Applications of a New Quantile Based Process Capability Index SpkQ$\mathbb {S}^Q_{pk}$ to Electronic and Food Industries

ABSTRACT This article presents a novel quantile‐based process capability index (PCI), denoted as , which is suitable for both normal and non‐normal process distributions, particularly in the cases where the process mean or process standard deviation cannot be easily evaluated. Here, we have considered the log‐logistic process distribution for this present study. Both point and interval estimates of the proposed PCI are derived using classical as well as Bayesian estimation methods. In the classical approach, five different point estimation methods are considered. For the Bayesian analysis, the symmetric loss function, namely, squared error loss function is incorporated to assess the proposed PCI . The Markov Chain Monte Carlo simulation technique has been effectively employed to obtain an approximate solution for . Interval estimation of the proposed index is obtained using both the asymptotic confidence interval and the parametric bootstrap confidence interval from the classical point of view and the Bayes credible interval is obtained from the Bayesian point of view. Finally, the paper compares the results through an extensive Monte Carlo simulation study with four real‐life data sets. This comparison highlights the applicability of the proposed index in practical scenarios.