Stress-strength reliability of Weibull distribution based on progressively censored samples

Abstract

Based on progressively Type-II censored samples, this pape\n\t\t\t\t r deals with inference for the stress-\n\t\t\t\t strength reliability\n\t\t\t\t R\n\t\t\t\t =\n\t\t\t\t P\n\t\t\t\t (\n\t\t\t\t Y\n\t\t\t\t <\n\t\t\t\t X\n\t\t\t\t ) when\n\t\t\t\t X\n\t\t\t\t and\n\t\t\t\t Y\n\t\t\t\t are two independent Weibull distributions with\n\t\t\t\t different scale parameters, but having the same shape param\n\t\t\t\t eter. The maximum likelihood esti-\n\t\t\t\t mator, and the approximate maximum likelihood estimator of\n\t\t\t\t R\n\t\t\t\t are obtained. Different confidence\n\t\t\t\t intervals are presented. The Bayes estimator of\n\t\t\t\t R\n\t\t\t\t and the corresponding credible interval using\n\t\t\t\t the Gibbs sampling technique are also proposed. Further, we\n\t\t\t\t consider the estimation of\n\t\t\t\t R\n\t\t\t\t when\n\t\t\t\t the same shape parameter is known. The results for exponenti\n\t\t\t\t al and Rayleigh distributions can\n\t\t\t\t be obtained as special cases with different scale parameter\n\t\t\t\t s. Analysis of a real data set as well a\n\t\t\t\t Monte Carlo simulation have been presented for illustrativ\n\t\t\t\t e purposes.