The efficacy of process capability indices using median absolute deviation and their bootstrap confidence intervals
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Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
The 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.
Description
Abstract. Full text article available at https://doi.org/10.1007/s13369-017-2699-4
Keywords
Nonparametric confidence intervals, Median absolute deviation, MAD, Percentile-t bootstrap (PTB) method, PTB method, Bias-corrected percentile, BCPB, Gamma distributions, Performance
Citation
Kashif, 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.