Process Capability Indices for Weibull Distributions and Upper Specification Limits

We consider a previously proposed class of capability indices that are useful when the quality characteristic of interest has a skewed, zero-bound distribution with a long tail towards large values and there is an upper specification with a pre-specified target value, T=0. We investigate this class of process capability indices when the underlying distribution is a Weibull distribution and focus on the situation when the Weibull distribution is highly skewed. We propose an estimator of the index in the studied class, based on the maximum likelihood estimators of the parameters in the Weibull distribution, and derive an asymptotic distribution for this estimator. Furthermore, we suggest a decision rule based on the estimated index and its asymptotic distribution and present a power comparison between the proposed estimator and a previously studied estimator. A simulation study is also performed to investigate the true significance level when the sample size is small or moderate. An example from a Swedish industry is presented. Copyright (C) 2008 John Wiley & Sons, Ltd.