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.
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:
- 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.
- 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.