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Measure Phase – Step 2&3 L1 Version 3.2 Slide 1 Proprietary to Wipro Ltd
A I CMD
DMAIC Steps
Establish Performance Parameters
Validate Measurement System for „Y‟
Establish Process Baseline
Define Performance Goals
Identify Variation Sources
Explore Potential Causes
Establish Variable Relationship
Design Operating Limits
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Step 8
Step 9
M
A
I
CValidate Measurement System for „X‟
Verify Process Improvement
Institutionalize New Capability
Step 10
Step 11
Step 12
Step 0
Step 1
Establish CTQ Characteristics
Define a Project D
DMAIC Road-Map
Introduction - MEASURE
A robust measurement system forms the basis of any Six Sigma project
A measurement system has two characteristics
Design of the measurement system
Precision of the measurement system
Step 2 of DMAIC
Step 3 of DMAIC
SIPOC
S I
P
O C
Suppliers Inputs
Process
Outputs Customers
Process Boundary
33
44
5511 22S I
P
O C
Suppliers Inputs
Process
Outputs Customers
Process Boundary
33
44
5511 22
SIP
OC
Tool
Baton Changes
S I
P
O CSuppliers Inputs
Process
Outputs Customers
Process Boundary
33
44
5511 22S I
P
O CSuppliers Inputs
Process
Outputs Customers
Process Boundary
33
44
5511 22
S I
P
O CSuppliers Inputs
Process
Outputs Customers
Process Boundary
33
44
5511 22S I
P
O CSuppliers Inputs
Process
Outputs Customers
Process Boundary
33
44
5511 22
Process 1
Process 2
Benefits of Process Mapping
Tremendous value in having teams just discuss the process
Simple & visible structure for thinking through a complex process
Enables seeing the entire process as a team
Enables seeing that changes are not made in a vacuum and will carry through,
affecting the entire process down the line
Creates a framework for designing performance standards for your project
Magnifies non value-added areas or steps
Identifies cycle times of each step in the process
Helps re-examine (if needed) the scope and charter of your project
Points to Look For
The pain areas (identified at the time of project selection) must be within the
selected scope
Between the “Start” and “End” of the process, there should be logical flow of units
leading towards creating an output
„Walk-through‟ the process
Guard against analyzing the process at this stage, just map as-it-is
Do not map the process as you would like it to be
What is a Unit?
A unit is the tangible & measurable characteristic of a process output
Defects are observed / counted in the output characteristic of a unit (denoted as ‟Y‟)
S I
P
O C
Suppliers Inputs
Process
Outputs Customers
Process Boundary
33
44
5511 22S I
P
O C
Suppliers Inputs
Process
Outputs Customers
Process Boundary
33
44
5511 22
Examples
In ticket booking example, each ticket booked could be a unit
In the above example, can „each filled requisition given‟ be a unit?
In a bug fix example , each bug that comes in can be considered as a Unit
2.3 Define Specifications and Defect
Key Concepts
Recall that customers are better off telling you what they do not want
A defect is an imperfection or deficiency in the output unit with respect to specifications
defined by the customer
Quality is absence of defects in the unit identified
Quality goes up as defects come down
Quality is inversely proportional to defects
Defects are defined by customers (VOC table can be used here, however, focus here is
to collect project CTQ’s)
A unit may have multiple defects depending upon customer CTQs
Defect is on a unit
A unit which has defects is called a Defective( Even one defect in a unit will make the unit defective)
What is a Specification?
A specification is a customer-defined tolerance for the output unit characteristics
Specifications can be one sided or two sided
Specifications form the basis of any defect measurement exercise
Specification example: Bug fix productivity should be at least 3 bugs / pw ( only LSL – one sided spec).
USL: Upper Specification Limit for „Y‟,
anything above this is a defect.
LSL: Lower Specification Limit for „Y‟,
anything below this is a defect.
Target: Ideally the middle point of USL & LSL.
LSL Target USL
What is Six Sigma?
High
Probability
of Failure
66807 Defects
Per Million
Opportunities
Much Lower
Probability
of Failure
3.4 Defects
Per Million
Opportunities
6 2‟s
1
6 2‟s
Mean / TargetLower
Specification Limit
Upper
Specification Limit
Higher this
number,
Lower the
chance of
producing a
defect
Higher these
numbers,
Lower the
chance of
producing a
defect
1
3 1‟s 3 1‟s
2.4 Understand Data Characteristics
Why Collect Data?
Successful organizations have a common language to communicate
Common language promotes objectivity in decision-making process
Don‟t come up with great solutions for problems that don‟t exist
A measure of „where we are‟ is critical to determining „where we should be‟
Have you reached where you intended to? -- only data answers that question
A good data collection simplifies the problem solving effort
If the solution costs more than the problem, it‟s not worth it. A good data collection
should concentrate as much on measuring problems as it does on measuring solutions
Key Concepts
Improvement can only occur if we understand where we are & where to go, supported
by a measurement system that validates both situations
If the tool, by which we measure a characteristic, is not appropriate, able, or accurate,
effective improvement will not occur
One must understand and quantify the measurement system
Examples
Discrete data - (Is Countable)
Data that can take a limited number of values (Pass / Fail, OK / Not OK, Win / Loss)
Examples
Number of Days in a week
Number of „yes‟ responses to a satisfaction survey
Number of bugs fixed
Number of test cases passed or number of test cases failed
Continuous Data - ( Is Measurable and can take on fractional Values)
Data that be expressed in either fractions or whole numbers
Examples
Time taken to fix a bug
Time taken to close a call
Productivity
Defect Density
Yield of a process
Temperature in the room
Height of a person
Discrete Data Characteristics
Usually illustrated in tables & graphs
Continuous Data Characteristics
Usually illustrated in tables & histograms / frequency polygons
A histogram or frequency distribution shows the number of data points in a data set that fall
into each of the frequency classes
A frequency polygon is constructed by connecting the mid-points of each of the vertical bar
in the Histogram
90 95 100 115 120 125 130
Continuous Data Characteristics
Location / Central Tendency
It is a measure of the center point of any data set
Spread / Dispersion
It is a measure of the spread of any data set around its center
Shape
It is a measure of symmetry of any data set around its center
Measuring the Location
Mean
Mean is the arithmetic average of all data points in a data set
Mode
Mode is the most frequently occurring data point in a data set
Median
Median is the middle data point of a data set arranged in an ascending / descending order
Y1 + Y2 + Y3 + ………. + Yn
nWhere n = number of data pointsY =
Odd number of data points Even number of data points
Average
Measuring the Spread
Range
Range is the difference between the maximum & minimum data point
Variance / Standard Deviation
Variance & standard deviation measure how individual data points are spread around mean
( Y1 - Y )2 + ( Y2 – Y )2 + ……. + ( Yn – Y )2
( n – 1 )Variance = s2 =
Standard Deviation = s = s2
Importance of Spread
Mean of Curve „A‟ is more representative of its data set as compared to Curves „B‟ & „C‟
Spread outside the specifications may result in defects; this information is not
provided by mean
From a process perspective, individual customers are subject to different behaviors
of the process
A
B
C
Normal Distribution
Introduction to Normal Distribution
It‟s a Probability Distribution, illustrated as N ( µ, σ )
Simply put, a probability distribution is a theoretical frequency distribution
Higher frequency of values around the mean & lesser & lesser at values away from mean
Continuous & symmetrical
Tails asymptotic to X-axis
Bell shaped
Total area under the Normal curve = 1
100 110 120 130908070
Figure 3.01
1 unit
of
standard
deviation
+ -
Normal Distribution with
Mean =100
Standard Deviation = 10
Standard Normal Distribution
Instead of dealing with a family of normal distributions with varying means & standard
deviations, a standard normal curve standardizes all the distributions with a single curve
that has a mean of 0 & standard deviation of 1
It‟s illustrated as N ~ ( 0,1 ), i.e. mean = 0 & standard deviation = 1
µ1 µ2 µ3 0 +1 +2 +3
+ -
-1-2-3
Normal Distribution Property
µ
Figure 3.02
+ -
- 1σ + 1σ
95.46%- 2σ + 2σ
68.26%
- 3σ + 3σ99.73%
+ 4σ99.9937%
- 5σ99.99943%
+ 5σ
- 6σ + 6σ99.999998%
- 4σ
Concept of Z Value
To standardize different measurement units; such as, inches, meters, grams; a
standard Z variable is used.
Where Y = Value of the data point we are concerned with
µ = Mean of the data points
σ = Standard Deviation of the data points
Z = Number of standard deviations between Y & the mean (µ)
Z value is unique for each probability within the normal distribution
It helps in finding probabilities of data points anywhere within the distribution
It is dimensionless
Z = Y - µ
σ
Example
It‟s found that time taken for resolution of customer complaints follow a normal distribution with
mean of 250 hours and standard deviation of 23 hrs. What is the probability that a complaint
resolution will take more than 300 hrs?
250 300
Z = 300 - 250
23= 2.17
Looking up Appendix 1 for Normal Distribution Table,
we find that Z value of 2.17 covers an area of 0.98499 under itself
Thus, the probability that a complaint resolution may take between 0 & 300 hrs is 98.5%
& thus, chance of problem resolution taking more than 300 hrs is 1.5%
Z
Example
For the same data, what is the probability that problem resolution will take between
216 & 273 hrs?
250273
Z1 = 273 - 250
23= 1
From Appendix 1:
Total area covered by Z1 = 0.841344740
Total area covered by Z2 = 1 - 0.929219087 = 0.0707
Intercepted area between Z1 & Z2 = 0.7705
Thus, probability that a problem resolution may take between 216 & 273 hrs is 77.05%
216
Z2 = 216 - 250
23= - 1.47
Z1
Z2
Measure Phase – Step 2&3 L1 Version 3.2 Slide 32 Proprietary to Wipro Ltd
Measuring the Shape
Symmetric Data set
It‟s a data set in which spread of the data set around its mean is identical
For such a data set - mean = mode = median
Asymmetric Data set
Positive / Right skewed Negative / Left skewed
- high spread on the right side of the mean - high spread on the left side of the mean
Mean,
Mode,
Median
Mean
Median
Mode ModeMean
Median
The Complete Picture
On CenterLarge Spread
LSL USLT
On CenterSmall Spread
LSL USLTLSL USLT
Off CenterSmall Spread
Off CenterLarge Spread
LSL USLT
Which Type of Data is Preferable?
Continuous data helps you to understand process variation
Sample size required is less
Discrete data does not allow to understand the process variation. It does not tell you
how bad is bad
You need larger samples with Discrete data
Class Exercise
Given below is the sample data on Customer complaint closure time in hrs.
Compute the Mean & Standard Deviation for each quarter.
Quarter 1 Quarter 2
Sample 1 204 145
Sample 2 202 150
Sample 3 205 140
Sample 4 196 165
Sample 5 198 134
Sample 6 190 130
Sample 7 196 170
Sample 8 205 132
Sample 9 200 145
Sample 10 199 164
Mean 199.5 147.5
Standard
Deviation5 14
2.5 Find Opportunities for Error
Opportunities for Error (OFE)
Opportunities for error in a process is the number of steps / tasks / actions in the
process, where there is a possibility of committing an error, that may result in a defect
OFEs are opportunities inside the process that can contribute to a defect
OFE enables to compare the output quality of dissimilar processes
Concept of OFE is applicable only when defect measurement is discrete
This is because data, on whether or not a defect is created, is discrete type (yes / no)
2.6 Design Sampling Plan for
Establishing Process Baseline
What is Baseline?
After the team has understood the unit & defect definition, it would need to analyze
the current performance level
„Baseline‟ refers to a reference point from where the improvement would be
measured
Sampling plan for baselining attempts to define the data collection approach only
Introduction to Sampling
We do sampling all the time
Populations & Samples
Practical aspects – Cost & Time
Sampling is done to study a representative portion of population
Any term describing the characteristics of a sample is called statistic
Any term describing the characteristics of a population is called parameter
Population
Sample
Sam
plin
g
Tool
Populations & Samples
Table 1.60 Population Sample
DefinitionCollection of items
being considered
Portion of the
population chosen for
study
Characteri
stics
‘Parameter’ ‘Statistic’
Population Size = N Sample Size = n
Population Mean = µ Sample Mean = Y
Population Standard
Deviation = σ
Sample Standard
Deviation = s
Types of Sampling
Random Sampling or Probability Sampling
All items in the population have an equal chance of being chosen in the sample
Example: A customer satisfaction survey team picking the customers to be contacted at random
Non-random Sampling or Judgment Sampling
Personal knowledge & opinion are used to identify items for the sample
It is also used to decide upon how to take a random sample later
Example: A forest ranger may decide on a sample of north-west area to cut lumber
Collect Fresh Data
Fresh data should be collected to ensure that the latest process trend is studied
Historical data may have measurement errors which would be validated in next step of
DMAIC
Sometimes, process may generically improve as compared to the „Define‟ phase
due to increased attention from the owners / error in sampling
In such cases, Champion & BB may review the project, address the „discipline‟ issues &
decide whether project needs to collect another sample or gets abandoned here
How Big a Sample?
Business criteria to select a sample size include cost, time & effort
Statistical criteria include the accuracy of the sample representing the population
Higher the sample size, better the accuracy of the information about the population
parameters ( µ & σ )
There must be a balance between the business & statistical criteria
Z1 with n = 25
Z2 with n = 16
Z3 with n = 4
Determinants of Sample Size - Continuous Data
The sample size is determined by answering 3 questions
How much variation is present in the population? ( σ )
In what interval does the true population mean need to be estimated? ( ± )
How much representation error is allowed in the sample? ( α )
Sample size formula for Continuous Data:
n = Z 1 – (α / 2) * σ
2
Estimating Population Parameter
What population parameters we want to estimate
Cost of sampling (importance of information)
How much is already known
Spread (variability) of the population
Practicality: how hard is it to collect data
How precise we want the final estimates to be
Example 1 - Continuous Data
Let‟s take the weight of fertilizer bags whose std packaging is 7 Kgs with a std
deviation of 3.78. Now if I want to take a sample of few bags & want their mean to be
within ± 2, i.e. 5 & 9, how many bags should I sample ?
= 2
σ = 3.78
Assume α = 0.05
From Appendix 1, Z 97.5 = 1.96
So, sample size n = [ (1.96 * 3.78) / 2 ]
= 14
That means 95% of the samples with size 14 will have its mean between 5 & 9
n = Z 97.5 * 3.78
2
2
2
Standard Sample Size Formula - Continuous Data
Usually, value of α is taken as 5%
Z 97.5 = 1.96
Thus, standardized sample size formula can be written as
n = 1.96 * σ
2
for Continuous Data
Standard Sample Size Formula - Discrete Data
Extending the same logic, we can find out the sample size required while dealing with
discrete population
If the average population proportion non-defective is at „p‟, population standard
deviation can be calculated as
n = 1.96
2
for Discrete Data
σ = p ( 1 – p)
Where = Tolerance allowed on either side of the population proportion average in %
p ( 1 – p)
Measure Phase – Step 2&3 L1 Version 3.2 Slide 50 Proprietary to Wipro Ltd
DMAIC
Step 3
Validate
Measurement System
for „Y‟
Introduction - MEASURE
A robust measurement system forms the basis of any Six Sigma project
A measurement system has two characteristics
Design of the measurement system
Precision of the measurement system
Measurement system for „Y‟ indicates that this step deals with the accuracy of defect
measurement & must be completed before proceeding to establish the process baseline
Step 2 of DMAIC
Step 3 of DMAIC
Deliverables of Step 3
3.1 Perform GRR study
3.2 Analyze results
3.1 Perform GRR Study
Count the Occurrence of letter „I‟ in the Paragraph
A country preacher was walking the back-road near a church. He became thirsty so
decided to stop at a little cottage and ask for something to drink. The lady of the house
invited him in and in addition to something to drink, she served him a bowl of soup by the
fire. There was a small pig running around the kitchen. The pig was constantly running up
to the visitor and giving him a great deal of attention. The visiting pastor commented that
he had never seen a pig this friendly. The housewife replied: "Ah, he's not that friendly.
Actually, that's his bowl you're using!"
Purpose of G R & R
A performance critical system was delivered and the customer complained that the performance
criteria is not met
What is this problem due to?
This could again be due to how one measures performance and whether the
customer sees performance the same way
GR & R prevents the following mistake:
Claiming that we delivered quality when we did not OR Claiming that
quality is bad when it is not. We are eliminating the influence of
measurement error from the performance
Not doing GR & R will cause you to tamper with the process when in fact
the process is fine but only measurement is the issue.
Objectives of a Measurement Study
Obtain information about the type of measurement variation associated with the
measurement system
Establish criteria to accept and release new measuring equipment
Compare measuring one method against another
Form basis for evaluating a method suspected of being deficient
Resolve measurement system variation in order to arrive at the correct baseline
Types of Measurement Errors
Measurement System Bias - Calibration Study
Measurement System Variation - GRR Study
µ total = µ process +/- µ measurement
σ2total = σ2
process + σ2measurement
Sources of Variation
Observed Process Variation
ActualProcessVariation
MeasurementVariation
Short-termProcessVariation
Long-termProcessVariation
Variationwithin aSample
Variationdue to
Operators
Variationdue toGage
RepeatabilityAccuracy
Reproducibility
Stability Linearity
Gage Repeatability
Gage Repeatability is the variation in measurements obtained when one operator uses
the same gage for measuring the identical characteristics of the same part
Repeatability
Gage Reproducibility
Gage Reproducibility is the variation in the average of measurements made by different
operators using the same gage when measuring identical characteristics of the same
part
Reproducibility
Operator 1
Operator 2
Component of GRR Study
Trial
Reading
#1
2
3 4
5 6
12
3 4
5 6
12
3 4
5 6
1
Trial
Reading
#2
Operator
A
Operator
B
Operator
C
Difference leads to
Repeatability Six Parts / Conditions
Difference leads
to Reproducibility
2
3 4
5 6
12
3 4
5 6
12
3 4
5 6
1
Measurement Resolution
What is measurement resolution?
Capability of the measurement system to detect the smallest tolerable changes
Number of increments in the measurement system at full range
Example – Using a truck weighing scale for measuring the weight of a tea pack
As a pre-requisite to GRR, ascertain that your gage has acceptable resolution
Data Collection
Usually 3 operators
Usually 10 units to measure
General sampling techniques should be used to represent the population
Each unit is to be measured 2-3 times by each operator (Number of trials)
Gage should have been calibrated properly
Resolution should have been ensured
First operator should measure all units in random order
Same order should be maintained for all other operators
Repeat for each trial
Methods of Performing GRR Studies
ANOVA Method
Measures operator & equipment variability separately with combined effect as well that better
defines causality
More effective when extreme values are present
ANOVA Method
ANOVA not only separates the equipment & operator variation, but also elaborates
on combined effect of operator & part
ANOVA uses the „standard deviation‟ instead of „range‟, & hence gives a better
estimate of the measurement system variation
ANOVA also may not need the „tolerance‟ value as an input
However, time, resource & cost constraints may need to be looked into
Let‟s see an example
GR
R –
AN
OV
A M
eth
od
Tool
GRR Example
Part Operator Trial Response
1 1 1 475
1 2 1 442
1 3 1 489
1 1 2 479
1 2 2 462
1 3 2 463
2 1 1 369
2 2 1 326
2 3 1 302
2 1 2 368
2 2 2 328
2 3 2 318
3 1 1 398
3 2 1 405
3 3 1 410
3 1 2 415
3 2 2 402
3 3 2 421
Measure Phase – Step 2&3 L1 Version 3.2 Slide 67 Proprietary to Wipro Ltd
Entering Data in Minitab
STAT > Quality Tools > Gage R&R Study (Crossed)
Measure Phase – Step 2&3 L1 Version 3.2 Slide 68 Proprietary to Wipro Ltd
Entering Data in Minitab
STAT > Quality Tools > Gage R&R Study (Crossed) > Options
Input USL-LSL for
two-sided specifications
on „Y‟
%Contribution
Source VarComp (of VarComp)
Total Gage R&R 430.9 9.05
Repeatability 98.4 2.07
Reproducibility 332.4 6.98
Operator 24.2 0.51
Operator*Part 308.2 6.47
Part-To-Part 4329.4 90.95
Total Variation 4760.3 100.00
StdDev Study Var %Study Var
Source (SD) (5.15*SD) (%SV)
Total Gage R&R 20.7572 106.900 30.09
Repeatability 9.9219 51.098 14.38
Reproducibility 18.2323 93.896 26.43
Operator 4.9216 25.346 7.13
Operator*Part 17.5555 90.411 25.44
Part-To-Part 65.7981 338.860 95.37
Total Variation 68.9946 355.322 100.00
Number of Distinct Categories = 4
%Tolerance
(SV/Toler)
42.76
20.44
37.56
10.14
36.16
135.54
142.13
Minitab gives the following output:
ANOVA Method
Here, Reproducibility is broken into two parts
If Tolerance
value is input
(say 250 in
this case),
this column
will appear
Measure Phase – Step 2&3 L1 Version 3.2 Slide 70 Proprietary to Wipro Ltd
M is c :
Toleranc e:
Reported by :
Date of s tudy :
Gage nam e:
0
500
400
300
321
Xbar Chart by Operator
Sam
ple
Mean
M ean=404
UCL=424.9
LCL=383.1
0
40
30
20
10
0
321
R Chart by Operator
Sam
ple
Range
R=11.11
UCL=36.30
LCL=0
321
500
400
300
Part
Operator
Operator*Part InteractionA
vera
ge
1
2
3
321
500
400
300
Operator
By Operator
321
500
400
300
Part
By Part
%Contribution
%Study Var
Part-to-PartReprodRepeatGage R&R
100
50
0
Components of Variation
Perc
ent
Gage R&R (ANOVA) for Response
ANOVA Method
GRR Example - Software
Module Estimator Trial Effort
1 1 1 276
1 2 1 240
1 1 2 278
1 2 2 262
2 1 1 169
2 2 1 126
2 1 2 168
2 2 2 128
3 1 1 198
3 2 1 205
3 1 2 215
Suppose effort for developing 3 different modules are estimated by 2 different people, each estimating
twice and data is tabulated as below.
Measure Phase – Step 2&3 L1 Version 3.2 Slide 72 Proprietary to Wipro Ltd
Entering Data in Minitab – Software Example
STAT > Quality Tools > Gage R&R Study (Crossed)
Measure Phase – Step 2&3 L1 Version 3.2 Slide 73 Proprietary to Wipro Ltd
STAT > Quality Tools > Gage R&R Study (Crossed) > Options
Input USL-LSL for
two-sided specifications
on „Y‟
Entering Data in Minitab – Software Example
ANOVA Method – Software Example
Minitab gives the following output:
%Contribution
Source VarComp (of VarComp)
Total Gage R&R 434.2 11.67
Repeatability 65.9 1.77
Reproducibility 368.3 9.90
Est 213.6 5.74
Est*Module 154.7 4.16
Part-To-Part 3285.0 88.33
Total Variation 3719.1 100.00
StdDev Study Var %Study Var
Source (SD) (5.15*SD) (%SV)
Total Gage R&R 20.8367 107.309 34.17
Repeatability 8.1189 41.812 13.31
Reproducibility 19.1898 98.828 31.47
Est 14.6145 75.265 23.96
Est*Module 12.4365 64.048 20.39
Part-To-Part 57.3146 295.170 93.98
Total Variation 60.9846 314.071 100.00
Number of Distinct Categories = 4
Key Concepts
Minitab output under “%Contribution”, illustrates the percent contribution
from part-to-part as compared to GRR. If former is significantly higher than latter,
it tells you that most of the variation is due to differences between parts; very little is due
to measurement system error
Number of distinct categories in the Minitab output illustrates the „number of groups
within your process data that your measurement system can discern‟
A value of 4 or more denotes a good measurement system
Continuous Data
GRR as a % of Contribution to Variation and Number of Distinct Categories
If GRR as % of contribution is about 10% of the total variation - acceptable
If number of distinct categories is >= 4 - acceptable
If none of the above criteria is met, do not proceed to the next step
If tolerance was known, GRR as a % of Tolerance should be used for decision as
explained in the previous slide
Continuous Data
GRR as a % of Tolerance( study var/Tolerance *100)
Study Var = SD * 5.15
If GRR as % of tolerance is less than 10% - excellent measurement system
If GRR as % of tolerance is between 10% to 30% - acceptable measurement system
However, discretion may be needed depending upon application of the process / equipment
If GRR as % of tolerance is above 30% - unacceptable measurement system
You should not proceed to next DMAIC step. Simplify process / explore root cause
GRR for Discrete Data
ANOVA methods apply to continuous data only
For discrete data, a relatively higher accuracy is desired
Usually, discrete data GRR is measured against the „true‟ value
Worksheet for Discrete Data
Data to be filled only in “YELLOW‟ cells
GR
R –
Dis
cre
te D
ata
Tool
Key Concepts
Operator Consistency (Trial Match)
% of times an operator repeats his observation in trial 2 as compared to trial 1
Mutual Consistency (Operator Agreement)
% of times both operators are in complete sync
Operator Efficiency (True Match)
% of times an operator has both his observations matched with true value
Measurement Efficiency (True Agreement)
% of times both operators are in complete sync with the true value
Class Exercise
Data is given on past matches played by Indian cricket team. Classify each match into „LOST‟
or „WON‟, as applicable to Indian team.
Once this is done, put the values in the „GRR – Discrete Data‟ worksheet given &
compute all the six measurements.
Discrete Data
Discrete data measurement system has to be perfect because of sample size limitations
Measurements for operator consistency & efficiency should be targeted at minimum 90%
failing which team may want to discuss with Champion & Black Belt for proceeding further
Key Concepts
Once the GRR has been found to be reduced to acceptable level, project team can
start collecting data
Using this data to arrive the Sigma multiple of the process shall be discussed in
Analyze phase
GRR Applicability for software
GRR Can be used to Calibrate
The Estimation process
the review effectiveness at start of project
Testing Effectiveness at start of project
In areas where measurement of repeatability and reproducibility is not applicable
The operational definition of measures, Units of measure, Data collection mechanism
Needs to be defined
Tollgate - Measure
Detailed As-is Process
Units, Specifications & Defects
Number of OFE‟s, if discrete data
GRR of the Measurement System
Action plan, if GRR is not acceptable
Reduction of GRR to acceptable level
All the Best
for
the
Quiz!!!!!!!!!
Quiz
MEASURE – Q1
Process Mapping helps in
a) Visualizing the activities
b) Understanding the big picture
c) Identifying bottlenecks
d) All of the above
MEASURE – Q2
„S‟ in SIPOC stands for
a) Sales
b) Supplier
c) Shop floor
d) Specifications
MEASURE – Q3
A unit is
a) Where we observe defects
b) Measurable characteristics of process output
c) Measurable characteristics of process input
d) a & b
MEASURE – Q4
GRR study is done on
a) Two gages
b) More than two gages
c) Only one gage
d) Any number is OK
MEASURE – Q5
Quality
a) Goes up as defects come down
b) Is absence of defects in the unit
c) Is defined by the customer
d) All of the above
MEASURE – Q6
Which are the characteristics of discrete data
a) Location
b) Spread
c) OFE
d) Shape
Appendix 1 – Normal Distribution Table
Area Below +ZLT
Z
Appendix 1 – Normal Distribution Table (contd.)
Z
Area Below +ZLT