Browsing by Author "Kashif, Muhammad"

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    Bootstrap confidence intervals of the modified process capability Index for weibull distribution
    (Springer, 2017) Kashif, Muhammad; Aslam, Muhammad; Rao, Srinivasa G.; AL-Marshadi, Ali Hussein; Jun, Chi-Hyuck
    The objective of the paper is to modify the existing process capability index (PCI) for a Weibull distribution and to construct bootstrap confidence intervals (BCIs) for the newly proposed index. Three BCIs that consist of standard, percentile and bias-corrected percentile bootstrap (BCPB) confidence intervals are constructed for the newly proposed index and the existing Pearn and Chen index. The efficiency of the newly proposed index CGPK is compared with Pearn and Chen index using their coverage probabilities and average widths. The coverage probabilities and average width of three BCIs were calculated using Monte Carlo simulation studies. The newly proposed index shows better performance than Pearn and Chen index. The results indicate that BCPB confidence interval was more efficient in both cases and outperform other two confidence intervals in all situations. The comparison of average width of BCPB apparently shows that the proposed index performed better in all cases. A real-life example is also provided for a practical application.
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    The efficacy of process capability indices using median absolute deviation and their bootstrap confidence intervals
    (Springer, 2017) Kashif, Muhammad; Aslam, Muhammad; Jun, Chi-Hyuck; Al-Marshadi, Ali Hussein; Rao, Srinivasa G.
    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.