Estimating of $P(Y<X)$ in the Exponential case Based on Censored Samples

TL;DR

This paper evaluates methods to estimate the probability that stress is less than strength in systems with exponential distributions, using censored data, comparing various estimators including MLE, UMVUE, and Bayesian approaches.

Contribution

It introduces and compares multiple estimation methods for reliability in exponential models with censored samples, including Bayesian and classical estimators.

Findings

Maximum likelihood estimators perform well in bias and variance.

Bayesian estimators provide robust estimates with prior information.

Interval estimates improve reliability assessment accuracy.

Abstract

In this article, the estimation of reliability of a system is discussed $p(y<x)$ when strength, $X$, and stress, $Y$, are two independent exponential distribution with different scale parameters when the available data are type II Censored sample. Different methods for estimating the reliability are applied. The point estimators obtained are maximum likelihood estimator, uniformly minimum variance unbiased estimator, and Bayesian estimators based on conjugate and non informative prior distributions. A comparison of the estimates obtained is performed. Interval estimators of the reliability are also discussed.