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Page 1: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

1Prof. Indrajit Mukherjee, School of Management, IIT Bombay

L eav in g th e o f f ic e

C h ec k th e t im e an d w eath er

W eath erc lear

Bef o r e5 .0 0 p m

C h ec k f o r c o n g es tio n o np r im ar y r o u te

p r im a r yc o n ge st e d

T ak e a lte r n a te "A"h o m e

D iv er t to a lte r n a te"B"

T ak e th e p r im ar yr o u te h o m e

Ar r iv e s af e ly

Ye

sY

es

Ye

s

N o

N o

N o

Th e B e s t W a y H o m e

Page 2: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

2Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Process Chart Symbols

Operations

Inspection

Transportation

Delay

Storage

Page 3: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

3Prof. Indrajit Mukherjee, School of Management, IIT Bombay

What value isAdded by:

Acknowledgments

SortingStoring

Transactions

Invoices

Rework

Loading / Unloading

Receiving ReportRepackaging

Returns to Suppliers

Scrap

Inspecting

Expediting(due to internal problems)

Moving

Counting

Page 4: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

4Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Lean Manufacturingis a manufacturing philosophy which shortens the time line between the customer order and the product shipment by identifying and eliminating waste.

CustomerOrder

CustomerOrder

Product Shipment

Product Shipment

Business as Usual

Waste

Lean Manufacturing

Waste

Time (Shorter)

Time

Page 5: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

5Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Introduction to Value Stream MappingDefinition of Value Stream

A Value Stream includes all elements (both value added and non-value added) that occur to a given product from its inception through delivery to the customer.

Requirements Design Raw Materials Parts Manufacturing

Assembly Plants Distribution Customer

Page 6: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

6Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Introduction to Value Stream MappingDefinition of Value Stream

Typically we examine the value stream from raw materials to finished goods within a plant.

VALUE STREAM

PROCESS PROCESS PROCESS

Stamping Welding AssemblyCell

Raw Material

Finished Product

It is also possible to map business processes using Value Stream Mapping.

Page 7: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

7Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Value Stream Mapping Symbols

Page 8: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

8Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Current State Map

Supermarket

Withdrawal Kanban

Production Kanban

Kanban Path

Kanban arrivingin batches

Physical Pull

Leveling

Kanban Post

Process Kaizen

First-In First-Out Flow

Page 9: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

9Prof. Indrajit Mukherjee, School of Management, IIT Bombay

( some) Value Stream Mapping Symbols

Process Box - Area where Value is added to Product

Functional Group - Processes Information but adds no Value to Product

Transportation - Indicates shipment of Product to/from external facility

Factory - a Customer or Vendor facility

Inventory - Product that is not being worked on

Page 10: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

10Prof. Indrajit Mukherjee, School of Management, IIT Bombay

How to calculate Total Lead Time &Processing Time

300 pieces 100 pieces

SCRIBE

C/T = 8 min

C/O = 20 min

Batch = 100 pcs.

Cycle Time

Changeover Time

Based on a customer demand of 100 parts/day

3 days 1 day

8 min.

Page 11: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

11Prof. Indrajit Mukherjee, School of Management, IIT Bombay

• Most basic tool of lean management

• Easy to create

• A Visual Representation of material & information flow

• Easy for everyone to understand

• Key to sustainable progress Through a

“current-state becomes future state”

management cycle

Stream Map

P rod u ct fam ily

C u rren t-S ta te D rawin g

F u tu re - S ta te D rawin g

W ork P lan

Page 12: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

12Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Pareto chart

Loose threads Stitching flaws Button problems Material flaws0

5

10

15

20

25

3028

16

12 12

6

43

Page 13: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

13Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Cause & Effect: Tool for Root Cause Analysis

Materials

Problem

Machinery

MethodManpower

Page 14: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

14Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Environment

Analytical Tools for Continuous Improvement: Cause &Effect or Ishikawa or Fish Bone Diagram

Machine ManMeasurement

Method Material

Effect

Potential causes: The resultsor effect

5’th M

Ishikawa

Page 15: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

15Prof. Indrajit Mukherjee, School of Management, IIT Bombay

InaccurateSubmission of

Billing to Client

Spine

Effect Box

Page 16: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

16Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Submission of Credit Card Billing to Client

Receive update/information of newly issued billings

Locate included clients’ file folders

File folders

Find and update clients’ billing statements

Locate included clients’ Buyers’ Information Sheet

Buyers’ Information Sheet

Call /inform each client on update

Send Billing Statements

Page 17: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

17Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Man

InaccurateSubmission of

Billing to Client

Method

Materials Machinery

Main Causes

Page 18: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

18Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Man

InaccurateSubmission of

Billing to Client

Methods

Materials Machinery

People fail to informclient thru call/e-mailErroneous sorting of

billing statements

Ignorance

Invalid list of updates

Unreliable email system Erroneous

Information In Buyers’ Information Sheet

No file for record of billing statements In clients’ folders

Phone line disconnected

Page 19: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

19Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Man

InaccurateSubmission of

Billing to Client

Method

Materials Machinery

Mixed updataInaccuracyinsortingdata

Manual fileorganization

Invalidlist ofupdates

Erroneoussortingof billingstatements

InaccuracyIn sortingdata

Mixedup data

Manual fileorganization Ignorance

Poortraining

Wrong phone number/e-mail information

Inaccuracy insorting data

Manual theorganization

Erroneous infoin BIS

People fail to informclient thrucall/e-mail

Ignorance

No training

Skipping payingmonthly bills

Poortraining

Phone linedisconnected

Nomoney

Erroneous info in BIS

Inaccuracy In Sorting data

Unreliableemail system

Manual file system

Inaccuracy in sortingAnd giving mail

Mixedup data

Manual fileorganization

Manual fileorganization

Mixed up data

Inaccuracy In Sorting data

Assorted recordsof billingstatementsin clients’ folders

Page 20: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

20Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Cause-and-Effect Diagram

Measurement

Materials

Methods“Men”

Machine “Environment/ Nature”

Y

Potential X’sResponse Variable

1X

5X

4X 3X 2X

Page 21: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

21Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Lathe

Cause and Effect Diagram Example

Manpower

Too many defects

Method

MachineryMaterials

Drill TiredOver Time

Old

Slow

Steel

Wood

Page 22: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

22Prof. Indrajit Mukherjee, School of Management, IIT Bombay

MethodsMaterials Machines

PersonnelMeasurement

Defects ontanks

Worn tool

Too muchplay

Surfacefinish

Wrongtool

Paint sprayspeed

Ambient temperature

too highDust

Paint flowrate

Primertype

Primer viscosity

Defective fromsupplier

Damaged in handling

Paint viscosity

Wrong worksequence

Planning

Materialshandling

Incorrectspecifications

Faultygauge

Inspectors don’tUnderstandspecification

Poorattitude

Insufficienttraining

InadequatesupervisionNew M

Page 23: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

23Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Intangible dominant

Service Quality

Service – Product Continuum (Shostack, 1977)

Consumerdurables

Automobile Spares

Fast food

Airline

Consulting

Teaching

FMCG

Tangible dominant

Health Care

Page 24: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

24Prof. Indrajit Mukherjee, School of Management, IIT Bombay

ServiceDelivery

Service QualityService Product

Tangible product

Servicescape

Page 25: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

25Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Reliability

Responsiveness

Assurance

Empathy

Tangibles

Comparison with Volvo Dealer

Weighted score

Improvement difficulty rank

Train

ing

Att

itud

e

Capaci

ty

Info

rmati

on

Equip

ment

9

7

246

2

5

5 5

97

8

693 3 2

Service Elements

Rela

tive

ImportanceCustomer Expectations

Relationships

Strong

Medium

Weak

Customer perceptionsO Village Volvo+ Volvo Dealer

127 82 63 102 65

4 5 1 3 2

+

-o

oo

oo

oo

oo

o

1 2 3 4 5

+

+

+

+

+

House of Quality in Service

***

Page 26: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

26Prof. Indrajit Mukherjee, School of Management, IIT Bombay

•Delight•Satisfaction•Dissatisfaction•Anger•Disgust

Service QualityService Quality

Expected Service

Gap in Service Quality

Actual/perceived Service

+

-

Page 27: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

27Prof. Indrajit Mukherjee, School of Management, IIT Bombay

ServiceDelivery

ServiceStandards

ManagementPerceptionsof CustomerExpectations

CustomerExpectations

CustomerPerceptions

Managing theEvidence

Conformance Service Design

Understandingthe Customer

Customer Satisfaction

Customer /Marketing Research

ConformanceGAP 3

DesignGAP2

CommunicationGAP4 GAP1

GAP5

Service Quality Gap Model

Page 28: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

28Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Desired service

Service ExpectationWhat service “can be”, “should be”

Customer willaccept variability

Minimum tolerableexpectationAdequate Service

Zone of Tolerance

Exp

ecta

tion

Level

Page 29: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

29Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Now Control for Quality can be exercised over

Are right processes operating?

RAWMATERIALS

Are raw Materials okay?

FINISHED GOODS

Are the goods okay to be sent to the customers?

PROCESS

What is Control?You are on a Boat…………..

Page 30: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

30Prof. Indrajit Mukherjee, School of Management, IIT Bombay

INPUTS PROCESS OUTPUTS

Materials Man MethodsMeasurementInstruments

Machines EnvironmentHumanInspectionPerformance

Page 31: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

31Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Data Collection and Statistical Analysis for Quality Improvement

Data Collection

Descriptive measures

Statistical inference

Organization and

Presentation

Predictive Statistics

Statistical methodology

SPC

Regression

analysis

Correlation analysis

Frequency distributions

Histograms

Centraltendency

DispersionHypothesis testing

Experimentaldesign

AnalysisOf variance

Page 32: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

32Prof. Indrajit Mukherjee, School of Management, IIT Bombay

L o t rece ived fo r in sp ec tio n

R esu lts co m p ared w ith accep tan ce cri te ria

A ccep t th e lo t R ejec t th e lo t

S en d to p ro d u c tio no r to cu s to m er D ec id e o n d is p o s itio n

S am p le se lec ted an d an a lyzed

Page 33: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

33Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Perc

ent

of

app

licati

on Acceptance

sampling

Process control

Design ofexperiments

Time0

100

Page 34: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

34Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Upper specification

limit

Process mean,µ

Lowerspecification

limit

Design ofexperimentsAcceptance

sampling

StatisticalProcess control

Page 35: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

35Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Analogy to Traffic Signal StopInvestigate/Adjust

Wait and Watch GoNo action on process

Page 36: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

36Prof. Indrajit Mukherjee, School of Management, IIT Bombay

47 48 49 50 51 52 53 54

Page 37: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

37Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Page 38: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

38Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Process withmean at lessthan target

Process withmean at target

Process withmean at more

than target

Page 39: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

39Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Page 40: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

40Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Page 41: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

41Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Page 42: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

42Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Page 43: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

43Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Process

Measurement EvaluatingMonitoring

And Control

InputRaw MaterialsComponents,

Subassemblies,And/or

information

Controllable inputs

Output ProductY=Quality Characteristic, (CTQs)

Uncontrollable inputs

Production process inputs and outputs

1x

Qz2z1z

2x px

Statistical Methods for Quality Control and Improvement

Page 44: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

44Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Control chartscan tell uswhen aprocesschanges

Histograms do nottake into accountchanges over time.

Page 45: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

45Prof. Indrajit Mukherjee, School of Management, IIT Bombay

• Control chart: A time-ordered diagram that is used todetermine whether observed variations are abnormal.

A sample statistic that falls between the UCL and the LCL indicates that the process is exhibiting common causes of variation; a statistic that falls outside the control limits indicates that the process is exhibiting assignable causes of variation.

Control Charts

Page 46: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

46Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Page 47: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

47Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Page 48: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

48Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Sample Observation and Normal Distribution

Page 49: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

49Prof. Indrajit Mukherjee, School of Management, IIT Bombay

STATISTICAL PROCESS CONTROL CHARTS

Process gone out of control?

Mean + 3sigma Upper controllimit

Mean

Mean-3sigma

Central line

Lower controllimit

Process under control

x

xx

xx

Page 50: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

50Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Figure Processimprovement using thecontrol chart.

Introduction to Control Charts

Basic Principles

Measurement system

ProcessInput Output

Verify and Follow up

DetectedAssignable

cause

ImplementCorrective

actionIdentify root

Cause problem

Page 51: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

51Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Statistical Process Control Steps

Produce GoodProvide Service

CreateControl Chart

Take Sample

Inspect SampleStop Process

Find Out AssignableCauses and eliminate

AssignCauses?

StartNo

Yes

Page 52: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

52Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Page 53: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

53Prof. Indrajit Mukherjee, School of Management, IIT Bombay

• Control limits are derivedfrom natural processvariability, or the naturaltolerance limits of a process

• Specification limits aredetermined externally, forexample by customers orDesigners

• There is no mathematicalor statistical relationshipbetween the control limitsand the specificationlimits

Control vs. Specification Limits

Page 54: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

54Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Control Chart Selection

Quality Characteristic

p-chart withvariable sample

size

p ornp

c u

n>1?

n>=5?

x and s

x and R

x and MR

ConstantSample

size

ConstantSample

unit

Variable Attribute

Defective Defect

NoYes

Yes

Yes

Yes

NoNo

No

Page 55: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

55Prof. Indrajit Mukherjee, School of Management, IIT Bombay

• Monitors performance of one or more processes over time to detect trends, shifts, or cycles• Allows a team to compare performance before and after implementation of a solution to measure its Impact• Focuses attention on truly vital changes in the Process• This is only monitoring tool and not control tool

Run Chart

*

*

**

* *

*

Page 56: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

56Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Example of Constructing a p-Chart:Required Data

1 100 42 100 23 100 54 100 35 100 66 100 47 100 38 100 79 100 1

10 100 211 100 312 100 213 100 214 100 815 100 3

Sample no.Subgroupsize

Number of Defective foundIn each sample

Page 57: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

57Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Example of Constructing a p-chart: Step 1

1. Calculate the sample proportions, p (these are what can be plotted on the p-chart) for each sample

sample n defectives p1 100 4 0.04

2 100 2 0.02

3 100 5 0.05

4 100 3 0.03

5 100 6 0.06

6 100 4 0.04

7 100 3 0.03

8 100 7 0.07

9 100 1 0.01

10 100 2 0.02

11 100 3 0.03

12 100 2 0.02

13 100 2 0.02

14 100 8 0.08

15 100 3 0.03

Page 58: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

58Prof. Indrajit Mukherjee, School of Management, IIT Bombay

sample value size sample value size1 2 50 14 3 502 4 50 15 5 503 6 50 16 3 504 1 50 17 2 505 2 50 18 1 506 3 50 19 4 507 5 50 20 3 508 2 50 21 5 509 1 50 22 2 50

10 3 50 23 1 5011 6 50 24 4 5012 1 50 25 2 5013 4 50

Initial 25 sample

Page 59: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

59Prof. Indrajit Mukherjee, School of Management, IIT Bombay

sample value size sample value size26 4 3950 38 8 5027 5 50 39 4 5028 3 50 40 5 5029 7 50 41 6 5030 4 50 42 3 5031 5 50 43 2 5032 2 50 44 4 5033 4 50 45 3 5034 1 50 46 5 5035 2 50 47 6 5036 3 50 48 9 5037 5 50 49 3 50

50 6 50

Monitoring Data

Page 60: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

60Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Hometown Bank(Home Exercise)

The operations manager of the booking services department of HometownBank is concerned about the number of wrong customer account numbersrecorded by Hometown personnel.

Each week a random sample of 2,500 deposits is taken, and the number ofincorrect (defective) account numbers is recorded. The results for the past 12 weeks are shown in the following table.

Is the booking process out of statistical control? Use three sigma control limits.

sample number

wrong account numbers samplenumber

wrong account numbers

1 15 7 242 12 8 73 19 9 104 2 10 175 19 11 156 4 12 3

total 147

Page 61: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

61Prof. Indrajit Mukherjee, School of Management, IIT Bombay

The Data (Insurance claim)

Complete sample data for the 25 samples is summarized below.

Day Number defective Day Number defective1 3 14 42 3 15 13 3 16 24 2 17 45 0 18 06 3 19 17 0 20 18 1 21 09 7 22 2

10 3 23 811 2 24 212 0 25 113 0

Page 62: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

62Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Application (2σ limit)

tube# lump s tube# lump s tube# lump s

1 6 5 6 9 5

2 5 6 4 10 0

3 0 7 1 11 9

4 4 8 6 12 2

Page 63: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

63Prof. Indrajit Mukherjee, School of Management, IIT Bombay

The Data

Complete sample data for the 20 samples is summarized below.

Sample Defects Sample Defects1 4 11 12 5 12 23 3 13 04 2 14 25 7 15 46 4 16 17 8 17 5

Page 64: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

64Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Attribute Control Charts

Sample Number of Defects Number of Defects Sample Number of Defects Number of Defects1 6 1.2 11 9 1.82 4 0.8 12 15 33 8 1.6 13 8 1.64 10 2 14 10 25 9 1.8 15 8 1.66 12 2.4 16 2 0.47 16 3.2 17 7 1.48 2 0.4 18 1 0.29 3 0.6 19 7 1.4

10 10 2 20 13 2.6

Page 65: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

65Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Most Common Type of Control Chart for Variable Data

Variable Control Chart

For trackingAccuracy

Mean Controlchart

For trackingPrecision

Rangecontrol chart

Page 66: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

66Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Establishing Control Chart

Lot Size Total number of items

51-90 20

91-150 32

151-280 50

281-500 80

501-1200 125

1201-3200 200

3201-10000 315

10001-35000 500

Page 67: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

67Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Typical Data Collection Sheet

Part operation Other details

SN date

time

Measurement Mean

Range

X1 X2 X3 X4

1

2

3

…..

25

Page 68: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

68Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Example - Data CollectionSubgroup

No.Subgroup Reading Mean

subgroupRange of subgroup

X1 X2 X3 X4 X5

1 47 45 48 52 51

2 48 52 47 50 50

3 49 48 52 50 49

4 49 50 52 50 49

5 51 50 53 50 48

6 50 50 49 51 47

7 51 48 50 50 54

8 50 48 50 50 52

9 48 48 49 50 51

Page 69: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

69Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Example - Calculation of subgroup Mean & Range

Subgroup No.

Subgroup Reading Mean subgroup

Range of subgroup

X1 X2 X3 X4 X5

1 47 45 48 52 51 48.6 7

2 48 52 47 50 50 49.4 5

3 49 48 52 50 49 49.6 4

4 49 50 52 50 49 50.0 3

5 51 50 53 50 48 50.4 5

6 50 50 49 51 47 49.4 4

7 51 48 50 50 54 50.6 6

8 50 48 50 50 52 50.0 4

9 48 48 49 50 51 49.2 3

10 49 50 50 52 51 50.2 3

Page 70: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

70Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Establishing Control Chart

Using following table of constants find trial control limit for mean and range control chart’

Subgroup size A2 D4 D3

2 1.880 3.267 0

3 1.023 2.527 0

4 0.729 2.282 0

5 0.577 2.115 0

6 0.483 2.004 0

7 0.419 1.924 0.076

Page 71: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

71Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Constants for Range Control chart

Sample size n

D4 D3 DWLR DWUR

2 3.27 0 0.04 2.81

3 2.57 0 0.18 2.17

4 2.28 0 0.29 1.93

5 2.11 0 0.37 1.81

6 2.00 0 0.42 1.72

7 1.92 0.08 0.46 1.66

Page 72: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

72Prof. Indrajit Mukherjee, School of Management, IIT Bombay

The Data

Ten more observations which were taken, as shown below.

Observations

Sample 1 2 3 4

31 4.92 5.54 5.00 5.42

32 4.65 5.14 4.26 4.71

33 5.78 5.50 5.05 4.79

34 5.95 3.83 4.30 4.44

35 4.92 4.80 4.75 5.59

36 5.68 5.74 4.65 4.65

37 4.78 5.79 5.20 4.70

38 4.43 4.81 5.27 4.87

39 6.04 4.47 5.18 5.41

40 4.96 5.18 5.48 4.73

Page 73: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

73Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Flow Chart for Establishing Control Chart

Start

Record observations

Decide subgroup size

Find mean and range ofeach subgroup

Calculate mean range, R

Page 74: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

74Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Flow Chart for Establishing Control Chart

UCLx = T + A2 x RLCLx = T - A2 x R

UCLr = D4 x RLCLr = D3 x R

Is anysub-group mean

or rangeout side the

controllimit ?

Drop thatGroup

Yes

No

Page 75: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

75Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Flow Chart for Control Chart

Select suitable scale formean control chart and

range control chart

Draw Lines forTarget, UCL, LCL for mean

Mean range, UCL , LCL for range

Stop

Page 76: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

76Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Example of x-bar and R Charts:Required Data

Sample/observation 1 2 3 4 5

1 10.68 10.689 10.776 10.798 10.714

2 10.79 10.86 10601 10746 10.79

3 10.78 10.667 10.838 10785 10.723

4 10.59 10.727 10812 10775 10.73

5 10.69 10.708 10.79 10.758 10.671

6 10.75 10.714 10.738 10.719 10.606

7 10.49 10.713 10.689 10.877 10.603

8 10.74 10.779 10.11 10.737 10.75

9 10.77 10.773 10.641 10.644 10.725

10 10.72 10.671 10.708 10.85 10.712

11 10.79 10.821 10.764 10.658 10.708

12 10.62 10.802 10.818 10.872 10.727

13 10.66 10.822 10.893 10.544 10.75

14 10.81 10.749 10.859 10.801 10.701

15 10.66 10.681 10.644 10.747 10.728

Page 77: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

77Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Example of x-bar and R charts: Step 1. Calculate sample means, sampleranges, mean of means, and mean of ranges.

Sample obs1 obs2 obs3 obs4 obs5 Avg Range

1 10.68 10.689 10.776 10.798 10.714 10.732 0.116

2 10.79 10.86 10601 10746 10.79 10.755 0.259

3 10.78 10.667 10.838 10785 10.723 10.759 0.171

4 10.59 10.727 10812 10775 10.73 10.727 0.221

5 10.69 10.708 10.79 10.758 10.671 10.724 0.119

6 10.75 10.714 10.738 10.719 10.606 10.705 0.143

7 10.49 10.713 10.689 10.877 10.603 10.735 0.274

8 10.74 10.779 10.11 10.737 10.75 10.624 0.699

9 10.77 10.773 10.641 10.644 10.725 10.71 0.132

10 10.72 10.671 10.708 10.85 10.712 10.732 0.179

11 10.79 10.821 10.764 10.658 10.708 10.748 0.163

12 10.62 10.802 10.818 10.872 10.727 10.768 0.25

13 10.66 10.822 10.893 10.544 10.75 10.733 0.349

14 10.81 10.749 10.859 10.801 10.701 10.783 0.158

15 10.66 10.681 10.644 10.747 10.728 10.692 0.103

Avg 10.728 0.2204

Page 78: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

78Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values

n A2 D3 D4

2 1.88 0 3.27

3 1.02 0 2.57

4 0.73 0 2.28

5 0.58 0 2.11

6 0.48 0 2

7 0.42 0.08 1.92

8 0.37 0.14 1.86

9 0.34 0.18 1.82

10 0.31 0.22 1.78

11 0.29 0.26 1.74

Page 79: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

79Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Subgroup size Factor for X chart Factors for R chart

n A2 D3 D4

2 1.88 0.00 3.27

3 1.02 0.00 2.57

4 0.73 0.00 2.58

5 0.58 0.00 2.11

6 0.48 0.00 2

7 0.42 0.08 1.92

8 0.37 0.14 1.86

9 0.44 0.18 1.82

10 0.11 0.22 1.78

11 0.99 0.26 1.74

12 0.77 0.28 1.72

13 0.55 0.31 1.69

14 0.44 0.33 1.67

15 0.22 0.35 1.65

16 0.11 0.36 1.64

17 0 0.38 1.62

18 0.99 0.39 1.61

19 0.99 0.4 1.61

20 0.88 0.41 1.59

Page 80: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

80Prof. Indrajit Mukherjee, School of Management, IIT Bombay

X-bar R-Chart Example

Observations(slip-ring Diameter,CM)Sample k 1 2 3 4 5 X R

1 5.02 5.01 4.94 4.99 4.96 4.98 0.082 5.01 5.03 5.07 4.95 4.96 5 0.123 4.99 5 4.93 4.92 4.99 4.97 0.084 5.03 4.91 5.01 4.98 4.89 4.96 0.145 4.95 4.92 5.03 5.05 5.01 4.99 0.0136 4.97 5.06 5.06 4.96 5.03 5.01 0.17 5.05 5.01 5.1 4.96 4.99 5.02 0.148 5.09 5.1 5 4.99 5.08 5.05 0.119 5.14 5.1 4.99 5.08 5.09 5.08 0.15

10 5.01 4.98 5.08 5.07 5.03 5.03 0.150.09 1.15

Page 81: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

81Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Week Cost x Week Cost x

21 305 31 310

22 282 32 292

23 305 33 305

24 296 34 299

25 314 35 304

26 295 36 310

27 287 37 304

28 301 38 305

29 298 39 333

30 311 40 328

Page 82: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

82Prof. Indrajit Mukherjee, School of Management, IIT Bombay

week costx week costx21 305 31 31022 282 32 29223 305 33 30524 296 34 29925 314 35 30426 295 36 31027 287 37 30428 301 38 30529 298 39 33330 311 40 328

Cost of processing Martgage Lon Application

Page 83: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

83Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Pre-ControlLSL USL

Red Zone

Red Zone

Green Zone

nominalvalue

Yellow Zones

Page 84: 1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay.

84Prof. Indrajit Mukherjee, School of Management, IIT Bombay

Analogy to Traffic Signal StopInvestigate/Adjust

Wait and Watch GoNo action on process


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