Quality and Reliability Engineering International

Process capability indices for one‐sided specification intervals and skewed distributions

Journal Article


One‐sided specification intervals are frequent in industry, but the process capability analysis is not well developed theoretically for this case. Most of the published articles about process capability focus on the case when the specification interval is two‐sided. Furthermore, usually the assumption of normality is necessary. However, a common practical situation is process capability analysis when the studied characteristic has a skewed distribution with a long tail towards large values and an upper specification limit only exists. In such situations it is not uncommon that the smallest possible value of the characteristic is 0 and that this also is the best value to obtain. We propose a new class of indices for such a situation with an upper specification limit, a target value zero, and where the studied characteristic has a skewed, zero‐bound distribution with a long tail towards large values. A confidence interval for an index in the proposed class, as well as a decision procedure for deeming a process as capable or not, is discussed. These results are based on large sample properties of the distribution of a suggested estimator of the index. A simulation study is performed, assuming the quality characteristic is Weibull distributed, to investigate the properties of the suggested decision procedure. Copyright © 2007 John Wiley & Sons, Ltd.

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