Modeling Systems With Two Dependent Components Under Bivariate Shock Models

Abstract

Series and parallel systems consisting of two dependent components are studied under bivariate shock models. The random variables N-1 and N-2 that represent respectively the number of shocks until failure of component 1 and component 2 are assumed to be dependent and phase-type. The times between successive shocks are assumed to follow a continuous phase-type distribution, and survival functions and mean time to failure values of series and parallel systems are obtained in matrix forms. An upper bound for the joint survival function of the components is also provided under the particular case when the times between shocks follow exponential distribution.