Conditional Distributions and Reliability Analysis Associated with Marshall-Olkin Bivariate Exponential Distribution

Marshall-Olkin bivariate exponential distribution

Abstract

By considering the bivariate exponential distribution due to Marshall and Olkin (1967), we derive the conditional distributions and regression equations. It is observed that the regression equations are non-linear. An alternative derivation for the moment generating function using three independent exponential distributions is also given. Assuming that the joint distribution of the
component failure times is bivariate exponential, we obtain the reliability measures for two-unit standby, parallel and series systems.