NG BB 24 Measurement System Analysis - Continuous

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National Guard
Black Belt Training

Module 24

Measurement
System Analysis (MSA)
Continuous Data
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CPI Roadmap – Measure
8-STEP PROCESS
6. See
1.Validate 2. Identify 3. Set 4. Determine 5. Develop 7. Confirm 8. Standardize
Counter-
the Performance Improvement Root Counter- Results Successful
Measures
Problem Gaps Targets Cause Measures & Process Processes
Through

Define Measure Analyze Improve Control

TOOLS
•Process Mapping
ACTIVITIES
• Map Current Process / Go & See •Process Cycle Efficiency/TOC
• Identify Key Input, Process, Output Metrics •Little’s Law
• Develop Operational Definitions •Operational Definitions
• Develop Data Collection Plan •Data Collection Plan
• Validate Measurement System •Statistical Sampling
• Collect Baseline Data •Measurement System Analysis
• Identify Performance Gaps •TPM
• Estimate Financial/Operational Benefits •Generic Pull
• Determine Process Stability/Capability •Setup Reduction
• Complete Measure Tollgate •Control Charts
•Histograms
•Constraint Identification
•Process Capability
Note: Activities and tools vary by project. Lists provided here are not necessarily all-inclusive. UNCLASSIFIED / FOUO

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Learning Objective
 Understand how to conduct and interpret a
measurement system analysis using Continuous Data

Measurement System Analysis (MSA) - Continuous UNCLASSIFIED / FOUO 3

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Acceptable Measurement Systems
Properties that all acceptable measurement systems must
have:
 The measurement system must be in control (only
common cause variation)
 Variability of the measurement system must be small in
relation to the process variation
 Variability of the measurement system must be small
compared with the specification limits (the tolerance)
 The increments of the measurement must be small
relative to the smaller of:
 the process variability or the specification limits
 Rule of thumb: increments are to be no greater than 1/10th of the smaller of
process variability or specification limits


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Measurement System Study- Prep
Plan the approach:
 Select number of appraisers, number of samples and
number of repeat measures
 Use at least 2 appraisers and 5 samples, where each
appraiser measures each sample at least twice (all using
same device)
 Select appraisers who normally do the measurement
 Select samples from the process that represent its entire
operating range. Label each sample discretely so the label is
not visible to the operator.
 Check that the instrument has a discrimination that is equal
to or less than 1/10 of the expected process variability or
specification limits

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Measurement Study – Prep (cont.)
 Assure that the gage/instrument has been maintained
and calibrated to traceable standards
 Parts are selected specifically to represent the full
process variation
 Parts should come from both outside the specs (high
side and low side) and from within the specification
range


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Running the Measurement Study
In order to run the MSA:
 Each sample should be measured 2-3 times by each operator
 Make sure the parts are marked for ease of data collection but
remain “blind”(unidentifiable) to the operators
 Be there for the study and record any unplanned influences.
 Randomize the parts continuously during the study to preclude
operators influencing the test
 The first time evaluating a given measurement process, let the
process run as it would normally run


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Running the Study – Guidelines
Because in many cases we are unsure of how “noise” can
affect our measurement system, we recommend the
following procedure:
 Have the first operator measure all the samples once in
random order
 Have the second operator measure all the samples once in
random order
 Continue until all operators have measured the samples
once (this is Trial 1)
 Repeat the previous two steps each time for the required
number of trials
 Use a form to collect information
 Analyze results
 Determine follow-up action, if any


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Exercise: Run MSA in Minitab
Can we trust our measurement system?
 The maintenance function at an ANG airlift wing is evaluating a
vendor’s non-destructive testing (NDT) method that claims to be
better, faster and less expensive
 Faster NDT reduces overall cycle time for inspections of airframe,
hence an Upper Specification Limit
 Faster is better, but too fast an NDT cycle time might mean an
inadequate time for the penetration of the dyes into hairline
fractures, hence the Lower Specification Limit
 USL minus LSL = Tolerance
 SL minus Mean Response = One Sided Tolerance
 This MSA evaluates the ability of the measurement system to
detect changes in overall NDT inspection cycle time

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MSA Example in Minitab
 Ten parts were selected that represent the expected range of
the part type variation. Three inspectors measured the ten
parts, three times per part, in a random order.
This data set is Gage3.mtw.
Column Name Description
C1 Part Part Number
C2 Operator Test Operator number
C3 Response Cycle Time for inspection
 Above is the description of the data from Minitab
 Is it short form?
 Long form?


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Data Set = Gage3.mtw
Stat>Quality Tools>Gage Study>Gage R&R Study (Crossed)

Note: Gage R&R Study (Crossed) is the most commonly used method for Variables
(Continuous Data). It is used when the same parts can be tested multiple times, i.e. NON
DESTRUCTIVE TESTS. GR&R (Nested) MSA is for DESTRUCTIVE TESTING. .


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Gage R&R in Minitab

Enter the variables (circled fields) in the above dialogue box and keep
the ANOVA method of analysis checked. The main difference between
ANOVA and Xbar and R is that ANOVA will estimate an operator by
part interaction. The ANOVA method is the preferred method.


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Gage R&R in Minitab (Cont.)
Gage R&R Study
(Crossed)
dialog box

After entering
the variables
in this dialog box,
click on Options
to view the
options dialog box

Options
dialog box


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Gage R&R in Minitab – Options
Options dialog box.
6.0 is the default for the number of sd in
the Study variation. This is the Z value
range that calculates a 99.73% potential
Study Variation based on the calculated
Standard Deviation of the variation seen
in the parts chosen for the study.
Alternatively, you may see texts use 5.15
sd, that corresponds to 99%.

The Spec Limits for the process are 10.75
as the USL and 8.75 as the LSL. You can
either enter these in the appropriate
boxes (be sure to click on Enter at least
one specification limit), OR you can
enter the Process tolerance (Upper
spec – Lower spec = 10.75 – 8.75 = 2.0)
by clicking and entering 2.0 in Upper
spec – Lower spec. (Either way gives
the same results.)
The Process Sigma has been 0.195. Enter .195 in the Dialog
Box for Historical standard deviation.

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Interpreting Acceptability
 If Process Tolerance and Historical Sigma values are not
used in Minitab, a critical assumption is then made that
the sample parts chosen for the study, truthfully exhibit
the true process variation. In this case, the acceptability
of the measurement system is based upon comparison
only to the part variation seen in the study. This can be
a valid assumption if care is taken in selecting the study
sample parts.
 One element of criteria whether a measurement system
is acceptable to analyze a process is the percentage of
the part tolerance or the operational process variation
that is consumed by measurement system variation.


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Minitab Gage R&R - ‘Six-Pack’
Gage R&R (ANOVA) for Response
Let’s look at these six
Reported by :
G age name:
D ate of study : charts one at a time
Tolerance:
M isc:

Components of Variation Response by Part
100 % Contribution
% Study Var 10.00
Percent

% Process
% Tolerance 9.75
50
9.50
0
Gage R&R Repeat Reprod Part-to-Part 1 2 3 4 5 6 7 8 9 10
Part
R Chart by Operator
1 2 3
Response by Operator
UCL=0.1073
0.10 10.00
Sample Range

_ 9.75
0.05
R=0.0417
9.50
0.00 LCL=0
1 2 3
Operator
Xbar Chart by Operator
1 2 3 Operator * Part Interaction
10.00 10.00 O perator
Sample Mean

1
_
_
Average

UCL=9.8422 2
X=9.7996 9.75
9.75 LCL=9.7569 3

9.50
9.50
1 2 3 4 5 6 7 8 9 10
Part


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Gage R&R - Relationships
A measurement process is said to be consistent when the results for
operators are Repeatable and the results between operators are
Reproducible
A gage is valid to detect part-to-part variation when the variability of
operator measurements is small relative to process variability or the
tolerance range
 The percent of process variation consumed by the measurement (%
R&R) is then determined once the measurement process is consistent
and can detect part-to-part variation


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Six Pack – #1 Components of Variation
 Focus on the 3 Bars to the
right in each cluster. These
represent the % of total
variance contributed from
the data. Gage R&R is the
total variation in our
measurement system
broken into repeatability
and reproducibility. The
part to part Study Variation
bar is an estimate of our
Total Gage R&R
process variation.
Operator + Between Inspectors
Equipment/Gage Or Insp. to Insp.  Remember why we
Operator measure?

An estimate of Process
Within the Gage
(or Part) Variation
Or one Inspector
unless the Historical
Equipment/Gage Sigma is entered Parts

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Six Pack – #2 R Chart By Operator
 Repeatability is checked by using a special Range Chart where the
differences in the measurements by each operator on each part is
charted. If the difference between the largest value of a measured
part and the smallest value of the same part does not exceed the UCL,
then that gage and operator are considered to be Repeatable.

Repeatability is indicated when virtually all of the range points
lie under the upper control limit on the range chart. Any points
that fall above the limit need to be investigated.

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Six Pack – #3 X bar Chart By Operator
 Reproducibility is best determined analytically using the
tabulation analysis in the Minitab Session (discussed in following
slides). Graphically it might be seen if there are significant
differences in the operator patterns generated by each operator
measuring the same samples.


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X bar Chart By Operator (Cont.)

 It is desirable to see plots that consistently go outside the UCL and LCL
because limits are determined by gage variance and these plots should show
that gage variance is much smaller than variability within the parts
 If the samples chosen do not represent the total variability of the process,
the gage (repeatability) variance may be larger than the part variance and
invalidate the distinct categories calculation
 If the patterns of the operators are not comparable, there may be significant
operator and part interactions (discussed on another slide)
On this chart you want At Least 50% of the
points to be Outside the Control Limits

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Gage R&R - Six Pack (Cont.)

What do these control
limits represent in
terms of our
Measurement System?

 Is the Range (R) Chart in control?
 Where do the limits on the Xbar Chart and the R Chart come from?
 Do we want the R Chart and the Xbar Chart in or out of control?

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Gage R&R – Six-Pack Charts (Cont.)
This graph shows the data for the
ten parts for all operators plotted
together. It displays the raw data
and highlights the average of
those measurements.
Part Issues

Similar to the top graph but the
data is presented by each
operator instead of by part.
This graph will help identify
Operator Issues.

This graph shows the data for each
operator for all ten parts. It is the
easiest to use to uncover
Operator & Part Interaction.


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Six Pack – #4 Response By Part

 This graph shows the data for all ten parts for all operators plotted
together. It should show plots that vary from the smallest dimensions
for the parts made by the process to the largest dimensions for the
same parts. Parts should be both in tolerance and out of tolerance if
the process makes them.
 If a part shows a large spread, it might be a poor candidate for the test
because the feature may not be clear on that part.

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Six Pack – #5 Response By Operator

 This graph shows the data for all ten parts for plotted by each
operator. The red line connecting the averages of all 10 parts
measured by each operator should be horizontal.
 Any significant slope is an indication that this operator has a general
bias to measure large or small when compared to the other operators


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Six Pack – #6 Operator * Part Interaction
 Operator Influence: If the lines connecting the plotted
average points diverge significantly, then there is a
relationship between the operator making the measurements
and the part that the operator is measuring. This is not good
and needs to be investigated.


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Minitab Gage R&R - Six-Pack (Cont.)
Questions on the graphical output?

Reported by :
G age name: Tolerance:
D ate of study : M isc:

100 % Contribution
% Study Var 10.00
Percent

% Process
% Tolerance 9.75
50
9.50
0
Part
R Chart by Operator
1 2 3
UCL=0.1073
0.10 10.00
Sample Range

_ 9.75
0.05
R=0.0417
9.50
0.00 LCL=0
1 2 3
Operator
10.00 10.00 O perator
Sample Mean

1
_
_
Average

UCL=9.8422 2
X=9.7996 9.75
9.75 LCL=9.7569 3

9.50
9.50
1 2 3 4 5 6 7 8 9 10
Part


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Gage R&R – Session Window
Let’s take this output
one chunk at a time.

These 3 Values should all be
Less Than 30% for process
improvement efforts

These values may not add to 100%

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Gage R&R - The Numerical Output (Cont.)
We would
like this
to be less
than 9%

This table is from the Minitab Session window. It is an easy-to-
understand tabulation of the amount of MSA variation from each
source. The first column represents the source of variation, the
second column is an estimate of the actual variation for each source
(factor). The third column is the linear % that each represents of the
total variation. It is depicted as the black bar on the Pareto in the six-
pack diagram.

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Gage R&R - The Numerical Output (Cont.)
These should all be
Less Than 30%

This should be
4 or More

 This tabulation from Minitab builds the % of Study Variation that each source contributes to a
calculated potential Total Variation seen in the study. The 6.0 * SD is how statistically 99.73% of the
Total Variation is calculated and this is assumed to equal 99.73% of the true process variation unless
the Historical Sigma is input into Minitab.
 The percentages are used to grade the validity of the measurement system to perform measurement
analysis using percentages already taught. If the process is performing well, the %Tolerance is then
important. The sum of the percentages might add to more than 100% due to the math.
 The Number of Distinct Categories represents the number of non-overlapping confidence intervals
that this measurement system can reliably distinguish in the product variation. We would like that
number to be 5 or higher. Four is marginal. Fewer than 4 implies that the measurement system can
only work with attribute data. DC= (s parts/s GRR total)* 2

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Interpreting Acceptability in Session Window
Category Acceptable Marginal Not Acceptable
(Green) (Yellow) (Red)

% Contribution < 1% 1% to 9% > 9%

% Study Var < 10% 10% to 30% > 30%

% Tolerance < 10% 10% to 30% > 30%

% Process < 10% 10% to 30% > 30%
Number of Distinct
Categories >5 4 <4
Marginal: Might be acceptable based upon the risk of the application,
cost of measurement device, cost of repair, etc.
Not Acceptable: Every effort should be made to improve the
measurement system

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Gage R&R - Conclusions
Is thisby :
Reported Measurement
D ate of study : M isc: System OK ?

100 % Contribution
% Study Var 10.00
Percent

% Process
% Tolerance 9.75
50
9.50
0
Part
R Chart by Operator
1 2 3
UCL=0.1073
0.10 10.00
Sample Range

_ 9.75
0.05
R=0.0417
9.50
0.00 LCL=0
1 2 3
Operator
10.00 10.00 Operator
Sample Mean

1
_
_
Average

UCL=9.8422 2
X=9.7996 9.75
9.75 LCL=9.7569 3

9.50
9.50
1 2 3 4 5 6 7 8 9 10
Part


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Let’s Do It Again
 Three parts were selected that represent the expected range of the
process variation. Three operators measured the three parts, three
times per part, in a random order.
 No History of the process is available and Tolerances are not
established
 Go to exercise set: Gage2.mtw
 This data set is used to illustrate Gage R&R Study and Gage Run Chart

Column Name Count Description
C1 Part 27 Part number
C2 Operator 27 Operator number
C3 Response 27 Measurement value
C4 Trial 27 Trial number


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Data Set = Gage2.mtw
Stat>Quality Tools>Gage Study>Gage R&R Study (Crossed)


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Filling in the Dialog Boxes
1. Set cursor in Part
numbers box and
double click on
C-1 Part
2. Set cursor in
Operators box and
double click on
C-2 Operator
3. Set cursor in
Measurement data
box and double click
on C-3 Response

4. Make sure ANOVA
is selected and
click on OK

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How Does This Measurement System Look?
Why is this study unacceptable?
Reported by :

100 % Contribution 600
% Study Var
Percent

400
50

200
0
Gage R&R Repeat Reprod Part-to-Part 1 2 3
Part
R Chart by Operator
1 2 3
400 UCL=376.5 600
Sample Range

400
200 _
R=146.3
200
0 LCL=0
1 2 3
Operator
UCL=555.8
O perator
500
Sample Mean

1
450
Average

_
_ 2
3
400 X=406.2 400

300 350
LCL=256.5
1 2 3
Part


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Gage2.mtw - Results

This should be
less than 30%
for process
improvement
efforts

What does
this tell
you?

Remember this?
What does this mean ?

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Gage2.mtw – Conclusions
What needs to be addressed first? Where do we begin
improving this measurement system?

Reported by :

100 % Contribution 600
% Study Var
Percent

400
50

200
0
Gage R&R Repeat Reprod Part-to-Part 1 2 3
Part
R Chart by Operator
1 2 3
400 UCL=376.5 600
Sample Range

400
200 _
R=146.3
200
0 LCL=0
1 2 3
Operator
UCL=555.8
O perator
500
Sample Mean

1
450
Average

_
_ 2
3
400 X=406.2 400

300 350
LCL=256.5
1 2 3
Part


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One-Sided Specifications
Typically, in the transactions environment, customer specifications are
only one-sided. For example, most of the time an upper specification
alone given on cycle time… faster is always better.
How does Minitab analyze and report findings for a GR&R for a one-sided
specification?

If only one specification limit is given, percent tolerance is the one-sided
process variation (OPV) divided by the one-sided tolerance, OST.
The one-sided process variation is Study Var divided by 2.
The one-sided tolerance (OST) is the absolute value of the given
specification limit subtracted from the average of all the measurements.

So, if for example, the USL was 10 and the mean for response was 5,
then the OST equals 10-5 or 5

Measurement System Analysis UNCLASSIFIED / FOUO 39

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Takeaways
 It is important to be able to rely on the accuracy of the
measurement system to make good decisions
 Understand the various types of measurement system variation
 Eliminate as much of the variation in the measurement system
as possible to focus on and improve the true cause of variation
in process performance
 Conduct a Gage R&R analysis to assess the measurement
system for continuous data

Measurement System Analysis UNCLASSIFIED / FOUO 40

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What other comments or questions
do you have?

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National Guard
Black Belt Training
APPENDIX

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Bias Evaluation (Percent Accuracy)
 Typically,metrology is responsible for the accuracy of the
measurement devices. Calibration typically addresses accuracy.
 Percent accuracy compared to a tolerance:
Average Value - Master Value
 (100)
Tolerance

 Rule of Thumb for Accuracy Acceptance:
 < 1% of process variation or tolerance is considered to be adequate
accuracy
 > 1 % of tolerance may warrant corrective action

A typical Measurement study will not address accuracy issues
unless it is specifically set up to do so (uses a standard instead
of parts)


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Measurement Variation vs. Tolerance
 Precision to Tolerance Ratio

515 * s MS
. Usually
P/T  expressed as a
Tolerance percent

Tolerance = USL - LSL

 Addresses what percent of the Tolerance is taken up by
measurement error
Note: 5.15 standard
 Best case: less than 10% deviations accounts
for 99% of MS
 Acceptable: up to 30%
variation
 Includes both repeatability and reproducibility: The use of 5.15 is an
industry standard
Operator x Unit x Trial experiment

 P/T Ratios are required by certain customers

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Measurement Variation vs. Process
 Percent Repeatability & Reproducibility (%R&R)

s MS ´
% R& R = 100 Usually expressed
s Total as a percent

 Addresses what percent of the Total Variation is taken up by measurement error
 Best case: less than 10%
 Acceptable: up to 30%
 Includes both repeatability and reproducibility
 Operator x Unit x Trial experiment
 Again, the stability in the repeated measurements as well as the degree of
discrimination could affect the validity of the SMS calculation
 %R&R is required by certain customers

 Another Analytical measure is the Discrimination Index defined by:

sP
D. I. = ´ 2 The D.I. Is similar to the “Number of Distinct
Categories” on the Gage R&R Statistics output
s MS

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Gage R&R Relationships
 If the number of distinct categories is less than two,
the measurement system is of no value in controlling
the process
 If the number of categories is two, it would mean that
the data can be divided into only high and low groups
 The number of categories must be at least five for the
measurement system to be acceptable for the analysis
of the process


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Gage R&R Statistics – Discrimination Index
Source % Contribution % Study Var % Tolerance This “discrimination index”
Total Gage R&R 70.62 84.04 225.35 represents the ability of the
Repeatability 6.89 26.25 70.40 measurement system to
discriminate between one
Reproducibility 63.73 79.83 214.07 item and another. We
Operator 29.55 54.36 145.76 typically want this number to
Oper*Part 34.18 58.47 156.78 be 5 or more!!
Part-To-Part 29.38 54.20 145.34 A “discrimination index” of 2
or 3 indicates a measurement
Total Variation 100 100 268.16 system that is only useable
for Attribute Inspection
Number of Distinct Categories = 1

 Note: The Discrimination Index is entirely different from the Measurement Unit
Discrimination discussed earlier
 The measurement UNIT discrimination, evaluated in the range chart,
determines if the units being used are sufficiently small enough to detect variation
(are we using a unit of time such as “days” when we need to be using “minutes”
 The Discrimination Index looks at Measurement Variation vs. Product Variation to
determine if the measurement system is capable of discriminating from item to item


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Discrimination – Using Control Charts

 Evaluate measurement unit
discrimination by considering
the range chart (and the raw
data)
 With the 1st insert R Chart:
There are only two layers of
measurement resolution
under the UCL. We should
see 5. Therefore: NOT OK.
Subgroup Minimum Number of
Size Measurement Units When the unit of measurement is larger
2 4 than the estimated standard deviation, the
3 5 control limits are unreliable
4 5
5 5
6 6

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MSA Effect on Capability Indexes
 We Know that:

USL  LSL
CpAct  where s Act  s2  s2
Obs MS
6s Act

 Therefore:

USL  LSL
CpAct 
6 s2  s2
Obs MS


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MSA Effect on Capability Indexes Cpk

 To include the effects of process centering, we
know:
 USL  X Act X Act  LSL 
Be careful of the
Cpk Act  MIN or  direction of the bias
 3s Act 3s Act  (the sign of the XMS)
 

s Act  s2  s2
Obs MS X Act  XObs  X MS

Where and

 Therefore: 
 USL  X Obs  X MS 
X Obs  X MS  LSL   
CpkAct  Min or 
 3 s2  s2 3 s2  s2 
 Obs MS Obs MS 


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References
 Automotive Industry Action Group, Measurement
Systems Analysis, 3rd Edition, 2nd Printing, 2003,
AIAG, Southfield, MI. (248) 358-3003, www.aig.org
 Minitab, StatsGuide


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AIAG Gage R&R Standards
 The Automotive Industry Action Group (AIAG) has two
recognized standards for Gage R&R:
 Short Form – Five samples measured two times by
two different individuals
 Long Form – Ten samples measured three times each
by three different individuals
 For good insight into Gage R&R, go to
[www.aiag.org]
 Remember that the Measurement System is
acceptable if the Gage R&R variability is small
compared to the process variability or specification
limits


NG BB 24 Measurement System Analysis - Continuous

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