Reliability Estimation for Unit Inverse Exponentiated Distributions

Mayank Kumar Jha (), Kundan Singh () and Yogesh Mani Tripathi ()
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Mayank Kumar Jha: E-Tailize Company
Kundan Singh: Indian Institute of Technology Patna, Department of Mathematics
Yogesh Mani Tripathi: Indian Institute of Technology Patna, Department of Mathematics

A chapter in Directional and Multivariate Statistics, 2025, pp 257-289 from Springer

Abstract: Abstract Estimation for multicomponent reliability is considered when underlying strength and stress variables follow unit inverse exponentiated distributions. We discuss structural properties for this distribution and then illustrate its applications in reliability engineering. Different estimators of reliability are derived from frequentist and Bayesian viewpoints. Maximum likelihood and Bayes estimators are discussed when a common parameter is unknown. Confidence intervals are constructed as well. Further uniformly minimum variance unbiased and exact Bayes estimators are obtained for the case common parameter is known. Point and interval estimators are compared numerically using simulations. Analysis of a real data set is presented for illustration purposes.

Keywords: Bayes estimator; Hazard rate; Highest posterior density interval; Maximum likelihood estimation; Multicomponent reliability (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-96-2004-3_14

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DOI: 10.1007/978-981-96-2004-3_14

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