STRESS-STRENGTH RELIABILITY for P(Xr:n1}<Yk:n2) in the EXPONENTIAL CASE

Year 2013, Volume: 6 Issue: 3, 92 - 102, 31.12.2013

Zohreh Pakdaman Jafar Ahmadi

Abstract

This paper deals with the estimation problem of the multicomponent stress-strength reliability parameter when  stress, strength variates are given by two independent one-parameter exponential distributions with different parameters. It is  assumed that Y₁,...,Y_n2 are the random strengths of n₂ components  subjected to random stresses X₁,...,X_n1. Our study is concentrated on  the probability P(X_r:n1<Y_k:n2) and   the problem of frequentist and Bayesian estimation of   P(X_r:n1<Y_k:n2)  based on  X and Y-samples are  discussed.  Some special cases are considered and the small sample comparison of the reliability estimates is made through Monte Carlo simulation.

Keywords

Stress-strength reliability , Squared error loss function , Uniformly minimum variance unbiased estimator , Maximum likelihood estimator , Parallel and series systems

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