ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Statistics and Probability
Volume 11 - 2025 | doi: 10.3389/fams.2025.1668809
Bootstrap confidence intervals of process capability indices Cpy and CNpmk using different methods of estimation for Frechet distribution
Provisionally accepted
- 1The University of Azad Jammu & Kashmir, Muzaffarabad, Pakistan
- 2Universita degli Studi di Padova, Padua, Italy
- 3National University of Sciences and Technology, Islamabad, Pakistan
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Process capability analysis is the statistical evaluation of process capability to examine how well it meets or exceeds the customers satisfaction. In present work, we are intended to evaluate two critical metrics for process quality assessment, Cpy and CNpmk for asymmetric Frechet distribution using different classical estimation methods namely: maximum likelihood, least squares, weighted least squares, Cramer-von-Mises, Anderson-Darling, right-tail Anderson-Darling, along Bayesian estimation using reference and Jeffreys priors. Furthermore, Monte Carlo simulations are conducted for comparative analysis of aforementioned estimation methods, using mean squared error and width of bootstrap confidence in-tervals. Comparative analysis demonstrates that Bayesian estimation using reference prior consistently producing smaller coefficient of mean squared errors and reduced width of bootstrap intervals for small to moderately large sample sizes. Moreover, the real data analysis is also validating the advantages of Bayesian estimations for process capability analysis.
Keywords: Process capability indices, Bayesian estimators, Classical estimators, Bootstrap confidence intervals, Mean squared errors
Received: 18 Jul 2025; Accepted: 22 Sep 2025.
Copyright: © 2025 Kanwal, Abbas, Zaman and Hussain. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Mehwish Zaman, mehwish.zaman@studenti.unipd.it
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