Availability of deteriorated system with inspection subject to common‐cause failure and human error

In this paper, a Markovian model was used to derive a closed form expression for the steady state availability for a system that is allowed to undergo several stages of deteriorations subject to several failures at each state. The failures include random failure, common‐cause failure and human error. The system is inspected after each deteriorated state, where one of the two actions is possible, no action or minimal repair which brings the system to the previous deteriorated state. A complete replacement is allowed after n deteriorated states. Moreover, the system is allowed to become as good as new after common‐cause or human error failures. The steady state availability is derived for the complete problem, and for three special cases. An example is provided to illustrate the performance of the different cases.