Robust process capability indices Cpm and Cpmk using Weibull process

Abstract

Abstract Process Capability Indices (PCIs) are very helpful to measure the manufacturing capability and production quality of the products in many manufacturing processes. These PCIs are calculated by using a relationship between process mean and standard deviation, provided that process follows a normal distribution. In case of non-normal processes many researchers recommended the use of robust PCIs by modifying the classical PCIs. In case of robust PCIs most of the work is reported on first- and second-generation PCIs but less work is reported on third generation PCIs. The objective of this work was to evaluate the efficiency of three dispersion measures, namely median absolute deviation (MAD), interquartile range (IQR), and Gini's mean difference (GMD), as a measure of dispersion in third generation PCIs and construct their bootstrap confidence intervals (CIs). The efficacy of these measures is compared with quantile-based PCIs under different asymmetric behaviour of the Weibull process. The results showed that quantile-based PCIs are strongly influenced by high asymmetry and IQR method provides a poor estimator across all sample sizes. On the other hand, the GMD method performed well under low, moderate, and high asymmetry of the Weibull process, but its irregular behavior needs to be addressed carefully. Among all selected four methods MAD-method performed better under low and moderate asymmetric conditions. In case of interval estimation, bias-corrected percentile (BCPB) CIs was recommended for quantile-based PCIs, while percentile (PB) and percentile-t (PTB) CIs were recommended for MAD-based PCIs under all asymmetric conditions. To validate the simulated findings, two real-world datasets were analyzed that supported the simulation results.