Markov process approach for analyzing periodically inspected competing-risk system embodying downtime threshold

Substantially, most repairable systems undergo ignored failure, i.e. if any failure is repaired quickly then it will not be affecting systems availability. The availability and cost for a periodically examined competing-risk system is studied embedding the downtime threshold concept. If the systems downtime is not more than a pre-specified limit, the system could be considered functional during that downtime period, i.e. the breakdown could be neglected. Contrarily, if the downtime extends that limit, the system is deemed to be functional from outset of failure till the downtime exceeding the preset limit, i.e. the breakdown is deferred. Moreover, the system is presumed to have a functional state and M modes of failure. The point and limiting availabilities are being analyzed for the aforementioned system employing the Markov process approach. Additionally, long-run average cost expression is also acquired for the proposed model. An example of a protection device is then utilized to demonstrate the drafted procedure.