An expression for the stress-strength reliability R = P( X 1 < X 2 ) is obtained when the
vector ( X 1 , X 2 ) follows a general bivariate distribution. Such distribution includes bivariate compound
Weibull, bivariate compound Gompertz, bivariate compound Pareto, among others. In the
parametric case, the maximum likelihood estimates of the parameters and reliability function R are
obtained. In the non-parametric case, point and interval estimates of R are developed using Govin-
darajulu's asymptotic distribution-free method when X 1 and X 2 are dependent. An example is given
when the population distribution is bivariate compound Weibull. Simulation is performed, based on
different sample sizes to study the performance of estimates.