Bayesian Estimation of Multicomponent Stress–Strength Model Using Progressively Censored Data from the Inverse Rayleigh Distribution

TL;DR

This paper introduces Bayesian methods to estimate reliability in a stress–strength model using censored data from an inverse Rayleigh distribution.

Contribution

The novelty lies in applying Bayesian estimation with various loss functions and gamma priors for a multicomponent stress–strength model under progressive censoring.

Findings

Bayesian estimators outperformed classical maximum likelihood estimators in simulation studies.

Lindley and MCMC methods were effective for Bayesian calculations under different loss functions.

The proposed methods were validated using both simulated and real-life data.

Abstract

This paper presents a comprehensive study on the estimation of multicomponent stress–strength reliability under progressively censored data, assuming the inverse Rayleigh distribution. Both maximum likelihood estimation and Bayesian estimation methods are considered. The loss function and prior distribution play crucial roles in Bayesian inference. Therefore, Bayes estimators of the unknown model parameters are obtained under symmetric (squared error loss function) and asymmetric (linear exponential and general entropy) loss functions using gamma priors. Lindley and MCMC approximation methods are used for Bayesian calculations. Additionally, asymptotic confidence intervals based on maximum likelihood estimators and Bayesian credible intervals constructed via Markov Chain Monte Carlo methods are presented. An extensive Monte Carlo simulation study compares the efficiencies of classical and Bayesian estimators, revealing that Bayesian estimators outperform classical ones. Finally, a real-life data example is provided to illustrate the practical applicability of the proposed methods.

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