Asymptotic availability of systems modeled by cyclic non-homogeneous Markov chains [substation reliability]

In this paper, a new approach is introduced in order to treat a particular type of Markov systems: nonhomogeneous Markov systems, that is Markov systems whose hazard rates are time-dependent. This dependence of the hazard rate function on time lead to an investigation of nonhomogeneous Markov chains, and particularly a model that undergoes cyclic behavior. In this model, the transition probabilities defined are time dependent, while they are constant in the homogeneous case. These transition probabilities are also cyclic of period d>1 which is a basic element for the asymptotic study. This paper, after a brief description of the transient analysis, deals with the asymptotic aspect of these chains where the structure of the associated graph is important. A new formulation for reliability and availability indicators is therefore be developed. The major result obtained from the use of nonhomogeneous chains is a more accurate method for modeling. Since this model integrates the entire evolution, in time, of the hazard rates, the new indicators contain a greater amount and a better quality of information. The introduction of the cyclic property of these systems also allowed asymptotic results to be obtained that can be easily used, such as the asymptotic availability. Finally, in order to illustrate the benefits of this modeling, a numerical example of a simplified electrical substation is solved.