Title: The asymptotic distribution of the estimated process capability index (C)over-tilde(pk)
Authors: Chen, SM
Pearn, WL
工業工程與管理學系
Department of Industrial Engineering and Management
Keywords: process capability index;asymptotic distribution;process mean;process standard deviation
Issue Date: 1997
Abstract: Bissell (1990) proposed an estimator <(C)over cap (pk)> for the process capability index C-pk assuming that P(mu greater than or equal to m) = 0, or 1, where mu is the process mean, and m is the midpoint between the upper and lower specification limits. Pearn and Chen (1996) considered a new estimator <(C)over tilde (pk)>, which relaxes Bissell's assumption on the process mean. The evaluation of <(C)over tilde (pk)> only requires the knowledge of P(mu greater than or equal to m) = p, where 0 less than or equal to p less than or equal to 1. The new estimator <(C)over bar (pk)> is unbiased, and the variance is smaller than that of Bissell's. In this paper, we investigated the asymptotic properties of the estimator <(C)over tilde (pk)> under general conditions. We derived the limiting distribution of <(C)over tilde (pk)> for arbitrary population assuming the fourth moment exists. The asymptotic distribution provides some insight into the properties of <(C)over tilde (pk)> which may not be evident from its original definition.
URI: http://hdl.handle.net/11536/811
ISSN: 0361-0926
Journal: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
Volume: 26
Issue: 10
Begin Page: 2489
End Page: 2497
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