Systems with randomly failing repairable components

Closed-form expressions are derived for the steady-state availability, mean rate of failure, mean duration of downtime and reliability of a general system with randomly and independently failing repairable components. Component failures are assumed to be homogeneous Poisson events in time and repair durations are assumed to be exponentially distributed.

The results are expressed in terms of the mean rates of failure and mean durations of repair of the individual components. These expressions also allow derivation of closedform expressions for the rates of change of the various probabilistic system performance measures with respect to the mean rate of failure and the mean duration of repair of each component.

These expressions provide a convenient framework for identifying important components within the system and for decisionmaking aimed at upgrading the system availability or reliability, or reducing the mean duration of system downtime. Example applications to an electrical substation system demonstrate the use of the formulas developed in the paper.