Reliability Prediction Studies of Complex Systems Having Many Failed States

Abstract

In this paper, the theory of discrete Markov processes is used to develop methods for predicting the reliability and moments of the first time to failure of complex systems having many failed states. It is assumed that these complex systems operate in a repair environment and are composed of subsystems that have known constant failure and repair rates. Specifically, complex systems composed of any finite number of subsystems are considered. The complex system at any time is in an acceptable state or in a failed state. The methods presented for the reliability modeling of such complex systems assume a state behavior that is characterizable by a stationary Markov process (also called Markov chain) with finite-dimensional state space and a discrete time set. It is shown that once the matrix of the constant failure and repair rates of the subsystems is known, and the state assignment is made, then it is a straightforward matter to obtain the probabilistic description of the complex system.