Reliability Evaluation of Non-repairable Multi-state Systems Considering Survival-Death Markov Processes

Abstract

Multi-state system (MSS) models have been extensively studied in recent years, because of their accuracy and flexibility for reliability evaluation of complex systems. One of the most important multi-state systems is the non-repairable multi-state system, which cannot be repaired during its operating time or whose repair is not economical. The “death” Markov process provides a basis for reliability analysis of the non-repairable multi-state system. It does not consider, however, the impact of start–up failures of components on system reliability. In this chapter, two models of modified “death” Markov processes considering component start–up failures are proposed. They are referred to as “survival-death” Markov processes and they differ in that the first model considers not only completely successful and failed start up but also partially successful start-up, whereas the second model only considers completely successful or failed start up. In such processes, the analytic expressions of the time-dependent transition probabilities can be obtained by using the Laplace-Stieltjes transform and the inverse Laplace-Stieltjes transform. The stochastic processes are combined with the Lz-transform technique for evaluating dynamic reliability of non-repairable MSS.