Multi-state device redundant systems with common-cause failures and one standby unit

Abstract This paper presents two mathematical models. Model I represents a two identical unit active redundant system whose units may fail in either of the two mutually exclusive failure modes. Similarly, model II represents a two non-identical unit active parallel system whose units either fail or survive. In addition, models I and II comprise the occurrence of common-cause failures and one standby unit. Systems are only repaired when all the system units fail (including the standby unit). System repair times are arbitrarily distributed. Laplace transforms of the state probability equations are developed.