Markov Chain Monte Carlo-Based Estimation of Stress–Strength Reliability Parameter for Generalized Linear Failure Rate Distributions

This paper provides Bayesian and classical inference of Stress–Strength reliability parameter, [Formula: see text], where both [Formula: see text] and [Formula: see text] are independently distributed as 3-parameter generalized linear failure rate (GLFR) random variables with different parameters. Due to importance of stress–strength models in various fields of engineering, we here address the maximum likelihood estimator (MLE) of [Formula: see text] and the corresponding interval estimate using some efficient numerical methods. The Bayes estimates of R are derived, considering squared error loss functions. Because the Bayes estimates could not be expressed in closed forms, we employ a Markov Chain Monte Carlo procedure to calculate approximate Bayes estimates. To evaluate the performances of different estimators, extensive simulations are implemented and also real datasets are analyzed.