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Lower confidence limits for process capability indices C p and C pk when data are autocorrelated
Author(s) -
Lovelace Cynthia R.,
Swain James J.,
Zeinelabdin Hisham,
Gupta Jatinder N. D.
Publication year - 2009
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.990
Subject(s) - estimator , statistics , confidence interval , mathematics , autocorrelation , autoregressive model , sampling (signal processing) , econometrics , process capability , sampling distribution , process capability index , index (typography) , computer science , engineering , operations management , filter (signal processing) , world wide web , computer vision , work in process
Many organizations use a single estimate of C p and/or C pk for process benchmarking, without considering the sampling variability of the estimators and how that impacts the probability of meeting minimum index requirements. Lower confidence limits have previously been determined for the C p and C pk indices under the standard assumption of independent data, which are based on the sampling distributions of the index estimators. In this paper, lower 100(1‐α)% confidence limits for C p and C pk were developed for autocorrelated processes. Simulation was used to generate the empirical sampling distribution of each estimator for various combinations of sample size (n), autoregressive parameter (ϕ), true index value (C p or C pk ), and confidence level. In addition, the minimum values of the estimators required in order to meet quality requirements with 100(1‐α)% certainty were also determined from these empirical sampling distributions. These tables may be used by practitioners to set minimum capability requirements for index estimators, rather than true values, for the autocorrelated case. The implications of these results for practitioners will be discussed. Copyright © 2008 John Wiley & Sons, Ltd.