Stress-strength reliability for general bivariate distributions

Abstract

An expression for the stress-strength reliability R=P(X1<X2) is obtained when the vector (X1, X2) 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 Govindarajulu's asymptotic distribution-free method when X1 and X2 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.

Keywords

• General bivariate distribution
• Parametric estimation of parameters and stress-strength reliability
• Govindarajulu's non-par-ametric interval bounds of R