On the reliability of the estimated incapability index

Abstract

Abstract Greenwich and Jahr‐Schaffrath (1995) introduced the process incapability index $C_{\rm pp}= C_{\rm ip}+ C_{\rm ia}$ , which provides an uncontaminated separation between information concerning the process precision $(C_{\rm ip})$ and process accuracy $(C_{\rm ia})$ . In this paper, we consider the three indices, and investigate the statistical properties of their natural estimators. For the three indices, we obtain their UMVUEs and MLEs, and compare the reliability of the two estimators based on the relative mean square errors. In addition, we construct 90%, 95%, and 99% upper confidence limits, and the maximum values of $\hat{C}_{\rm pp}$ for which the process is capable 90%, 95%, and 99% of the time. The results obtained in this paper are useful to the practitioners in choosing good estimators and making reliable decisions on judging process capability. Copyright © 2001 John Wiley & Sons, Ltd.

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