The efficacy of process capability indices using median absolute deviation and their bootstrap confidence intervals

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dc.creatorKashif, Muhammad
dc.creatorAslam, Muhammad
dc.creatorJun, Chi-Hyuck
dc.creatorAl-Marshadi, Ali Hussein
dc.creatorRao, Srinivasa G.
dc.date2020-11-25T08:27:13Z
dc.date2020-11-25T08:27:13Z
dc.date2017
dc.date.accessioned2022-10-20T13:09:19Z
dc.date.available2022-10-20T13:09:19Z
dc.descriptionAbstract. Full text article available at https://doi.org/10.1007/s13369-017-2699-4
dc.descriptionThe process capability indices (PCIs) Cp and C pk are commonly used in industry to measure the process performance.The implementation of these indices required that process should follow a normal distribution. However, in many cases the underlying processes are non-normal which influence the performance of these indices. In this paper, median absolute deviation (MAD)is used as a robust measure of variability in two PCIs, Cp and Cpk . Extensive simulation experiments were performed to evaluate the performance of MAD-based PCIs under low, moderate and high asymmetric condition of Weibull, Log-Normal and Gamma distributions. The point estimation of MAD-based estimator of Cp and Cpk is encouraging and showed a good result in case of Log- Normal and Gamma distributions, whereas these estimators perform very well in case of Weibull distribution. The comparison of quantile method and MAD method showed that the performance of MAD-based PCIs is better for Weibull and Log-Normal processes under low and moderate asymmetric conditions, whereas its performance for Gamma distribution remained unsatisfactory. Four bootstrap confidence intervals (BCIs) such as standard (SB), percentile (PB), bias-corrected percentile (BCPB) and percentile-t (PTB) were constructed using quantile and MAD methods under all asymmetric conditions of three distributions under study. The bias-corrected percentile bootstrap confidence interval (BCPB) is recommended for a quantile (PC)-based PCIs, whereas CIs were recommended for MAD-based PCIs under all asymmetric conditions of Weibull, Log-Normal and Gamma distributions. A real-life example is also given to describe and validate the application of proposed methodology.
dc.identifierKashif, M., Aslam, M., Jun, C. H., Al-Marshadi, A. H., & Rao, G. S. (2017). The efficacy of process capability indices using median absolute deviation and their bootstrap confidence intervals. Arabian Journal for Science and Engineering, 42(11), 4941-4955.
dc.identifierDOI:10.1007/s13369-017-2699-4
dc.identifierhttp://hdl.handle.net/20.500.12661/2621
dc.identifier.urihttp://hdl.handle.net/20.500.12661/2621
dc.languageen
dc.publisherSpringer
dc.subjectNonparametric confidence intervals
dc.subjectMedian absolute deviation
dc.subjectMAD
dc.subjectPercentile-t bootstrap (PTB) method
dc.subjectPTB method
dc.subjectBias-corrected percentile
dc.subjectBCPB
dc.subjectGamma distributions
dc.subjectPerformance
dc.titleThe efficacy of process capability indices using median absolute deviation and their bootstrap confidence intervals
dc.typeArticle

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