Inference on P(Y<X) in Bivariate Rayleigh Distribution

TL;DR

This paper estimates the reliability measure R = P(Y < X) for components with bivariate Rayleigh distributed strength and stress, deriving estimators, confidence intervals, and testing procedures with simulation validation.

Contribution

It introduces maximum likelihood estimation, asymptotic and bootstrap confidence intervals, and hypothesis testing methods for R in the bivariate Rayleigh context, with comprehensive simulation analysis.

Findings

MLE of R and its asymptotic distribution derived

Bootstrap and computational confidence intervals proposed

Simulation confirms effectiveness of methods

Abstract

This paper deals with the estimation of reliability $R=P(Y<X)$ when $X$ is a random strength of a component subjected to a random stress $Y$ and $(X,Y)$ follows a bivariate Rayleigh distribution. The maximum likelihood estimator of $R$ and its asymptotic distribution are obtained. An asymptotic confidence interval of $R$ is constructed using the asymptotic distribution. Also, two confidence intervals are proposed based on Bootstrap method and a computational approach. Testing of the reliability based on asymptotic distribution of $R$ is discussed. Simulation study to investigate performance of the confidence intervals and tests has been carried out. Also, a numerical example is given to illustrate the proposed approaches.