‎Stress-Strength Reliability of a Weibull-Standard Normal Distribution Based on‎ ‎Type-II Progressive Censored Samples

Abstract

In this paper, under the Type-II progressive censored scheme, we obtain the point and interval estimates of stress-strength parameter (R), when stress and strength are two independent Weibull-standard normal variables. We study the problem in three cases. First, assuming that stress and strength have the different scale parameters and the common shape parameter, we obtain maximum likelihood estimation, approximation maximum likelihood estimation and two Bayesian approximation estimates due to the lack of explicit forms. Also, we construct the asymptotic and highest posterior density intervals for R. Second, assuming that common shape parameter is known, we derive the maximum likelihood estimation and Bayes estimate and uniformly minimum variance unbiased estimate of R. Third, assuming that all parameters are unknown and different, we achieve the statistical inference of R, namely maximum likelihood estimation, approximation maximum likelihood estimation and Bayesian inference of R. Furthermore, we use the Monte Carlo simulations to compare of the performance of different methods.