Bayesian and non-Bayesian analysis with MCMC algorithm of stress-strength for a new two parameters lifetime model with applications

A parallel system is one of the special redundant systems that industrial systems frequently use to increase reliability and prevent unexpected failures. In this paper, a new two-parameter model called the Poisson Rayleigh distribution (PRD) is studied. Some of its statistical properties are given. Particularly, we emphasize the study of the stress–strength (SS) reliability parameter, R = p(Y < X), when X and Y have a PRD. Maximum likelihood, maximum product spacing, and Bayesian strategies are utilized to estimate the parameters. Maximum likelihood, maximum product spacing, and Bayesian techniques for R are computed. To assess how each estimation method performs, a simulation study is conducted. In order to demonstrate the adaptability of the suggested model, its goodness of fit for the PRD comparison with other models is demonstrated by application to real datasets. Finally, the SS model for the PRD was applied with two applications of real data depicting the failure times for two types of electrical insulators and pertaining to customer wait times at two banks.