Skewed zero-bound distributions and process capability indices for upper specifications

Malin Albing and Kerstin Vannman

Journal of Applied Statistics, 2009, vol. 36, issue 2, 205-221

Abstract: A common practical situation in process capability analysis, which is not well developed theoretically, is when the quality characteristic of interest has a skewed distribution with a long tail towards relatively 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 this is also the best value to obtain. Hence a target value 0 is assumed to exist. We investigate a new class of process capability indices for this situation. Two estimators of the proposed index are studied and the asymptotic distributions of these estimators are derived. Furthermore, we suggest a decision procedure useful when drawing conclusions about the capability at a given significance level, based on the estimated indices and their asymptotic distributions. A simulation study is also performed, assuming that the quality characteristic is Weibull-distributed, to investigate the true significance level when the sample size is finite.

Keywords: capability index; skewed distributions; one-sided specification interval; upper specification limit; zero-bound process data; target value 0; hypothesis testing; Weibull distribution (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1080/02664760802443954

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