Bayesian-bootstrap process capability analysis for mixture model - Kanwal, Tahira; Abbas, Kamran; Shamoon, Imran; Zaman, Mehwish; Hussain, Zamir (Frontiers in Applied Mathematics and Statistics, 2026)
This research contributes valuable insights into the evaluation of process capability indices, Spmk and CPY, through the development of a mixture model of two components: Frechet distributions based on maximum likelihood and the Bayesian estimation methods. Furthermore, 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 counterpart in terms of mean squared errors and width of bootstrap confidence intervals for smaller to larger sample sizes. The real-life data results reinforce 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.