Statistical Computation of Hjorth Competing Risks Using Binomial Removals in Adaptive Progressive Type II Censoring

Refah Alotaibi, Mazen Nassar and Ahmed Elshahhat ()
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Refah Alotaibi: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Mazen Nassar: Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Ahmed Elshahhat: Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt

Mathematics, 2025, vol. 13, issue 12, 1-34

Abstract: In complex reliability applications, it is common for the failure of an individual or an item to be attributed to multiple causes known as competing risks. This paper explores the estimation of the Hjorth competing risks model based on an adaptive progressive Type II censoring scheme via a binomial removal mechanism. For parameter and reliability metric estimation, both frequentist and Bayesian methodologies are developed. Maximum likelihood estimates for the Hjorth parameters are computed numerically due to their intricate form, while the binomial removal parameter is derived explicitly. Confidence intervals are constructed using asymptotic approximations. Within the Bayesian paradigm, gamma priors are assigned to the Hjorth parameters and a beta prior for the binomial parameter, facilitating posterior analysis. Markov Chain Monte Carlo techniques yield Bayesian estimates and credible intervals for parameters and reliability measures. The performance of the proposed methods is compared using Monte Carlo simulations. Finally, to illustrate the practical applicability of the proposed methodology, two real-world competing risk data sets are analyzed: one representing the breaking strength of jute fibers and the other representing the failure modes of electrical appliances.

Keywords: reliability; Hjorth competing risks; censoring; binomial mechanism; Bayesian; Markov chains; data modeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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