Availability analysis for periodically inspected systems subject to multiple failure modes

The instantaneous availability and steady-state availability of a competing-risk system undergoing periodic inspections are studied in this paper. Specifically, a repairable system with a working state and M failure modes is considered. Each failure mode has a random failure time. When the system fails from the ith(i = 1, 2,.., M) failure mode, corresponding corrective repair (CR) is performed which takes a random time Y_i (i = 1, 2,.., M). Two maintenance models are formulated. At the time of inspection, if the system is working, then the system is restored to as good as new condition in Model 1 while no maintenance actions are taken in Model 2. Some analytical results on the instantaneous availability and the steady-state availability for the two models are derived. A numerical example for an Integrated Digital Communication System is presented to demonstrate the application of the developed approach.