On estimation of P(Y < X) for inverse Pareto distribution based on progressively first failure censored data

• Published in: PloS one Vol. 18; no. 11; p. e0287473
• Main Authors: Alharbi, Randa, Garg, Renu, Kumar, Indrajeet, Kumari, Anita, Aldallal, Ramy
• Format: Journal Article
• Language: English
• Published: San Francisco, CA USA Public Library of Science 30.11.2023; Public Library of Science (PLoS)
• Subjects: Data mining; Engineering and Technology; Evaluation; Markov processes; Medicine and Health Sciences; Monte Carlo method; Physical sciences; Quality control; Research and analysis methods; Saudi Arabia
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0287473

The stress-strength reliability (SSR) model ϕ = P ( Y < X ) is used in numerous disciplines like reliability engineering, quality control, medical studies, and many more to assess the strength and stresses of the systems. Here, we assume X and Y both are independent random variables of progressively first failure censored (PFFC) data following inverse Pareto distribution (IPD) as stress and strength, respectively. This article deals with the estimation of SSR from both classical and Bayesian paradigms. In the case of a classical point of view, the SSR is computed using two estimation methods: maximum product spacing (MPS) and maximum likelihood (ML) estimators. Also, derived interval estimates of SSR based on ML estimate. The Bayes estimate of SSR is computed using the Markov chain Monte Carlo (MCMC) approximation procedure with a squared error loss function (SELF) based on gamma informative priors for the Bayesian paradigm. To demonstrate the relevance of the different estimates and the censoring schemes, an extensive simulation study and two pairs of real-data applications are discussed.