Bayesian inference of reliability in the case of zero-failure data for the binomial distribution

Document Type : Original Article

Authors

• Yuting Jiang ¹
• Xuefeng Feng ²

¹ Southwest Jiaotong University Hope College‎, ‎Chengdu 610400‎, ‎China

² Department of Statistics‎, ‎Southwest Jiaotong University‎, ‎Chengdu 611756‎, ‎China‎

10.22067/smps.2024.45973

Abstract

This article explores Bayesian inference for the reliability of the binomial distribution in cases with zero-failure data‎. ‎We propose Expected-Bayesian (E-Bayesian) and hierarchical Bayesian estimators of reliability‎, ‎considering three different joint prior distributions of hyper-parameters in the prior distribution of reliability‎, ‎which is assumed to follow a beta distribution‎. ‎We derive closed-form expressions for the E-Bayesian estimators of reliability and propose hierarchical Bayesian estimators‎, ‎which are subsequently evaluated using Monte Carlo simulations‎. ‎Furthermore‎, ‎we study the one-sided modified Bayesian (M-Bayesian) lower credible limits for reliability‎. ‎The performance of the proposed methods is demonstrated through Monte Carlo simulations‎. ‎Finally‎, ‎a real data example is analyzed for illustrative purposes‎.‎

Keywords

• E-Bayesian
• Hierarchical Bayesian
• M-Bayesian
• Reliability
• Zero-failure data

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