stress-strength reliability of a non-identical-component- strengths system under the progressive censoring sample from the two parameter rayleigh distribution

This paper deals with the statistical inference of the stress-strength reliability of a multi-component system with non-identical-component strengths based on the progressively type-ii censored sample from the two-parameter rayleigh distribution‎. ‎both stress and strength are assumed to have a rayleigh distribution with different scale parameters yet similar location parameters‎. ‎its maximum likelihood estimate‎, ‎asymptotic confidence interval‎, ‎bayes estimates‎, ‎and highest posterior density are derived‎. ‎the uniformly minimum-variance unbiased estimator and bayes estimations for the reliability are obtained when the common location parameter is known‎. ‎different methods are compared using monte carlo simulations‎. ‎{the results demonstrate that bayes estimates outperform maximum likelihood estimates‎, ‎highest posterior density intervals outperform asymptotic intervals‎, ‎and in bayes estimates‎, ‎informative priors outperform non-informative priors.} finally‎, ‎a dataset is analyzed for illustrative purposes.