  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.
