Estimating the Reliability Function

Abstract

ABSTRACT:

This paper considers the problem of estimation of Rp = Pr(_Yp > max(Y₁, …, Y_p-1)) where Y1; Y2; …, Y_p are all independent random variables following one parameter exponential distributions. As an application, Rp is the stress-strength reliability of a component having strength Y_p and is subjected to several independent stresses Y1; Y2; …, Y_p-1. Apart from providing several estimators of Rp, the main thrust is on the derivation of uniformly minimum variance unbiased estimator (UMVUE). A simulation study is performed to compare the estimators obtained in this paper.