Process Analysis Gage Repeatability and Reproducibility - Components of Variance

Click the Range method variance estimate or ANOVA method variance estimate button on the Quick tab of the Gage Repeatability & Reproducibility Results dialog to display a spreadsheet with the estimated standard deviations (Sigmas) for the different components. The spreadsheet will also report the proportion of the variability that is due to variability between trials (repeatability) and between appraisers or gage operators (reproducibility). Refer to the Technical Notes for computational details.

Percent of Process Variation and Tolerance

The Range method percent tolerance and ANOVA method percent tolerance buttons on the Quick tab of the Gage Repeatability & Reproducibility Results dialog are used to evaluate the performance of the measurement system with regard to the overall process variation and the respective tolerance range. After you click on either button, you will be prompted to specify the tolerance range (Total tolerance for parts) and the Number of sigma intervals. The latter value is used in the computations to define the range (spread) of the respective (repeatability, reproducibility, part-to-part, etc.) variability. Specifically, the default value (5.15) defines 5.15 times the respective Sigma estimate as the respective range of values; if the data are normally distributed, then this range defines 99% of the space under the normal curve, that is, the range that will include 99% of all values (or reproducibility/repeatability errors) due to the respective source of variation.

Percent of process variation

This value reports the variability due to different sources relative to the total variability (range) in the measurements.

Analysis of Variance

Rather than computing variance components estimates based on ranges, an accurate method for computing these estimates is based on the ANOVA mean squares (see Duncan, 1974, ASQC/AIAG, 1990; see also the Technical Notes).

You can treat the three factors in the R & R experiment (Operator, Parts, Trials) as random factors in a three-way ANOVA model (see ANOVA/MANOVA). For details concerning the different models that are typically considered, refer to ASQC/AIAG (1990, pages 92-95), or to Duncan (1974, pages 716-734). Customarily, it is assumed that all interaction effects by the trial factor are non-significant. This assumption seems reasonable, since, for example, it is difficult to imagine how the measurement of some parts will be systematically different in successive trials, in particular when parts and trials are randomized.

However, the operator by parts interaction may be important. For example, it is conceivable that certain less experienced operators will be more prone to particular biases, and hence will arrive at systematically different measurements for particular parts. If so, then one would expect a significant two-way interaction (again, refer to ANOVA/MANOVA if you are not familiar with ANOVA terminology).

In the case when the two-way interaction is statistically significant, then one can separately estimate the variance components due to operator variability, and due to the operator by parts variability

Note: in the results spreadsheet, 90% confidence limits for the variance estimates are also reported. In the case of significant interactions, the combined repeatability and reproducibility variability is defined as the sum of three components: repeatability (gage error), operator variability, and the operator-by-part variability.

If the operator by part interaction is not statistically significant a simpler additive model can be used without interactions. The Gage Repeatability & Reproducibility Results dialog contains options for reviewing the results with or without interactions.