Abstract
The process capability indices (PCIs) \(\hbox {C}_{{p}}\) and \(\hbox {C}_{{pk}}\) 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, \(\hbox {C}_{{p}}\) and \(\hbox {C}_{{pk}}\). 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 \(\hbox {C}_{{p}}\) and \(\hbox {C}_{{pk}}\) 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.
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07 September 2017
An erratum to this article has been published.
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The original version of this article was revised: The spelling of the fourth author’s name has been corrected.
An erratum to this article is available at https://doi.org/10.1007/s13369-017-2807-5.
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Kashif, M., Aslam, M., Jun, CH. et al. The Efficacy of Process Capability Indices Using Median Absolute Deviation and Their Bootstrap Confidence Intervals. Arab J Sci Eng 42, 4941–4955 (2017). https://doi.org/10.1007/s13369-017-2699-4
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DOI: https://doi.org/10.1007/s13369-017-2699-4