Performance indexes use the global standard deviation statistic to describe the past. Capability indexes use a within-subgroup measure of dispersion to characterize the process potential. However, some within-subgroup measures are better than others. This article will explain why you should not use the square root of the pooled variance statistic to compute either capability indexes or limits on process behavior charts.

The pooled variance statistic

The purpose of statistical analysis is to detect signals by first filtering out the noise. One of the major statistical advances of the 20th century was the use of the within-subgroup variation as the filter. In the analysis of variance (ANOVA), this is done by computing the pooled variance: A variance statistic for each treatment (subgroup) is found, and these values are averaged. In ANOVA, this pooled variance, also known as the mean square within (MSW), is the denominator of the F-ratio.

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