Dependability analysis of systems modeled by non-homogeneous Markov chains

The case of time non-homogeneous Markov systems in discrete time is studied in this article. In order to have measures adapted to this kind of systems, some reliability and performability measures are formulated, such as reliability, availability, maintainability and different time variables including new indicators more dedicated to electrical systems like instantaneous expected load curtailed and the expected energy not supplied on a time interval. The previous indicators are also formulated in the case of cyclic chains where asymptotic results can be obtained. The interest of taking into account hazard rate time variation, is to get more accurate and more instructive indicators but also be able to access new performability indicators that cannot be obtained by classical methods. To illustrate this, an example from an Electricité De France electrical substation is solved.