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    Title: A note on the asymptotic distribution of the process capability index C pmk
    Authors: Wu, Shu-Fei;Liang, Mei-Chu
    Contributors: 淡江大學統計學系
    Keywords: process capability index;asymptotic distribution;confidence interval
    Date: 2010-02
    Issue Date: 2011-10-23 16:24:21 (UTC+8)
    Publisher: Abingdon: Taylor & Francis Ltd.
    Abstract: Process capability indices have been widely used to evaluate the process performance to the continuous improvement of quality and productivity. The distribution of the estimator of the process capability index C pmk is very complicated and the asymptotic distribution is proposed by Chen and Hsu [The asymptotic distribution of the processes capability index C pmk , Comm. Statist. Theory Methods 24(5) (1995), pp. 1279–1291]. However, we found a critical error for the asymptotic distribution when the population mean is not equal to the midpoint of the specification limits. In this paper, a correct version of the asymptotic distribution is given. An asymptotic confidence interval of C pmk by using the correct version of asymptotic distribution is proposed and the lower bound can be used to test if the process is capable. A simulation study of the coverage probability of the proposed confidence interval is shown to be satisfactory. The relation of six sigma technique and the index C pmk is also discussed in this paper. An asymptotic testing procedure to determine if a process is capable based on the index of C pmk is also given in this paper.
    Relation: Journal of Statistical Computation and Simulation 80(2), pp.227–235
    DOI: 10.1080/00949650802592416
    Appears in Collections:[統計學系暨研究所] 期刊論文

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