ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Statistics and Probability
Bayesian-Bootstrap process capability analysis for mixture model
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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This research contributes valuable insights into the evaluation of process capability indices Spmk and CP Y through the development of a mixture model of two components Frechet distributions based on maximum likelihood and the Bayesian estimation methods. Further, bootstrapping is used to assess the stability and performance of the estimated process capability indices. The comparative study revealed that the Bayesian estimators outperform the counter part in terms of mean squared errors and width of bootstrap confidence intervals for smaller to larger sample sizes. The real life data results reinforces the findings across different analytical approaches and these findings hold implications for researchers and the quality control experts engaged in manufacturing, services, and other industries and emphasizing the importance of methodological selections in ensuring robust and accurate process capability analysis in situations where the underlying process distribution is complex and possibly multimodal.
Keywords: Bayesian estimators, bootstrapping, Maximum likelihood estimators, Mean squared errors, Mixed Frechet distribution
Received: 12 Nov 2025; Accepted: 15 Dec 2025.
Copyright: © 2025 Kanwal, Abbas, Shamoon, 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
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