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Obtaining confidence intervals for C pk using percentiles of the distribution of Ĉ p
Author(s) -
Hoffman Lorrie L.
Publication year - 2001
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.389
Subject(s) - estimator , percentile , confidence interval , inverse , mathematics , statistics , pascal (unit) , computation , distribution (mathematics) , algorithm , computer science , mathematical analysis , geometry , programming language
Abstract Ĉ pk is used as an estimate of process capability and can reflect performance degradation due to both shifts in the process mean and variability. Exact upper and lower confidence limits for the actual parameter value are elusive. Objections to existing estimators focus on two areas: the difficulty of executing the needed computations and the excessive widths of those confidence bounds. The CPE estimator (so called since it relies on Ĉ p ) which we derive in this paper is formed by simply multiplying Ĉ pk by a value from the inverse chi‐square distribution. A PASCAL computer program is supplied which generates those percentiles. Our CPE is compared via simulation to other estimators and is shown to be the preferred selection in most cases by providing the requisite probability coverage and narrow interval widths. Copyright © 2001 John Wiley & Sons, Ltd.