1. MSA / Gage Capability (GR&R)

2. Cause & Effect Diagram for a Measurement Process

3. Properties of Measurement Processes
Repeated measurements will disagree
Means of repeated measurements will disagree
Measurements made at different times, or by different operators,
or on different instruments will disagree
The measured value and the true value will disagree
Waste due to poor quality test data
Rejection of “good” material
Acceptance of “bad” material
Adjusting the process when not needed
Failure to adjust when needed
Loss of “goodwill” between production and test people

4. The High Cost of Poor Quality Measurements
Materials, lost time, wasted effort
Lower capacity and productivity
Higher manufacturing costs
Lower outgoing quality levels
Late delivery
Unhappy customers
Loss of customers??
In any program of control we must start with observed data. Of what value is the theory of control, i.e. SQC, if the observed data going into it is bad?
Dr. Walter A. Shewhart
1931

5. Gage Capability
Gage Capability is a method to determine how much of your observed process variation is due to measurement system variation.
A Gage Capability Study will break down the total variation into two categories, part-to-part variation and measurement system variation.
Measurement system variation is then partitioned into its two components – Repeatability and Reproducibility
Overall Variation
Measurement Variation
Part-to-Part Variation
Repeatability
(Variation due to gage)
Reproducibility
(Variation due to operators)
Operator-by-Part Interaction1
Operator
1 – available from the ANOVA method only.

6. Repeatability and Reproducibility
The variation obtained when one operator uses the same gage for obtaining
replicate measurements of the identical characteristics on the same parts
Obtained under a limited set of operating conditions (see below)
Reproducibility
The variation in the average of measurements made by different operators
using the same gage when measuring identical characteristics of the same parts
Obtained under a broader set of operating conditions (see below)

7. Gage R&R (GR&R) Basics
Select the gage and test characteristic to be evaluated
Select 10 parts for the study
Select 3 operators for the study
Each operator tests all 10 parts and records the measurements
Each operator repeats this step a second time
Each operator repeats this step a third time
Operators do not have access to his/her previous results or the results of others
Tests are done in random order
Data (90 data points) entered into the computer (Recommended to use Minitab)
Tolerance (USL minus LSL) entered into computer
Software prints out information, including:
- GR&R % of Tolerance
- GR&R % of Study Variation
- Other statistical measures and graphs
General requirements:
- GR&R % of Tolerance not more than 25% for key dimensions
- GR&R % of Tolerance not more than 35% for non-key dimensions
GR&R % of Tolerance = the percentage of allowable tolerance occupied by test variation (repeatability and reproducibility) alone.

8. Comparison of Various GR&R % of Tolerance
LSL
USL
GR&R = 25%
GR&R = 30%
GR&R = 40%
GR&R = 50%
GR&R = 100%

9. The Impact of GR&R on Specification Limits
Assume:
An in-control, unbiased measurement process
GR&R % of Tolerance = 20%
Lower Spec Limit
Upper Spec Limit
Say you test a part and get a result right here. X
The test result indicates “in-spec”.

10. The Impact of GR&R on Specification Limits
Assume:
An in-control, unbiased measurement process
GR&R % of Tolerance = 20%
Lower Spec Limit
Upper Spec Limit
Because of test variability however, you know that the “true” value might be higher or lower than the measured value. X
Because the GR&R is 20%, you know that the “true” value may lie anywhere in a region this wide.
The problem is, where do you place this interval, with respect to your measured value?

11. The Impact of GR&R on Specification Limits
Assume:
An in-control, unbiased measurement process
GR&R % of Tolerance = 20%
Lower Spec Limit
Upper Spec Limit X
Do you place it here?
Or do you place it here?
Do you place it here?
Which is correct?

12. The Impact of GR&R on Specification Limits
Assume:
An in-control, unbiased measurement process
GR&R % of Tolerance = 20%
Lower Spec Limit
Upper Spec Limit
You can see that there is a distinct probability, however small, that an additional test result will indicate “out-of-spec”. X
You treat this question as follows:
Consider your current test result to be your best estimate of where the mean of this interval lies, and center the interval on the test result.
Let’s generalize this issue with an example that uses three different parts.

13. Wrap-up: The Impact of GR&R on Specification Limits
Three different parts: 1, 2, & 3
Each part is represented by a distribution representing known measurement variability, rather than an interval.
For judging conformance to spec, the GR&R will not be a factor for parts 1 & 3.
As in the previous example, the test result for sample #2 presents a distinct probability that the part may actually be out-of-specification, even though the test result is within spec.
Whenever a single test result falls directly on a spec limit, there is a 50:50 chance that the part may be in-spec or out-of-spec. This is true regardless of how “good” the GR&R is.
For these reasons, it is always best for the process average to be at or near the target value.

14. Determining the “Tolerance”
Case 1 - Bilateral Specs:
Upper Spec Limit (USL) and Lower Spec Limit (LSL) available
Tolerance = USL minus LSL
Case 2A - Unilateral Specs, Target = 0; Have USL:
Tolerance = USL minus Zero
Case 2B - Unilateral Specs, Have USL or LSL but not both:
Tolerance = 2 * X – Spec Limit
where, = absolute value, X = process average
Note: Minitab software uses this method, starting with Release 14.2
Case 3 – No Specs, but have production data:
Tolerance = 6 * process standard deviation
Results in a GR&R % of Process Capability

17. Two Types of GR&R XBar & R Method and ANOVA Method
The calculations used in the XBar and R method are simpler, however the ANOVA method is preferred because 1) it uses standard deviation rather than Range statistics and is more accurate, and 2) provides the statistical significance level for operator-part interaction.
If the software offers both methods, use the ANOVA method.
The method used should provide an Xbar chart and a Range chart.
The R chart shows the difference between the largest and smallest measurement for each part for each operator. Because the points are arranged by operator, you can see how consistent each operator is.
Ideally, you would like to see that the average Range is about the same for each operator, and that no points exceed the upper control limit.
The Xbar chart shows the average for each part by each operator. Because the points are arranged by operator, you can see how each operator’s averages compare.
Unlike a conventional control chart, you want the gage study Xbar chart to show many points exceeding the control limits.
If no points exceed the Xbar control limits, it means that the test method cannot distinguish between different parts.
The more out-of-control Xbar points, the better.

18. Software Example – Minitab Analysis
This is how you arrange the data for Minitab.
Use one column for sample number, one for operator number or name, and one for the data values.
For 10 samples, 3 operators and 3 replicates, you should have 90 data points.
Choose the ANOVA method for your analysis.
Choose six standard deviations for the Study Variation. Previous versions of Minitab used 5.15 standard deviations. 6 standard deviations however is more in line with conventional estimates of capability.
Input the tolerance. Examples:
If specs are +/ ”, the tolerance is 0.062”
If specs are –0.005” ”, tolerance is 0.030”
If specs are 0.08” max and a target of 0” is assumed, tolerance is 0.08”.

20. GR&R for Length, Part # 12345

21. Minitab will also show the “Number of Distinct Categories”
Minitab will also show the “Number of Distinct Categories”. This is the number of distinct categories of parts that the measurement process is currently able to distinguish. The lower the %GR&R, the higher this number will be. Ideally you should have 5 or more distinct categories. This example had only 2 distinct categories, but only because the variability of the 10 parts was small when compared to the allowable specifications.
If the GR&R % of Tolerance is acceptable and GR&R % of Study Variation is too high, it means that your parts are too uniform to use the % of Study Variation as a reliable measure of gage capability.

22. Example #2 (GR&R = 12.3% of Tolerance)

23. Example #3 (One Distinct Category, GR&R = 114% of Tolerance)
Handling Interaction
If the ANOVA table shows a statistically significant interaction, it may or may not be real. If you cannot get it to repeat, conclude that it is probably not a true interaction.

24. In-Class Gage R&R Demonstration
Parts to be tested: Golf Tees Specs: / ”
Gage to be used: 6-inch Calipers
Software: Minitab (ANOVA Method)
Perform the GR&R, add the data to Minitab and review results.

25. What do I do if the GR&R fails to meet requirements?
Eliminate obvious causes:
- Poor repeatability for one or two operators – training
- Poor reproducibility among one or more operators – investigate for cause
Significant interaction – investigate; if not confirmed as real and/or repeatable,
disregard
Poor repeatability for all operators – inadequate training is possible, but check
for excessive within-part variability
(If %GR&R is poor due to within part variability, don’t blame the gage or the operators – the fault is with the process).
Use the Advanced GR&R Procedure (on the CD) to troubleshoot other aspects of the measurement system, as appropriate:
Gage Run chart
Accuracy (bias from the true value)
Statistical differences between operators (mean and/or variation)
Stability of the measurement process over time
Linearity (mean and/or variation)

26. Questions?
Comments?