Comparison of two processes based on quantile-based process capability indices by using fiducial generalized confidence interval

Article Type

Research Article

Publication Title

Journal of Statistical Computation and Simulation

Abstract

Selection of the better of two suppliers or assessing whether a process has improved after taking some corrective actions are important tasks in the manufacturing industry. Process capability indices (PCIs) are often used in such situations. In this paper, we propose a method to compare the performance of two processes or two suppliers based on PCIs. Estimation of fiducial generalized confidence interval (FGCI) of the difference and ratio of two well-known quantile-based process capability index (PCI) of two processes are discussed when the underlying distribution is a location-scale distribution or transformable to a location-scale distribution such as log location-scale distribution. We discuss the case of four important distributions namely normal, lognormal, Weibull and gamma distributions. Fiducial quantities (FQ) are estimated using the maximum likelihood estimator (MLE). The performance of the estimated FGCI is compared with three non-parametric bootstrap confidence intervals (BCIs) namely, standard bootstrap (SB), percentile bootstrap (PB) and bias-corrected percentile bootstrap (BCPB) in terms of coverage probability (CP) and average width (AW) via Monte Carlo simulation. It is observed through simulation that our proposed method performs better even for small sample sizes. Two examples are given to illustrate the applicability of our proposed method.

First Page

1071

Last Page

1090

DOI

10.1080/00949655.2024.2446381

Publication Date

1-1-2025

Link to Full Text

Share

COinS