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Confidence intervals and sample size determination for C pm
Author(s) -
Zimmer LS,
Hubele NF,
Zimmer WJ
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.380
Subject(s) - sample size determination , confidence interval , estimator , statistics , range (aeronautics) , sample (material) , process capability , sampling (signal processing) , graph , mathematics , taguchi methods , process capability index , computer science , engineering , work in process , combinatorics , chemistry , operations management , filter (signal processing) , chromatography , computer vision , aerospace engineering
The capability index, C pm , sometimes called the Taguchi index, has the desirable characteristic of being sensitive to both dispersion and deviation of the process average from the engineering target. As a result, the proposed estimators of C pm have a sampling distribution that is dependent on the non‐central chi‐square distribution. Hence, constructing confidence intervals, performing hypothesis testing or estimating sample size requirements necessitates manipulation of a rather complex functional expression, typically beyond the capabilities of practitioners who need readily available tools. Here, a simple graphical procedure is proposed and illustrated for obtaining exact confidence intervals for C pm . The graphical procedure allows the user to simply enter the graph with an estimate of the index and a value of the non‐centrality parameter for a given sample size to arrive at end‐points of 90%, 95% or 99% one‐sided or two‐sided confidence intervals. Detailed tables are also provided to assist the user for a wider range of sample values and sample sizes. In addition, a procedure is also presented for determining the minimum sample size required for attaining a pre‐specified level of accuracy of the C pm . Extensive tables are provided for the user with a simple example illustrating the facility of the technique. Copyright © 2001 John Wiley & Sons, Ltd.