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
2Prof. Indrajit Mukherjee, School of Management, IIT Bombay
Process Chart Symbols
Operations
Inspection
Transportation
Delay
Storage
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
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
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
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.
7Prof. Indrajit Mukherjee, School of Management, IIT Bombay
Value Stream Mapping Symbols
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
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
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.
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
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
13Prof. Indrajit Mukherjee, School of Management, IIT Bombay
Cause & Effect: Tool for Root Cause Analysis
Materials
Problem
Machinery
MethodManpower
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
15Prof. Indrajit Mukherjee, School of Management, IIT Bombay
InaccurateSubmission of
Billing to Client
Spine
Effect Box
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
17Prof. Indrajit Mukherjee, School of Management, IIT Bombay
Man
InaccurateSubmission of
Billing to Client
Method
Materials Machinery
Main Causes
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
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
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
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
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
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
24Prof. Indrajit Mukherjee, School of Management, IIT Bombay
ServiceDelivery
Service QualityService Product
Tangible product
Servicescape
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
***
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
+
-
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
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
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…………..
30Prof. Indrajit Mukherjee, School of Management, IIT Bombay
INPUTS PROCESS OUTPUTS
Materials Man MethodsMeasurementInstruments
Machines EnvironmentHumanInspectionPerformance
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
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
33Prof. Indrajit Mukherjee, School of Management, IIT Bombay
Perc
ent
of
app
licati
on Acceptance
sampling
Process control
Design ofexperiments
Time0
100
34Prof. Indrajit Mukherjee, School of Management, IIT Bombay
Upper specification
limit
Process mean,µ
Lowerspecification
limit
Design ofexperimentsAcceptance
sampling
StatisticalProcess control
35Prof. Indrajit Mukherjee, School of Management, IIT Bombay
Analogy to Traffic Signal StopInvestigate/Adjust
Wait and Watch GoNo action on process
36Prof. Indrajit Mukherjee, School of Management, IIT Bombay
47 48 49 50 51 52 53 54
37Prof. 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
39Prof. Indrajit Mukherjee, School of Management, IIT Bombay
40Prof. Indrajit Mukherjee, School of Management, IIT Bombay
41Prof. Indrajit Mukherjee, School of Management, IIT Bombay
42Prof. 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
44Prof. Indrajit Mukherjee, School of Management, IIT Bombay
Control chartscan tell uswhen aprocesschanges
Histograms do nottake into accountchanges over time.
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
46Prof. Indrajit Mukherjee, School of Management, IIT Bombay
47Prof. Indrajit Mukherjee, School of Management, IIT Bombay
48Prof. Indrajit Mukherjee, School of Management, IIT Bombay
Sample Observation and Normal Distribution
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
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
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
52Prof. 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
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
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
*
*
**
* *
*
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
83Prof. Indrajit Mukherjee, School of Management, IIT Bombay
Pre-ControlLSL USL
Red Zone
Red Zone
Green Zone
nominalvalue
Yellow Zones
84Prof. Indrajit Mukherjee, School of Management, IIT Bombay
Analogy to Traffic Signal StopInvestigate/Adjust
Wait and Watch GoNo action on process