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A graphical approach to obtaining confidence limits of C pk
Author(s) -
Tang Loon Ching,
Than Su Ee,
Ang Beng Wah
Publication year - 1997
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/(sici)1099-1638(199711/12)13:6<337::aid-qre103>3.0.co;2-z
Subject(s) - confidence interval , statistics , mathematics , process capability , coverage probability , range (aeronautics) , process capability index , limit (mathematics) , cdf based nonparametric confidence interval , measure (data warehouse) , parametric statistics , index (typography) , computer science , data mining , engineering , mathematical analysis , operations management , world wide web , aerospace engineering , work in process
The process capability index C pk has been widely used as a process performance measure. In practice this index is estimated using sample data. Hence it is of great interest to obtain confidence limits for the actual index given a sample estimate. In this paper we depict graphically the relationship between process potential index ( C p ), process shift index ( k ) and percentage non‐conforming ( p ). Based on the monotone properties of the relationship, we derive two‐sided confidence limits for k and C pk under two different scenarios. These two limits are combined using the Bonferroni inequality to generate a third type of confidence limit. The performance of these limits of C pk in terms of their coverage probability and average width is evaluated by simulation. The most suitable type of confidence limit for each specific range of k is then determined. The usage of these confidence limits is illustrated via examples. Finally a performance comparison is done between the proposed confidence limits and three non‐parametric bootstrap confidence limits. The results show that the proposed method consistently gives the smallest width and yet provides the intended coverage probability. © 1997 John Wiley & Sons, Ltd.