Modeling the evolution of system reliability performance under alternative environments

The dynamics of a system represented by a finite-state Markov process operating under two alternating regimes, for example, day/night, machine working/machine idling, etc., are modeled in this article. The transition rate matrices under the two regimes will usually be different. Also, the set of states of the system that are regarded as satisfactory may depend on the regime in operation: for example, a particular state of the system that may be regarded as satisfactory by day might not be tolerated at night (e. g., the headlights on a car not working). It is assumed that the regime durations are random variables and results are obtained for the availability of such a system and probability distributions for uptimes. Results and numerical examples are also given for two special cases: (i) when the regimes are of fixed duration; and (ii) when the regime durations have negative exponential distributions.