Bayesian Inference on Stress–Strength Reliability with Geometric Distributions

This paper investigates the estimation of the stress–strength reliability parameter ρ=P(X≤Y), where stress (X) and strength (Y) are independently modeled by geometric distributions. Objective Bayesian approaches are employed by developing Jeffreys, reference, and probability-matching priors for ρ, and their effects on the resulting Bayes estimates are examined. Posterior inference is carried out using the random-walk Metropolis–Hastings algorithm. The performance of the proposed Bayesian estimators is assessed through extensive Monte Carlo simulations based on average estimates, root mean squared errors, and frequentist coverage probabilities of the highest posterior density credible intervals. Furthermore, the applicability of the methodology is demonstrated using two real data sets.