Modeling of Markov Repairable System with Multi-Operating Levels and its Performance Analysis

To describe precisely the performance characteristics of Markov repairable systems, the model of Markov repairable systems with multi-operating levels was introduced. According to their performance levels, the working states were aggregated into several operating levels in the systems. The Laplace transforms of probability density functions of times that the system stays in distinct operating levels were obtained by using ion-channel theory and Laplace transformations. Also, the mean staying time of them were given. The numbers that the system visits distinct operating levels were studied and their means were presented. A numerical example was given to illustrate the results from the research in this paper.