Semi-Markov Processes

3.4 Reliability and maintainability characteristics

Reliability and maintainability characteristics and parameters in semi-Markov models are presented in many books: [6, 7, 11, 24, 32, 60, 72, 90, 93]. Assume that the evolution of a system’s reliability is described by a finite state space S SMP $\{\text{X}(\text{t}):\text{t }\ge 0\}$. Elements of a set S represent the reliability states of the system. Let S₊ consists of the functioning states (up states) and S_- contains all the failed states (down states). The subset S₊ and S_- form a partition of S, i.e., $S=S_{+}\cup S_{-}$ and ${\text{S}}_{}$