Some reliability indexes and sojourn time distributions for a repairable degradation model

In this article, a degradation model for repairable systems is developed, based on a continuous-time Markov process with multiple discrete states. The discrete states are divided into two types: up and down states, and represent that the system is undergoing a range of degradation levels from perfect functioning to complete failure. The closed-form expressions of four common reliability indexes are derived using the technique of aggregated stochastic process. The indexes include point availability, multi-point availability, interval availability and multi-interval availability. Also, the analytical solution to lower degradation probabilities and some sojourn time distributions are derived using the technique of aggregated stochastic process. Finally, numerical examples are given to illustrate the results obtained in the article.

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