Confidence Intervals for Cp and Cpk

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Title: Confidence Intervals for Capability Indices
Author: Keith M. Bower
Publication Source: International Society of Six Sigma Professionals, EXTRAOrdinary Sense, Vol. 2 No. 4, August 2001, pp. 6-7.

Abstract

This article investigates the use of confidence intervals for Cp and Cpk. The appropriateness of reporting confidence intervals, along with the point estimates of capability for a stable process is illustrated by way of an example.

Notes

When the paper was written, confidence intervals were not integrated into the statistical software I use when teaching. This is why a (now redundant) macro is referenced in the text. I am personally very keen to see more widespread use of confidence intervals for capability estimates.

Considering the Shewhart-Deming approach, of which I am a firm believer, this is a prime instance in which confidence intervals have a meaningful interpretation, if one recalls the assumptions upon which confidence intervals are based.

In practice, I encounter situations when practitioners blindly monitor just the point estimate of one or more capability indices. Little or no attention is paid to the sample sizes used to obtain the estimates. As indicated in the paper, small sample sizes can lead to extremely wide confidence intervals for capability indices. This needs to be an important consideration for practitioners.

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