Reliabilities of a single-unit system with multi-phased missions

Phased-mission systems (PMS) can be widely found in a lot of practical application areas. Reliability evaluations and analysis for this kind of systems become important issues. The reliability of PMS is typically defined as the probability that the system successfully accomplishes the missions of all phases. However, the k-out-of-n system success criterion for PMS has not been investigated. In this paper, according to this criterion, we develop two new models, which are static and dynamic, respectively. The assumptions for these two models are described in detail as well. The system reliabilities for both models are presented for the first time by employing finite Markov chain imbedding approach (FMCIA). In terms of FMCIA, we define different state spaces for the two models, and transition probability matrices are obtained. Then some numerical examples are given to illustrate the application of FMCIA. Finally, some discussions are made and conclusions are summarized.