Erratum to: The Efficacy of Process Capability Indices Using Median Absolute Deviation and Their Bootstrap Confidence Intervals

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.