Multi-State Reliability Systems Under Discrete Time Semi-Markovian Hypothesis

We consider repairable Multi-state reliability systems with components, the lifetimes and the repair times of which are -independent. The -th component can be either in the complete failure state 0, in the perfect state , or in one of the degradation states . The sojourn time in any of these states is a random variable following a discrete distribution. Thus, the time behavior of each component is described by a discrete-time semi-Markov chain, and the time behavior of the whole system is described by the vector of paired processes of the semi-Markov chain and the corresponding backward recurrence time process. Using recently obtained results concerning the discrete-time semi-Markov chains, we derive basic reliability measures. Finally, we present some numerical results of our proposed approach in specific reliability systems, namely series, parallel, k-out-of-n:F, and consecutive-k-out-of-n:F systems.