Objective Framework for Bayesian Inference in Multicomponent Pareto Stress–Strength Model Under an Adaptive Progressive Type-II Censoring Scheme

Young Eun Jeon, Yongku Kim () and Jung-In Seo ()
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Young Eun Jeon: Department of Data Science, Gyeongkuk National University, Andong 36729, Republic of Korea
Yongku Kim: Department of Statistics, Kyungpook National University, Daegu 41566, Republic of Korea
Jung-In Seo: Department of Data Science, Gyeongkuk National University, Andong 36729, Republic of Korea

Mathematics, 2025, vol. 13, issue 9, 1-23

Abstract: This study introduces an objective Bayesian approach for estimating the reliability of a multicomponent stress–strength model based on the Pareto distribution under an adaptive progressive Type-II censoring scheme. The proposed method is developed within a Bayesian framework, utilizing a reference prior with partial information to improve the accuracy of point estimation and to ensure the construction of a credible interval for uncertainty assessment. This approach is particularly useful for addressing several limitations of a widely used likelihood-based approach in estimating the multicomponent stress–strength reliability under the Pareto distribution. For instance, in the likelihood-based method, the asymptotic variance–covariance matrix may not exist due to certain constraints. This limitation hinders the construction of an approximate confidence interval for assessing the uncertainty. Moreover, even when an approximate confidence interval is obtained, it may fail to achieve nominal coverage levels in small sample scenarios. Unlike the likelihood-based method, the proposed method provides an efficient estimator across various criteria and constructs a valid credible interval, even with small sample sizes. Extensive simulation studies confirm that the proposed method yields reliable and accurate inference across various censoring scenarios, and a real data application validates its practical utility. These results demonstrate that the proposed method is an effective alternative to the likelihood-based method for reliability inference in the multicomponent stress–strength model based on the Pareto distribution under an adaptive progressive Type-II censoring scheme.

Keywords: adaptive progressive Type-II censoring scheme; multicomponent stress–strength model; objective Bayesian analysis; reference prior; reliability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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