Journal of Quality Engineering and Management

Abstract In this paper, the Bayesian estimation of the reliability parameter, R = P (X <Y), in the two-parameter Riley distribution, is investigated under increasingly censored bond samples. This issue is studied in three different ways. In the first case, assuming that the variables stress, X, and resistance, Y, both have a common location parameter and non-common scale parameters, and all of these parameters are unknown, the Bayesian estimate R is examined. Since in this case Bayesian estimation does not have a closed form, it is approximated by both Lindley and MCMC methods. In the second case, assuming that the stress and resistance variables have a known common place parameter and the common and unknown scale parameters, the exact Bayesian estimate for R is calculated. In the third case, assuming that all parameters are different and unknown, the Bayesian R estimate is calculated using the MCMC approximate method. Bayesian belief intervals are also obtained in all methods. Finally, using Monte Carlo simulations, the performance of different estimators is compared.