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

We consider repairable reliability systems with m components, the lifetimes and repair times of which are independent. The l-th component can be either in the failure state 0 or in the perfect state dl or in one of the degradation states {1, 2, . . . , dl − 1}. The time of staying in any of these states is a random variable following a discrete distribution not geometric. Thus, the state of every component and consequently of the whole system is described by a discretetime semi-Markov chain together with the backward recurrence chain. Using recently obtained results concerning the discrete-time semi-Markov chains, we derive basic reliability measures in a general form. Finally, we present some numerical results of our proposed approach in specific reliability systems. 1 The General Model Let us consider a multi-state system (MSS) of order m, which means that it consists of m components which in their run are multi-state. As usually, the states of components determine the state of t...

• Type: Journal
• Year: 2011
• Where: TR
• Authors: Ourania Chryssaphinou, Nikolaos Limnios, Sonia Malefaki
• Keywords: Semi-markov Chain, State Dl, Time Semi-Markov Chain, TR 2011