Stochastic analysis of a dependent parallel system

This article discusses the stochastic behaviour of a two-unit parallel redundant repairable system with statistically dependent units. Important performance measures for the system, namely reliability, mean time to system failure, availability, stationary availability, joint availability and interval reliability are obtained in an explicit form. The transient behaviour of the system is characterised for a wide class of repair time distributions. The lifetimes of the units are modelled as bivariate exponential to capture the statistical dependence of the units. The article concludes with a detailed investigation of the stochastic point process induced by entries to various states, which correspond to the number of failed components in the system.