? 64 How is fatigue eliminated by motion time study (MTS)? 65 Plot a graph of heart beat V/s clothe wear and state its features. 66 How are links used as indexes of interrelationships? 67 What are the quantitative solutions to arrangement problems? 68 What are the various visual components and hand controls? 69 Why controls requiring forces used? 70 How is specific arrangement of components done in ergonomics? 71 What are the external guidelines for designing individual workplaces? 72 How is hearing loss caused by continuous and non- continuous noise? 73 What are the effects of noise on performance and how is noise problem handled? 74 What are the effects of whole body vibration on performance? 75 Explain the psychological effects of weightlessness. 76 How does acceleration of body effect the performance? 77 What are the body changes caused by heat during thermal adjustmen? 78 What are the factors effecting heat exchange? 79 Sketch the various illumination standards. 80 Explain the influence of climate on human efficiency. 81 List the layouts of panels and machines used in man-machine systems.

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82 Explain the factor affecting productivity 83 Explain the human resources 84 Explain the productivity measurement system 85 Explain the advantages of work study 86 Explain the process chart symbols 87 Explain the flow diagram 88 Discus about the string diagram 89 Explain the rules concerning human body 90 Explain the rules concerning time conservation 91 Explain the stop watch time study 92 Discus the process allowances 93 What is the standard data 94 Briefly explain the method study 95 Discus about work factor in work study 96 Explain the work sampling 97 Explain the work place layout 98 Why working environment should be good 99 Discus the ergonomics 100 Briefly Explain the method study procedure

MVJCE 56

06IM55 – CAD / CAM

MVJCE 57

CAD / CAM Sub Code: 06IM55 IA Marks: 25 Hrs/week: 05 Exam Hours:03 Total Lecture Hrs: 62 Exam Marks: 100

1. Introduction: Role of computers in design and manufacturing. Influence of computers in

manufacturing environment. Product cycle in conventional and computerized manufacturing environment. Introduction to CAD, Introduction to CAM. Advantages and disadvantages of CAD and CAM 03 hrs

Hardware for CAD: Basic Hardware structure. Working principles, usage and types of hardware for CAD – Input devices. Output devices, memory, and CPU, hardcopy and storage devices. 04hrs 2. Computer Graphics: Software configuration of a graphic system.

Functions of graphics Package. Construction of Geometry. Wire frame and solid modeling. CAD/CAM integration. Desirable modeling facilities. Introduction to exchange of modeling data – Basic features of IGES, STEP, DXF, DMIS. 06 hrs

3. Introduction to Finite Element analysis: Introduction, Basic concepts, discretization, element

types, nodes and degrees of freedom mesh generation, constraints, loads, preprocessing, and application to static analysis. 06 hrs

4. NC, CNN, DNC Technologies: NC, CNC, DNC modes, NC elements, advantages and

limitations of NC, CNC. Functions of computer in DNC 06 hrs PART - B

5. CNC Machine Tools: Turning tools geometry, milling tooling systems, tool presetting, ATC work holding. CNC machine tools, Overview of different CNC machining centers, CNC turning centers, high speed machine tools. 07 hrs 6. CNC programming: Part program fundamentals – steps involved in development of a part

program. Manual part programming, milling, turning, turning center programming. 08 hrs 7. APT PROGRAMMING: APT Programming in drilling, milling and turning with problems Materials. Stress concentration, Determination of Stress concentration factor 06 hrs 8.Introduction to robotics: Introduction, robot configuration, robot motion, programming of robots, end effectors, work cell, control and interlock, robot sensor, robot applications. 06 hrs Suggested Text Books:

1. CAD/CAM Principles and Applications by P.N. Rao, Tata McGraw Hill, 2002 2. CAD/CAM by Mikell P-Groover, Emory W. Zimrners Jr Pearson Education Inc, 2003

MVJCE 58

REFERENCE BOOKS: 1. Principles of Interactive Computer Graphics - Newman and Sproull, Tata McGraw Hill, 1995 2. NC Machine programming & software Design -Chno-Hwachang, Michel.A. Melkanoff, Prentice Hall, 1989. 3. Computer Graphics - Steven Harrington, McGraw Hill Book Co. 4. CAD/CAM -Ibrahim Zeid, Tat McGraw Hill, 1999 5. Computer Aided Manufacturing - P.N. Rao, N.K. Tewari and T.K. Kundra Tata McGraw Hill 1999. 6. Introduction to FEM - T Chandra Patta Ashok D Bebgundu, 2002 7. Computer Graphics - Pradeep K Bhatia, I K International Publishing house Pvt. Ltd. 8. Basic Computer Aided Geometric Design - Ganesh. M – I. K. International, New Delhi - 2008

MVJCE 59

LESSON PLAN

Sub Code: 06IM55 I.A. Marks: 25 Hours / Week: 05 Total Hours: 62 Subject: CAD/CAM Sem:V

Hour. No Topics to be covered

1. Role of computers in design and manufacturing. Influence of computers in manufacturing environment

2. Product cycle in conventional and computerized manufacturing environment 3. Introduction to CAD & CAM. Advantages (benefits) and disadvantages of CAD

and CAM 4. Introduction to computer and its Basic structure – generations, types, computer

languages, data representation 5. Introduction to Memory, Main memory, Auxiliary memory, Cache memory –

RAM, ROM, CD-ROM, Magnetic disks 6. Revision/quiz/surprise test. 7. Computer registers and it functions 8. Input devices – key board, mouse, touch screens, light pen, joy stick, track balls,

digitizer, tablet 9. Out put devices – Cathode Ray Tube (CRT) display (Stroke writing display and

Raster scan display), Plasma panel display, Liquid crystal display (LCD) 10. Hard copy devices – Graphical printers, plotters, photographic devices 11. Introduction to computer graphics, software configuration of a graphic system 12. Revision/quiz/surprise test. 13. Functions of graphics package, construction of geometry 14. Introduction to geometric modeling – wire frame and solid modeling 15. CAD/CAM integration, desirable modeling facilities. 16. Introduction to exchange of modeling data – basic features of IGES, STEP, DXF,

DMIS 17. Introduction to finite element analysis, basic concepts. 18. Revision/quiz/surprise test. 19. Discretisation, element types – triangular, rectangular, polynomial 20. Nodes and degrees of freedom, mesh generation on models 21. Constraints, loads, pre-processing, processing, post-processing 22. Application to static analysis 23. Simple exercices on finite element analysis 24. Revision/quiz/surprise test. 25. Introduction to Numerical Control (NC) – its basic components (elements), trends

and new developments in NC and advanced NC systems. 26. Advantages and limitations of NC, NC motion control systems, NC coordinates systems –

fixed zero and floating zero – absolute positioning and incremental positioning 27. Introduction to Computer Numerical Control (CNC) and its functions. Advantages of

CNC

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28. Introduction to Direct Numerical Control (DNC) and its functions – advantages 29. Introduction to CNC tooling, Turning tool geometry 30. Revision/quiz/surprise test. 31. Milling tooling system and its factions 32. Tool presetting, Automatic Tool changers (ATC) 33. Work holding devices for different types of machines 34. Introduction to CAM programming, overview of different CNC milling centers 35. Overview of different CNC turning centers 36. Revision/quiz/surprise test. 37. High speed machine tools, MCE 38. Introduction CNC programming – punched tap in NC, tape coding and format 39. NC part programming languages 40. Introduction to Manual part programming (MPP) and steps involved in wring part

programming. 41. Exercises on MPP – turning 42. Revision/quiz/surprise test. 43. Exercises on MPP – milling 44. Exercises on MPP – drilling 45. Computer assisted part programming (CAPP)– part programmer’s job and

computer’s job 46. Types of part programming languages in CAPP – APT language – geometry

statements 47. Motion statements – auxiliary statements – processing statements 48. Revision/quiz/surprise test. 49. Exercises on APT language 50. Turning center programming 51. NC programming with interactive graphics, Advantages of CAD/CAM in NC part

programming 52. Introduction to Robotics – different types of configuration, basic robot motions 53. Robot anatomy – joints, links, pitch, yawn, degrees of freedom 54. Revision/quiz/surprise test. 55. Important technical features in robots such as work volume, precision of

movement, speed of movement, weight-carrying capacity 56. Types of drive systems – Accuracy and repeatability of robot motion. 57. Programming of robots – different types of programming methods used in robots.

Robot programming languages – lead through programming, offline programming 58. End effectors – types of end effectors and applications, advantages and

disadvantages of each and end effectors, tools as end effectors 59. Robotic sensors, categories of sensors – application of sensors. 60. Work cell, control and interlock 61. Robot applications – general considerations in robot applications- application

areas for industrial robots like material transfer, welding, loading etc., 62. Revision/quiz/surprise test.

MVJCE 61

QUESTION BANK

01 What is the function of CAD? Mention important benefits of CAD. 02 Explain CAM. 03 Explain the product cycle. 04 How manufacturing database is created? What are the two basic approaches of solid

modeling? Explain. 05 What is the basic structure of digital computer? Discuss. 06 What is computer register? Explain the functions of these registers. 07 Explain the following terms: Raster Scan, Application software, CSG modeling, Host

satellite computer 08 Discuss the Data Representation. 09 Explain in brief with sketch the hardware component of CAD system. 10 Compare “Wire frame “ and “Solid modeling” graphics systems used in CAD 11 Briefly explain the fundamental reasons for implementing computer aided design system. 12 Explain with block diagram how the various design related tasks are performed by the

modern CAD system. 13 Briefly explain the fundamental reasons for implementing computer aided design system. 14 What is the programmable controller? What are the functions of programmable

controller? 15 What are the advantages of programmable controller? 16 Explain the CAD system. 17 What is the application of computers for design. 18 Describe the principle of working of a CRT. 19 What are the important output devices used in CAD? 20 How do you classify modeling package? 21 Compare 2D and 3d wire frame models. 22 What is a database ? What are the objectives of Database? 23 What are the advantages and disadvantages of Database? 24 Explain different types of modelers. 25 Explain DXF, DMIS, STEP and IGES. 26 Explain the construction of Geometry. 27 What are the four classes of data in manufacturing? 28 What is FEM. 29 Explain pre-processor, processor and post-processor in FEM. 30 Explain Nodes and selection of nodes. 31 Explain the discrimination of elements in FEM. 32 What is Numerical control? What are the applications of NC. 33 What are the Basic components of NC? Explain. 34 Discuss the Coordinate System and Machine Motions in NC. 35 What are the different types of NC systems? Explain. 36 Explain the component of MCU and their function. 37 State the various characteristics of jobs for which NC is most appropriate. 38 Explain accuracy and repeatability. 39 Explain with block diagram the various component of NC production system.

MVJCE 62

40 Explain the feature of a contouring NC system. How does it differ from a straight NC Machine?

41 What is a punched tape? How instructions are formed. 42 What are the different types of tape formats used in NC. 43 What are the different types of NC words used in the formation of a block? 44 Explain the Manual part programming. 45 Explain with a neat sketch the computer’s job in CAPP. 46 Discuss briefly the various programming methods used in NC system. 47 Explain the APT language. What are the different types of statements in the APT

language? 48 Write a manual part programming for different shapes. 49 Write a APT language for different shapes. 50 Explain following terms: i. CNC and DNC ii. MACRO iii. Check Surface vi. Drive

Surface v. Part surface 51 What are the strategies used in adaptive control? Explain briefly. 52 Explain the controlling surface of a cutter in a contouring motion. 53 Explain the following: i. Manual Data Input ii. NC Part Programming Using CAD/CAM

iii. Computer-Automated Part Programming 54 What are the problems with conventional NC? 55 Explain the two types of DNC with sketches and advantages of DNC? 56 Explain the CNC control features. 57 Explain with a sketch a typical adaptive control machining system that uses cutter force as

the measured process variable. 58 Briefly discuss the part programmer and computer job in computer assisted part

programming. 59 Explain different types of work holding and tool holding devices used in NC machines. 60 Explain ATC. 61 Explain the different types of working centers used in different NC machines. 62 What is an Industrial Robot? Explain different types of Industrial Robot Joints and links

with neat sketch. 63 Discuss the different types of robot configurations with sketches. 64 Explain the Robot control systems. 65 Explain the following Robot technical features: i. Work Volume ii. Precision of

movement iii. Speed of movement vi. Weight carrying capacity v. Drive system vi. SCARA Robot

66 What are end effectors? What are most common grasping methods used in robot grippers? 67 What are the different types of sensors used in robotics? Explain. 68 What is work cell control and interlocks? 69 Explain the following: Lead through Programming, Off-line programming 70 Explain the Robot languages. 71 What are the characteristics of Robot applications? 72 Explain difference between the powered lead through programming and manual lead through

programming. 73 Explain the Robot cell design. 74 Discuss the application areas for Industrial robots.

MVJCE 63

06IM56-DESIGN OF MACHINE ELEMENTS

MVJCE 64

06IM56 – DESIGN OF MACHINE ELEMENTS Sub Code: 06IM56 IA Marks: 25 Hrs/week: 05 Exam Hours:03 Total Lecture Hrs: 62 Exam Marks: 100

PART A

UNIT I DESIGN FOR STATIC STRENGTH: Design considerations: Codes and Standards, Static strength; Static loads and factor of safety; Theories of failure -Maximum normal stress theory, maximum shear stress theory, Distortion energy theory; Failure of brittle materials, Failure of ductile materials. Stress concentration, Determination of Stress concentration factor. Combined Stress concentration factor. 07 Hrs UNIT II DESIGN FOR FATIGUE STRENGTH: Introduction, S -N diagram, Low cycle fatigue, High cycle fatigue, Endurance limit. Modifying factors -size effect, surface effect, Stress concentration effects; Fluctuating stresses, Fatigue strength under fluctuating stresses, Goodman and Soderberg relationship; Stresses due to combined loading, cumulative fatigue damage. 06 Hrs UNIT III JOINTS AND COUPLING : Design of rigid flange coupling & Bushed pin type flexible coupling. Cotter and Knuckle joints. 06 Hrs UNIT IV DESIGN OF SHAFTS: Torsion of shafts, design for strength & rigidity, with steady loading, ASME & BIS codes for design of transmission shafting, shafts under fluctuating loads and combined loads 07 Hrs

PART B

UNIT V DESIGN OF GEARS: Introduction to Spur, Helical & Bevel gears. Design of spur gear, stresses in gear tooth, Lewis equation, form factor- dynamic and wear load. 06 Hrs UNIT VI MECHANICAL JOINTS: Riveted Joints -Types, rivet materials, Failures of Riveted joints, Efficiency, Welded Joints -Types, Strength of butt and fillet welds. 07 Hrs UNIT VII DESIGN OF SPRINGS: Types of springs -stresses in Coil springs of circular and non circular cross sections. Tension and compression springs. Stress in Leaf springs (Simple problems).

06 Hrs UNIT VIII LUBRICATION AND BEARINGS: Mechanisms of Lubrication -Viscosity, bearing modulus, coefficient of friction, minimum oil film thickness-Heat Generated, Heat dissipated, bearing materials, lubricants and properties. Examples of journal bearing and thrust bearing design, Ball and Roller Bearings: Bearing life, equivalent bearing load, selection of bearings of different types. 07 Hrs TEXTBOOKS: 1. Mechanical Engineering Design -Joseph Edward Shigley, Tata McGraw Hill, New Delhi 1986 2. Machine Design -.VL. Maleev and Hartman, CBS Publishers & Distribution, Delhi, 1983 .

MVJCE 65

Design Data Hand Books : 1. Design Data Hand Book, K. Mahadevan and Balaveera Reddy , CBS Publication. 2. Design Data Hand Book Vol.l & Vol.2 -Dr. K. Lingaiah, Suma Publications, Bangalore. 3. Design Data Hand Book -Prof. H. a. Patil, Shri Shastri Prakashan, Belgaum. REFERENCE BOOKS: 1. Machine design -Robert .L. , Norton -Pearson Education Asia, New Delhi, 2001 2. Theory and Problems of Machine Design, Hall, Holowinko, Laughlin, -Schaums Outline Series, 2002 3. Elements of Machine Design -N. C. Pandey and C. S. Shah, 2002 -Chorotar Publishing House 4. Design of Machine Elements -V. B. Bahandri, -Tata McGraw Hill Publishing Co. Ltd., New -Delhi. 5. Machine Component & Design -William Orthwan, Jaico Publishing Co. 6. Fundamentals of Design -Benerad J Hamrock, Bo -Jacobson & Steven R. Schmid. 7. Fundamentals of Machine Design Component -Robert C. Juvinall and Kurt M. Marshek -John & sons 8. Machine Design -R. K. Jain , Khanna Publications, New Delhi.

MVJCE 66

LESSON PLAN

Hour. No Topics to be covered

1. Syllabus, Scheme of examination, Textbooks and Reference books. 2. Design considerations: Codes and Standards 3. Strength; Static loads and factor of safety 4. Theories of failure -Maximum normal stress theory, maximum shear stress theory

5. Maximum shear stress theory, Distortion energy theory

6. Exercises 7. Failure of brittle materials, Failure of ductile materials 8. Stress concentration, Determination of Stress concentration factor. Combined

Stress concentration factor 9. Introduction, S -N diagram, Low cycle fatigue, High cycle fatigue, 10. Endurance limit. Modifying factors -size effect. 11. Stress concentration effects; Fluctuating stresses, 12. Exercises 13. Fatigue strength under fluctuating stresses, Goodman and Soderberg

Relationship;. 14. Stresses due to combined loading 15. Stresses due to combined loading 16. Introduction, Design of rigid flange coupling. 17. Design of rigid flange coupling problems. 18. Exercises 19. Bushed pin type flexible coupling . 20. Bushed pin type flexible coupling problems 21. Cotter and Knuckle joints. 22. Cotter and Knuckle joints problems. 23. Torsion of shafts 24. Exercises 25. design for strength & rigidity with steady loading,

26. ASME & BIS codes for design of transmission shafting 27. shafts under fluctuating loads and combined loads

28. Shaft Design problems 29. Shaft Design problems.

30. Exercises

31. Shaft Design problems

Sub Code: 06IM56 I.A. Marks: 25 Hours / Week: 05 Total Hours: 62 Subject: Design Of Machine Elements Sem: V

MVJCE 67

32. Introduction to Spur, Helical & Bevel gears 33. Design of spur gear 34. Stresses in gear tooth, Lewis equation 35. Form factor- dynamic and wear load. 36. Exercises 37. Gear Design problems. 38. Gear Design problems – 39. Riveted Joints -Types, rivet materials. 40. Failures of Riveted joints, Efficiency

41. Welded Joints -Types, 42. Exercises 43. Strength of butt and fillet welds 44. Riveted joints design problems. 45. Riveted joints design problems. Welded joints design problems 46. Welded joints design problems 47. Introduction of springs, Types of springs 48. Exercises 49. Stresses in Coil springs of circular and non-circular cross sections. 50. Tension and compression springs. 51. Stress in Leaf springs. 52. Design problems 53. Design problems 54. Exercises 55. Mechanisms of Lubrication -Viscosity, bearing modulus, 56. Coefficient of friction, minimum oil film thickness-Heat Generated, Heat

dissipated, bearing 57. Materials, lubricants and properties 58. Examples of journal bearing and thrust bearing design, 59. Roller Bearings: Bearing life, equivalent bearing load, selection of bearings of

different types. 60. Design problems. 61. Design problems 62. Design problems

MVJCE 68

QUESTION BANK

01 Explain the maximum shear stress theory and maximum strain theory

02 A bolt is subjected to a tensile load of 20 kn and to a shear load of 15 kn .suggest a suitable size of the bolt according to various theories of failure .take yield stress =300N/mm2 ,n=2.5 .v=.25

03 Define static loading and dynamic loading 04

A machine component is subjected to varying bending stress ranging from 250 N/mm2 tension to 100 N/mm2 compression. Determine the ultimate strength required for the material using soderberg, Goodman and gerber relations.

05

Calculate the life of a circular shaft subjected to a completely reversed bending stress of magnitute 390 N/mm2 .the material of the shaft is C 45.

06

A circular bar of length 600 mm is supported at its ends.it is acted upon by a concentrated cyclic load at its centre which varies from 20 KN to 50 KN .if the factor of safety is 1.5, surface finish factor is 0.9 and the size effect is 0.85,find the diameter of the bar. The ultimate strength of the bar is 650 N /mm2, yield strength is 500 N/mm2 and endurance strength is 350N/mm2.

07 A mild steel shaft has transmit 80 KW at 200 rpm .the allowable shear stress in the shaft is limited to 45 N/mm2 .allowable shear stress for key material is 45 N/mm2 ,crushing stress for bolt and key is 160 N/mm2 ,shear stress for cast iron = 8 N/mm2 ,design and draw a cast iron flange coupling of protected type .

MVJCE 69

08

A bushed pin type flange coupling is to be designed to transmit 25 KW at a speed of 1000 rpm .the following permissible stresses are used : shear stress for the shafts and keys -55 N/mm2 ,shear stress for the pin 28 N/ mm2 ,and crushing stress for the key 100 N/mm2.

09 Design a cotter joint to transmit a load of 120 KN in tension or compression. assume tensile stress =85 N/mm2 ,shear stress 70 N/mm2,compression stress =165 N/mm2

10 Design a spindle for a milling machine .maximum power transmitted is 5 KW at 1000 rpm .angle of twist per meter length of spindle should not exceed 0.25. Material used is 20 Mn 2. take G =0.8 X 10 5 N/mm2

11 A hollow shaft of 600 mm outside diameter and 400 mm inside diameter is used to drive a propeller of a marine vessel. the shaft is supported on bearings 6 m apart and transmits 5000 KW at 150 rpm .maximum axial propeller thrust is 500 KN .shaft weighs 75 KN. maximum shear stress developed and angular twist between bearings

12 A solid shaft transmits a torque of 800 Nm at a shearing stress of 25 N/ mm2. Determine the wall thickness of a hollow shaft having an inside diameter equal to that of the solid shaft that can transmit the given torque at the same maximum stress.

13 In an axial flow rotary compressor, the shaft is subjected to a maximum torque of 1500 Nm and maximum bending moment of 3000 Nm.neglating the axial load on the compressor shaft ,determine the diameter of the shaft .assume that the load is applied gradually .the shear stress in the shaft is limited to 50 N/MM2. also design a hollow shaft for the above compressor taking inner diameter as 0.4 times the outer diameter .what is the percentage of material saving in hollow shaft?

14 A steel shaft transmits 15 KW AT 500 rpm .it is supported on two bearings 800 mm apart and has two gears keyed to it .the pinion having 30 teeth of 5 mm module is located 120 mm to the left of the right hand bearings and delivers power horizontally to the right .the gear having 100 teeth of 5mm module is located ,150 mm to the right of the left hand bearing and receives power (ccw viewed from the left end ) from below .determine the diameter of the shaft.

15 A machinery shaft is to transmit 65 KW at 1200 rpm with mild shock .the shaft is subjected to an axial load of 85 KN and maximum bending moment of 1000 Nm.the shaft is supported at intervals of 2.5 m.take C 45 as the shaft material and determine the diameter of the shaft neglecting keyway.

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16 a. Write a note on interference in gears b. A pair of Spur gears is to transmit 20 kW when the pinion rotates at 300 r.p.m. The

velocity ratio is 1: 3. The allowable static stresses for the pinion and gear materials are 120 MPa and 100 MPa respectively. The pinion has 15 teeth and its face width is 14 times the module. Determine a) module ; b) face width ; and c) pitch circle diameters of both pinion and gears from standpoint of strength only, considering the dynamic loading effect only, given that :

Tooth form factor teethofNo

Y..

912.0154.0 −=

Velocity factor v

Cv +=

3

3 where v is mtrs /sec

17 In a spur gear A 11KW motor running at 1450rpm drives a shaft trough a pair of spur gears with a velocity ratio is 4.5:1. Forged steel SAE 1045 pinion and CI gear are specified. Design the gear and check for the dynamic and heat load considerations

18 a. Derive an expression for beam strength of a spur gear tooth (Lewis equation) using standard notations. State the assumptions under which this equation is valid

b. It is desired to transmit 11 kW from a motor shaft rotating at 1440rpm to a low speed shaft with a speed reduction of 3:1. Single stage spur gear drive is employed for this purpose. The gear teeth are 200 FDI. Pinion has 25 teeth. Starting torque is 50% higher than running torque. Both the pinion and gear are made of heat treated steel with a maximum allowable stress of 210Mpa. Design the suitable spur gear drive from the point of view of dynamic and wear strength

19 a. Derive an expression for the load carrying capacity of helical gear tooth. b. Determine the module and face width of a helical gear tooth for a helical gear pair to

transmit a power of 25KW from a shaft rotating at a speed of 1500rpm to a parallel shaft to be 360rpm maintaining a center distances of 180mm

20 a. Explain clearly the meaning of formative number of teeth as referred to bevel gear. b. A pair of bevel gear is required to transmit 30 kW at 500 rpm. The output shaft is

running at 200 rpm and is at right angles to input shaft. The gears are of 200 involute stub teeth. The pinion is cast steel; the safe static strength is 142 MPa. The gear is of cast iron, whose static strength is 71 MPa . Design the gear drive.

21 Design a worm drive to connect two shafts 300 mm apart and to transmit 10 kW. The transmission ratio is 20:1 and worm shaft is to make 400 rpm. The lead angle is to be within 200. The worm is made of hardened steel (σ0 = 210 MPa) and worm gear of phosphor bronze (σ0 = 105 MPa). Determine the probable temperature to which the gears may be heated and the efficiency.

22 A pair of straight bevel gears has a velocity ratio of 2:1. The pitch circle diameter of the pinion is 80 mm. 5kW power is supplied to the pinion, which rotates at 800 rpm. The pressure angle is 200. Design the gears.

23 Design a worm gear drive to transmit a power of 2kW at 1000 rpm. The speed ratio is 20 and the center distance is 200 mm.

24 Explain self-locking as referred to worm gear drive. b) Design a worm gear reducer to transmit 7.5 kW at 100 rpm. The input speed from the motor is 1500rpm. Calculate the efficiency of the drive

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25 A full journal bearing of 50mm dai. And 100mm long has a bearing pressure of 1.4Mpa. Speed of journal is 900rpm and ratio of journal dai. To the diametrical clearance is 1000. The bearing is lubricated with oil whose observed viscosity at operating temperature of 75 degree C may be taken as 0.011Kg/m-s. The temperature is 35 degree C. find the amount of artificial cooli8ng required and mass of lubricating oil required, if the difference between the outlet and inlet temperature of oil is 10degreeC. Take Sp. Heat of oil as 1850J/Kg/degreeC.

26 A 150mm dai shaft runs at 1500rpm, supporting a load of 10KN. The shaft runs in a bearing of length 1.5 times the shaft dai. The clearing ratio is 0.015. The absolute viscosity of the oil is 11cp. At its operating temperature, find the power lost in friction.

27 Determine the dimension of the bearing and journal to support a load of 6KN at 750rpm using hardened steel journal and bronze backed babit bearing. An abundance of oil provided which has a specific gravity of 0.95 at 15.50 C and viscosity of 9.5centistrokes at 820C that may be taken to the limiting temperature of oil. Assume a clearance of 0.001mm per mm of diameter is allowed.

28 Derive Petroffs equation for the co-efficient of friction in a lightly loaded bearing 29 A shaft running at 600 rpm is supported in a bearing of 60mm dai and 60mm long. The

viscosity of oil is 0.014Pa s and the temperature of oil is 1100C. The radial clearance is 0.03mm. Determine temperature of still air in the bearing if there is no external cooling is provided. The temperature of still air in the room is 200C

30 A journal bearing is to be design for the main bearing of a four-stroke oil engine to sustain a load of 50KN for shaft diameter of 50mm. The engine runs at speed of 1500rpm determine i. The length and diameter of the bearing ii. Viscosity of oil to be used as lubricant, hence suggest a suitable oil iii. The co-efficient of friction of the bearing and the heat generated.

31 Design the journal bearing for a centrifugal pump from the following data. Load on the journal=10KN, speed on the journal=900rpm, Ambient temperature=150C.

32 A 40BC03(SKF6308) single- row, deep groove ball bearing, which is to operate at 80 rpm is acted on by a 8KN radial load and 6KN thrust load. The outer ring rotates, and the bearing is subjected to light shock. Determine the rating and median life of the bearing in hours.

33 Select a single- row, deep groove ball bearing to carry a radial load of 4KN, and a thrust load 5KN operating speed of 1200rpm, for an average life of 15years at 10 hours per day. Assume there are 250 working days per year. The loads are steady and the outer ring rotates.

34 Design a riveted joint for the longitudinal and circumferential seam of a boiler 2.1 m in diameter to withstand a pressure of 1 N/mm2 . the ultimate strength of the the plate material is 380N/mm2 and a FS of 5 is recommended .permissible stress in the shearing of rivets is 60 N/mm2 and in crushing 100 N/mm2..

MVJCE 72

35 A bracket is riveted to a column by rivets of equal size and loaded as shown in fig .if the maximum shear stress is limited to 65 N/mm2 find the diameter of the rivet .

36

Design a closed coil helical spring for a service load ranging from 2250N to 2757N. The axial deflection for the load range is 6mm, assume the spring index=5, permissible shear stress is 420Mpa and modulus of rigidity is 840Gpa. Neglect the effect of stress concentration

37

A helical spring is used in a pressure relief valve. The spring is preloaded to relieve the pressure at 5Mpa. The diameter of the valve is 20mm. The spring has to undergo a deformation of 3mm to allow for fluid flow, the additional force caused due to this should not exceed 10% of the force required to relieve the pressure. The material for the spring is hot drawn wire having an elastic strength of 520Mpa.Under torsion. Take a factor of safety of 1.5 and determine all the dimension of the spring if the diameter of the spring is not to exceed 10mm

38

Design a valve spring of a petrol engine for the following operating conditions: Spring load when valve is open = 400N Spring load when valve is closed = 250N Max. Inside dai. Of spring = 25mm Length of spring when valve is open = 40mm Length of spring when valve is closed = 50mm

Max strength = 400Mpa

39

Design a helical spring for a safety valve. The valve must blow off at a pressure of 1.2 MPa and should lift by 3mm for 5% increase in pressure. The valve diameter is 60mm. The max allowable shear stress is 400MN/m2 and the modulus of rigidity is 2.7X103MN/m2 take the spring index as 8

40

a. Explain equalizing the stresses in leaf springs b.A semi elliptic leaf spring used for automobile suspension consists of three full-length leaves and 15 graduated leaves including the master leaf. The center distance between the two eyes of the spring is 1m. The maximum force that acts on the spring is 75kN. The ratio of width to thickness is 9:1 the modulus of rigidity is 80 Gpa. The leaves are pre-stressed in such a way that the force is maximum the stress induced in the spring is 450Mpa. Determine 1) the width and thickness of the leaves 2) The initial gap 3) The load required

MVJCE 73

41 A journal bearing is to be design for the main bearing of a four-stroke oil engine to sustain a

load of 40KN for shaft diameter of 50mm. The engine runs at speed of 2000rpm determine iv. The length and diameter of the bearing v. Viscosity of oil to be used as lubricant, hence suggest a suitable oil vi. The co-efficient of friction of the bearing and the heat generated.

42 Design the journal bearing for a centrifugal pump from the following data. Load on the journal=18KN, speed on the journal=500rpm, Ambient temperature=130C.

43

A 40BC03(SKF6308) single- row, deep groove ball bearing, which is to operate at 100 rpm is acted on by a 6KN radial load and 8KN thrust load. The outer ring rotates, and the bearing is subjected to light shock. Determine the rating and median life of the bearing in hours.

44

Select a single- row, deep groove ball bearing to carry a radial load of 4KN, and a thrust load 7KN operating speed of 1200rpm, for an average life of 15years at 10 hours per day. Assume there are 250 working days per year. The loads are steady and the outer ring rotates.

45

Design a riveted joint for the longitudinal and circumferential seam of a boiler 2.1 m in diameter to withstand a pressure of 10 N/mm2 . the ultimate strength of the the plate material is 380N/mm2 and a FS of 5 is recommended .permissible stress in the shearing of rivets is 80 N/mm2 and in crushing 100 N/mm2..

MVJCE 74

46 A bracket is riveted to a column by rivets of equal size and loaded as shown in fig .if the maximum shear stress is limited to 85 N/mm2 find the diameter of the rivet .

47

Design a closed coil helical spring for a service load ranging from 2250N to 2500N. The axial deflection for the load range is 6mm, assume the spring index=5, permissible shear stress is 320Mpa and modulus of rigidity is 840Gpa. Neglect the effect of stress concentration

48

A helical spring is used in a pressure relief valve. The spring is preloaded to relieve the pressure at 5Mpa. The diameter of the valve is 15mm. The spring has to undergo a deformation of 3mm to allow for fluid flow, the additional force caused due to this should not exceed 10% of the force required to relieve the pressure. The material for the spring is hot drawn wire having an elastic strength of 520Mpa.Under torsion. Take a factor of safety of 1.5 and determine all the dimension of the spring if the diameter of the spring is not to exceed 8mm

49

Design a valve spring of a petrol engine for the following operating conditions: Spring load when valve is open = 300N Spring load when valve is closed = 150N Max. Inside day. Of spring = 25mm Length of spring when valve is open = 40mm Length of spring when valve is closed = 50mm

Max strength = 400Mpa

50

Design a helical spring for a safety valve. The valve must blow off at a pressure of 1.2 MPa and should lift by 5mm for 5% increase in pressure. The valve diameter is 60mm. The max allowable shear stress is 400MN/m2 and the modulus of rigidity is 2.7X103MN/m2 take the spring index as 7

51

A semi elliptic leaf spring used for automobile suspension consists of three full-length leaves and 15 graduated leaves including the master leaf. The center distance between the two eyes of the spring is 1.5m. The maximum force that acts on the spring is 75kN. The ratio of width to thickness is 9:1 the modulus of rigidity is 70 Gpa. The leaves are pre-stressed in such a way that the force is maximum the stress induced in the spring is 350Mpa. Determine 1) the width and thickness of the leaves 2) The initial gap 3) The load required

MVJCE 75

MECHANICAL LABORATORY

Sub Code 06IML57 IA Marks 25 Hrs/ Week 03 Exam Hours 03 Total Hrs. 42 Exam Marks 50 PART- A: (Individual experiments) 1. Determination of Flash point and Fire point of lubricating oil using Abel Pensky Martins Apparatus 2. Determination of Calorific value of solid and gaseous fuels. 3. Determination of Viscosity of a lubricating oil using Redwoods and say bolts – Viscometers. PART-B: Group experiments 1. Performance Tests on Four stroke Diesel Engines, Calculations of IP, BP, Thermal efficiencies, SFC, FP, heat balance sheet for 2. Multi cylinder petrol / diesel engine (Morse Test) 3. Calibration of venturi meter 4. Flow through pipes 5. Performance test on centrifugal and reciprocating pumps Scheme of Examination 1 PART A 20 Marks 2 PART B 20 Marks 3. Viva Voce 10 Marks 4. Total 50 Marks

MVJCE 76

LESSON PLAN

Sub Code: 06IML57 I.A. Marks: 25 Hours / Week: 03 Total Hours: 42 Subject: Mechanical Laboratory Sem: V

No of hours Topics to be covered 1. Determination Of Flash And Fire Points By Abel Flash - Point Apparatus and

Pensky Martins Flash Point Apparatus 2. Determination Of Calorific Value By Bomb Calorimeter 3. Determination Of Viscosity Of Oil By Red Wood Viscometer 4. Determination Of Viscosity Of Oil By Saybolt Viscometer 5. Performance Testing On Four Stroke Single Cylinder Diesel Engine With

Mechanical Dynamometer 6. Performance Testing And Morse Test On Four Stroke Four Cylinder Petrol Engine

With Hydraulic Dynamometer 7. Performance Testing On Four Stroke Twin Cylinder Diesel Engine With Electrical

Dynamometer 8. Determination Of Co-Efficient Of Friction Of Flow In A Pipe 9. Determination Of Co-Efficient Of Friction Of Flow In A Pipe 10. Calibration Of Orifice Plate 11. Calibration Of Venturimeter 12. Performance Testing Of Single Stage Centrifugal Pump 13. Performance Testing Of Multi Stage Centrifugal Pump 14. Performance Testing Of Reciprocating Pump 15. Performance Test Of Two Stage Reciprocating Air Compressor

MVJCE 77

VIVA-QUESTIONS 1. The efficiency of a Carnot engine depends on 2. Carnot cycle is the 3. Why Diesel cycle efficiency is maximum when the cut off is 4. Which is the unit of energy? 5. Which gases possesses maximum heat content at 100o c 6. All the commercial liquid fuels are derived from 7. Specific fuel consumption is defined as 8. Flameless combustion means 9. Submerged combustion involves 10. The working cycle in case of four-stroke engine is completed in how many revolutions of crankshaft 11. In a Diesel engine, the fuel is ignited by 12. Scavenging air in diesel engine means 13. Supercharging is the process of 14. Compression ratio of I.C engines is 15. The calorific value of gaseous fuels is expressed in terns of 16. Indicated power of a 4- stroke engine is equal to 17. If the intake air temperature of I.C engine increases, its efficiency will 18. An engine indicator is used to determine the 19. The pressure at the end of compression in the case of diesel engine is of the order of 20. The maximum temperature in the I.C engine cylinder is of the order of 21. Combustion in the compression ignition engine is 22. The fuel in diesel engine is normally injected at pressure of 23. The specific fuel consumption per BHP hour for diesel engine is approximately 24. Compression loss in I.C engines occurs due to 25. The inlet valve of a four-stroke cycle I.C engine remains open for nearly 26. If one cylinder of a diesel engine receives more fuel than the others then for that cylinder the 27. It the temperature of intake air in I.C engines is lowered, then its efficiency will 28. As result of detonation in an I.C engines 29. Most high-speed compression engines operate on 30. The accumulation of carbon in a cylinder results increase of 31. The air fuel ratio of the petrol engine is controlled by 32. Diesel fuel compared to petrol is 33. Engine pistons are usually made of aluminum alloy because it 34. Most high speed compression engines operates on 35. The size of inlet valve of an engine in comparession to exhaust valve is 36. In a cycle the spark lasts roughly for 37. The minimum cranking speed in case of petrol engine is about 38. Flash point of fuel oil is 39. Air fuel ratio for idling speed of a petrol engine is approximately 40. A diesel engine has how many valves 41. The knock in diesel engine occurs due to 42. Which is more viscous lub oil 43. Ignition quality of petrol is expressed by

MVJCE 78

44. Petrol is distilled at temperature in range 45. Kerosene is distilled at 46. Self –ignition temperature of petrol is of the order of 47. Define Iso- octane 48. Define Cetane 49. Define Normal heptane 50. Ignition lag is 51. The spark plug gap is normally maintained at 52. The delay period in petrol engine is of the order of 53. If overhead clearance is less then the type of engine should be selected 54. Piston rings are usually made of 55. The top piston ring nearer to the piston crown is known as 56. In order to prevent Knock in the S.I engines the charge away from the spark plug should have 57. A fuel will detonate less if it has 58. Injection lag is 59. Calorific value of diesel is of the order of 60. Carbon residue in diesel oil should not be more than 61. The specific gravity of diesel oil is 62. Freezing temperature of petrol is 63. The specific gravity of petrol is 64. The efficiency of I.C engines normally is of the order of 65. The ash content in diesel oil should not be more than 66. Fuel consumption with increase in back pressure will 67. Air injection in I.C engines refers to injection of 68. Solid injection in I.C engines refers to injection of 69. The most effective air cleaner incase of diesel engine is 70. The thermal efficiency of a diesel engine is of the order of 71. Bomb calorimeter is used to find the calorific value of 72. The most important solid fuel is 73. A chemical fuel is a substance which release on combustion 74. Define flash and fire point 75. Properties of fluid 76. Compression ratio of diesel engine is 77. Carburetor is used for 78. Firing order of four stroke diesel engine 79. Bernoulli’s equation is application 80. A ventrimeter is used to measure 81. Types of orifice 82. Co-efficient of contraction 83. Co-efficient of discharge & resistance 84. What is mean by Throat? 85. Efficiencies of centrifugal pump 86. Manometric efficiency 87. A multi stage pump is used to 88. Slip of the pump 89. Negative slip

MVJCE 79

90. Types of reciprocating pump 91. Function of air vessels 92. Units of mass density 93. The property of fluid, which enables it to resist tensile stress, is known as 94. Specific weight of water in S.I unit is equal to 95. Unit of viscosity is 96. Kinematic viscosity is equal to 97. Manometer is used to measure 98. Choking in pipe flow implies 99. For pipe flow at constant diameter capacity is proportional to 100. Friction factor for pipes depends on

MVJCE 80

INDUSTRIAL ENGINEERING LABORATORY Sub Code: 06IML58 IA Marks 25 Hrs/Week 03 Exam Hours 03 Total Hrs. 42 Exam Marks 50 PART A - METHOD STUDY 1. Recording Techniques: Preparing the following charts and diagrams (Minimum 3 Charts) - Outline process chart - Multiple Activity Chart - Flow process chart and Flow diagram - String diagram, 2. Experiments on the Application of principle of motion economy Two-handed process chart 3. Exercises on conducting method study for assembling simple components and office work. 4. Development of Layout plans using SLP technique 5. Experiments on Line balancing. PART B – WORK MEASUREMENT 6. Rating practice using walking simulator 7. Rating practice using pin board assembly 8. Rating practice for dealing a deck of cards 9. Rating practice for marble collection activity 10. Determining the standard time for simple operations using stopwatch time study 11. Exercises on estimating standard time using PMTS. 12.Determination of standard time using PDA device and time study software 13. Experiments on office work measurement through work sampling 14. Measurement of parameters (heart beat rate, calorie consumption) using walking simulator 15. Measurement of parameters (heart beat rate, calorie consumption, revolutions per minute) using ergometer 16. Effect of Noise, Light, Heat on human efficiency in work environments. Note: Minimum 14 Exercises to be conducted in this lab. Reference Books: 1. Work Study by Ralph & Barnes 2. Introduction to Work Study by ILO Scheme of Examination 1 PART A 20 Marks 2 PART B 20 Marks 3.Viva Voce 10 Marks Total 50 Marks

MVJCE 81

LESSON PLAN

Sub Code: 06IML58 I.A. Marks: 25 Hours / Week: 03 Total Hours: 42 Subject: Industrial Engineering Laboratory Sem:V

Sl No. Experiments

1. Method Study and Time Study on Pin Board Assembly

2. Flow Process Chart-Man Type

3. Two Handed Process chart for Nut and Bolt Assembly

4. Out Line Process Chart, Multiple activity Chart

5. Flow Diagram

6. String Diagram

7. Travel chart

8. Design of Cellular layout

9. Performance Rating Through Walking Simulator, Performance Rating through Marble collection

10. Time Study on 5Amp Plug Assembly

11. Pace rating Through Playing Cards

12. Timing Practice through Computer Aided Element Generator

13. Advanced Work Measurement using MTM-Coaster Assembly

14. Measurement of human body parameters for a person walking on a walking simulator, Measurement of human body parameters for a person working on the Ergo meter

15. Conduction of work sampling study in the shop floor environment to determine shop floor utilization.

16. Determining the effect of noise, light, heat on Human Efficiency in work environment

MVJCE 82

QUESTIONS

1. What is Industrial Engineering? 2. Mention applications of IE in Engineering? 3. What do you understand by Basic time? 4. What is meant by Break point? 5. What is meant by Check time? 6. What is an allowance? 7. What are the different types of allowance? 8. What is a contingency allowance? 9. What is Timing? 10. What is cumulative timing? 11. What is fly back timing? 12. What are the different types of stop watches used for study purpose? 13. What is meant by cycle time? 14. What is meant by elapsed time? 15. What is meant by Element? 16. What is meant by Constant element? 17. What does Foreign Element mean? 18. What does Governing Element mean? 19. What does Machine Element mean? 20. What does Manual Element mean? 21. What does Occasional Element mean? 22. What does Repetitive Element mean? 23. What does Variable Element mean? 24. What is a Fatigue allowance? 25. What are the different recording techniques used for capturing data? 26. What is a Flow diagram? 27. What is a String diagram? 28. What is a travel chart? 29. What are cycle graphs and chrono-cycle graphs? 30. What are process charts & Flow process charts? 31. What are the different types of flow process charts? 32. What is a SIMO chart? 33. What is a spaghetti diagram? 34. What are two handed process charts? 35. What is a multiple activity chart? 36. What do understand by productivity? 37. How is productivity measured? 38. What are the advantages of increasing productivity? 39. Define Work-study? 40. What are the steps used in Work-study? 41. Define Method study? 42. Define Time study? 43. What is the prerequisite for Time study?

MVJCE 83

44. What is meant by work measurement? 45. What are the different techniques used for work measurement? 46. What does work sampling mean? 47. What is meant by idle time? 48. What is meant by Inspection? 49. What is an Interference allowance? 50. What is meant by Interference time? 51. What does Job Break down mean? 52. What is meant by Load factor? 53. What are the essential qualities of a work-study analyst? 54. What is meant by Machine ancillary time? 55. What is meant by Machine available time? 56. What is meant by Machine capacity? 57. What is meant by Machine controlled time? 58. What is meant by Machine down time? 59. What is meant by Machine interference? 60. What is meant by Machine maximum time? 61. What is meant by Machine utilization Index? 62. What do understand by MTM? 63. What is meant by observed time? 64. What is an outline process chart? 65. What is meant by predetermined time standards? 66. Who is a qualified worker? 67. What is meant by Rating? 68. What does a Rating scale mean? 69. What are the different rating scales available? 70. What is meant by restricted work? 71. What is an relaxation allowance? 72. What is meant by standard performance? 73. What do you mean by standard time? 74. What is a string diagram? 75. What is meant by tool allowance? 76. What is work content? 77. What is a work cycle? 78. What is meant by work specification? 79. What do you understand by an workplace layout? 80. What are gang process charts? 81. What are Therbligs? 82. What are the fundamental Hand movements? 83. What is Micro motion study? 84. What is the purpose on Micro motion study? 85. What are the limitations of Micro motion study? 86. What is a Centiminute? 87. What is a Wink? 88. What are the principles of motion economy? 89. What is a plant layout?

MVJCE 84

90. What are the different types of plant layouts? 91. Who is an Average worker? 92. What are the characteristics of a sound rating system? 93. What is a learning curve? 94. What are the different methods of rating? 95. What are the different classes of reach? 96. What are the different classes of move? 97. What are the different classes of position? 98. What are the different classes of release? 99. What are the different classes of search?

100. What is 1TMU? 101. What is fatigue? 102. What are the implications of fatigue?