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- Title
Parametric inference of the loss based index Cpm for normal distribution.
- Authors
Saha, Mahendra; Dey, Sanku; Wang, Liang
- Abstract
The process capability index (PCI) has been introduced as a tool to aid in the assessment of process performance and most of the traditional PCIs performed well when process follows the normal behavior. In this article, we consider a PCI, Cpm for normal random variables. The objective of this article is five fold: First, six different methods of estimation of the PCI Cpm are addressed from frequentist approaches and compare them in terms of their mean squared errors using extensive numerical simulations. Second, we compare three bootstrap confidence intervals (BCIs) of the PCI Cpm including standard bootstrap, percentile bootstrap, and bias‐corrected percentile bootstrap. Third, Bayesian estimation is considered under four loss functions (symmetric as well as asymmetric) using normal prior for location parameter and inverse gamma prior for the scale parameter for the considered model. Also, we obtain highest posterior density (HPD) credible intervals of the PCI Cpm. Fourth, a new cost effective PCI, namely, Cpmc is introduced by incorporating tolerance cost function in the index Cpm. Fifth, the power of the test is obtained, and Monte Carlo simulation study has been carried out to compare the performances of the classical BCIs and HPD credible intervals of PCIs Cpm and Cpmc in terms of average widths and coverage probabilities. Finally, two real data sets have been analyzed for illustrative purposes.
- Subjects
GAUSSIAN distribution; MONTE Carlo method; BAYES' estimation; RANDOM variables; COST functions
- Publication
Quality & Reliability Engineering International, 2022, Vol 38, Issue 1, p405
- ISSN
0748-8017
- Publication type
Article
- DOI
10.1002/qre.2987