Intro to MSA of Continuous Data – Part 7: R&R using Wheeler’s Honest Gage Study

[Miner]

This is the seventh in a series of articles about MSA. The focus of this article will be on alternative approaches to evaluating the repeatability and reproducibility (R&R) of a measurement system.

The de facto standard for R&R studies has been the approach documented in the AIAG MSA manual and required of companies certified to ISO TS 16949. As quality personnel move from the automotive industry into other industries, this approach has gained widespread familiarity (and notoriety). However, common usage does not mean that this is the best approach or even that it is correct. Donald J. Wheeler and Donald S. Ermer, have published several articles that point out the statistical errors of the AIAG approach, the most significant of which is the use of ratios based on the standard deviation (% Study Variation and % Tolerance). See “An Honest Gauge R&R Study” by Donald J. Wheeler, “Improved Gage R&R Measurement Studies” Quality Progress March 2006 and “Appraiser Variation in Gage R&R Measurement” Quality Progress May 2006 by Donald S. Esmer for very thorough discussions.

Wheeler’s article introduces a number of notable differences:

• Metrics based on the variance (σ2) instead of the standard deviation. These metrics are additive and total 100% unlike the AIAG metrics, which do not total to 100%.
• Fisher’s Intraclass Correlation, which measures the product variation to total variation.
• Probable Error, which estimates the effective resolution of a single measurement. This provides a guideline for the physical resolution of the gauge. The physical gauge resolution should be between the Smallest and Largest Effective Measurement Increments (based on the Probable Error).
• Process Signal Attenuation, which estimates the percentage by which the information provided by the process variation is degraded by the measurement variation.
• Monitor Classes, which classify the gauge into one of four groups:

• First Class Monitors have at least a 99% probability of detecting a 3 Standard Error shift in the process using Western Electric’s Detection Rule 1.
• Second Class Monitors have at least an 88% probability of detecting a 3 Standard Error shift in the process using Detection Rule 1 and a virtual certainty using rules 1 through 4.
• Third Class Monitors have a 91% probability of detecting a 3 Standard Error shift in the process using Detection Rule 1 through 4.
• Fourth Class Monitors should not be used. Note: the AIAG guidelines will reject all gauges except First Class Monitors.

• X% Manufacturing Specs (a.k.a. Guard Bands), which are tolerances deliberately tightened to minimize the acceptance of nonconforming product due to measurement error. This provides a sound statistical basis for establishing guard band tolerances.

I have attached an Excel file based on Wheeler’s “An Honest Gauge R&R Study” below. The file remains true to Wheeler’s approach, but also incorporates a few enhancements of my own:

• This file uses the ANOVA method to calculate the variances instead of the Range method. This provides better estimates of the variance and provides information on the Operator x Part interaction.
• The user selects one of three ANOVA tables on which to base the results:
• Full ANOVA table with interaction
  • ANOVA table with a non-significant interaction pooled into Repeatability
    • ANOVA table with a non-significant interaction and a non-significant Operator effect pooled into Repeatability
• Variance Components tables are provided for each ANOVA table.
• Links to articles written by Donald J. Wheeler are provided in relevant sections of the report to further explain some of the metrics introduced.
  
  
• “An Honest Gauge R&R Study”

​

• “Good Data, Bad Data and the Process Behavior Chart”
• “How to Establish Manufacturing Specifications”
• “Relative Probable Error”

If you have an option on the methodology used to conduct an R&R study, give serious consideration to Wheeler’s methods. While the methods documented in the AIAG MSA Manual go under the guise of guidelines and are introduced as recommended approaches, customers and ISO TS16949 auditors tend to give them the weight of requirements. Depending on your customer(s)/auditor(s), you may be able to sell them on this approach, but there are no guarantees.

The next article will be:
Intro to Measurement System Analysis (MSA) of Continuous Data – Part 8: Comparison of Two Gages

 

[Atul Khandekar]

Thank you!

 

[Ehsan Heidari]

Thanks Miner,
can we use from ANOVA table for calculation AV% , EV%, %R&R ? (you have been attached MSA 3th.xls before but it is on X-bar R method)

 

[Miner]

Thanks Miner,
can we use from ANOVA table for calculation AV% , EV%, %R&R ? (you have been attached MSA 3th.xls before but it is on X-bar R method)

You can use the VarComp column from the Variance Components table in the GRR Report tab.

These are variances, so take the square root of these to get the standard deviation. Once you have the standard deviation, you can calculate the AV% , EV%, %R&R using the AIAG formulae.

 

[Ehsan Heidari]

Thank you, I did it.
Actually, your file is so useful!!!

 

[Guest]

I have a question on Wheeler's paper "How to Establish Manufacturing Specifications". In it he he lists 99.9% chance of shipping good stuff for limits tightened by 4*PE. What is the chance when limits are tightened by 5*PE and 6*PE?
Thanks.

 

[Miner]

I researched Wheeler's papers on this topic and could not find the equations used to calculated these percentages. Out of curiosity, why would you want percentages higher than 99.9%?

 

[Guest]

In the semiconductor industry, we have customers who want us to guarantee less than 100 ppm defective parts. I did end up solving the problem using integrals of the bivariate normal distribution, which Wheeler describes in the ManSpec paper. Guess there is no simple equation to get at it.

 

[Guest]

Could you check J23 on the Graph Worksheet. It appears that STDEV is mistakenly using the variance? This is noticed when I was comparing test data from MSA3 to this and the NDC was showing an error on the EMP one. Thanks..

Sorry, let me clarify: J21 should be =SQRT('GRR Report'!E93) ????? Appears that this worksheet was copied over and modified from MSA 3rd Ed.xls...

Please advise

 

[Miner]

Could you check J23 on the Graph Worksheet. It appears that STDEV is mistakenly using the variance? This is noticed when I was comparing test data from MSA3 to this and the NDC was showing an error on the EMP one. Thanks..

Sorry, let me clarify: J21 should be =SQRT('GRR Report'!E93) ????? Appears that this worksheet was copied over and modified from MSA 3rd Ed.xls...

Please advise

I will check it out. Thank you for pointing out this possible error, and yes, I did develop this from my earlier MSA 3rd edition, so I may have overlooked this.