System States Analysis and Flow Graph Diagrams in Reliability

A method is described which permits rapid evaluation of reliability functions and some probabilistic parameters related to the operation of systems. The method is based on the concept of system states and on the observation that, in terms of such states, the probabilistic behavior of systems is well described by the Markov process in infinitesimal dt, whenever subsystems behave independently of each other and randomly in time. Out of many methods useful to determine the probability that a system is in state Sj at time t, i. e., to solve the set of system state differential equations, the algorithm of the signal flow diagram has been emphasized here. Actually, such an algorithm gives us a Laplace transform of the reliability function rapidly and easily, from which one can evaluate some probabilistic parameters related to the reliability of systems (as the well-known mean time between failures) without passing through time-domain. Several applications have been examined, some of which can be resolved with intuitive methods, while some others cannot.