Confidence intervals and sample size determination for Cpm

The capability index, Cpm, sometimes called the Taguchi index, has the desirable characteristic of being sensitive to both dispersion and deviation of the process average from the engineering target. As a result, the proposed estimators of Cpm have a sampling distribution that is dependent on the non-central chi-square distribution. Hence, constructing confidence intervals, performing hypothesis testing or estimating sample size requirements necessitates manipulation of a rather complex functional expression, typically beyond the capabilities of practitioners who need readily available tools. Here, a simple graphical procedure is proposed and illustrated for obtaining exact confidence intervals for Cpm. The graphical procedure allows the user to simply enter the graph with an estimate of the index and a value of the non-centrality parameter for a given sample size to arrive at end-points of 90%, 95% or 99% one-sided or two-sided confidence intervals. Detailed tables are also provided to assist the user for a wider range of sample values and sample sizes. In addition, a procedure is also presented for determining the minimum sample size required for attaining a pre-specified level of accuracy of the Cpm. Extensive tables are provided for the user with a simple example illustrating the facility of the technique. Copyright © 2001 John Wiley & Sons, Ltd.