Distributions of the Estimated Process Capability Index Cpk

Lin G. H. and Pearn W. L.
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Lin G. H.: Department of Transportation & Logistic Management, National Penghu Institute of Technology, Taiwan
Pearn W. L.: Department of Industrial Engineering & Management, National Chiao Tung University, Taiwan

Stochastics and Quality Control, 2003, vol. 18, issue 2, 263-279

Abstract: Process capability indices Cp and Cpk have been widely used to provide numerical measures on process potential and process performance. While Cp measures process variation relative to the specification tolerance, which only reflects process potential, Cpk considers process variation as well as process centering, which gives an approximate measure of process yield. In this paper, the statistical properties of the estimated Cpk for two classes of stable processes are investigated under different real-world conditions: (1) normal processes with constant mean, and (2) normal processes with known probability P(μ ≥ m) = p, 0 ≤ p ≤ 1, where m is the mid-point of the specification interval. For the two classes of processes, the distributions, the probability density functions, the asymptotic behaviors, and other statistical properties of their estimators are derived.

Keywords: Process capability index; natural estimator; non-central t-distribution; asymptotic distribution (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1515/EQC.2003.263

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