Confidence intervals and sample size determination for C pm

The capability index, C pm , 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 C pm 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 C pm . 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 C pm . Extensive tables are provided for the user with a simple example illustrating the facility of the technique. Copyright © 2001 John Wiley & Sons, Ltd.