The Expected Number of Visits to State k before a Total System Failure of a Complex System with Repair Maintenance

This paper investigates the stochastic behavior before a total system failure for a standby redundant system with repair maintenance. It derives the expected number of visits to state k before a total system failure and other measures explicitly by considering “taboo” probabilities for an imbedded Markov chain generated by the system. The transition probabilities and the first-passage distributions are also discussed. Numerical examples are presented.