On estimation of P(Y < X) for inverse Pareto distribution based on progressively first failure censored data
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Date
2023-11
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Abstract
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 ran dom 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.