Estimations for the Kumaraswamy distribution with a partially observed competing-risks model under progressive censoring data

This research examined the application of a two-competing-risks framework using the Kumaraswamy distribution within the context of progressive Type-Ⅱ censoring. In this study, we assumed that the model follows the Kumaraswamy distribution and that the failure modes are independent and partially observed. The Type-Ⅱ progressive censoring scheme, a cornerstone of modern reliability studies, was employed here as the primary data collection framework, particularly when evaluating highly reliable products where testing time and cost are significant factors. Maximum likelihood estimators (MLEs) were established. Also, the corresponding confidence intervals for the unknown parameters were computed, and the existence and uniqueness of these estimates were rigorously proven. Furthermore, approximate confidence intervals are constructed using the observed Fisher information matrix and the percentile bootstrap interval. In the Bayesian framework, Bayes estimates and their associated credible intervals were obtained utilizing Markov chain Monte Carlo (MCMC) sampling methods. Finally, a real-world application and simulation studies were presented to illustrate the practical utility of the proposed methodology.