Reliability analysis of a repairable system with repairmen selected randomly

In this paper, we deal with a repairable system with repairmen whom can be selected randomly. In reliability study, it is ordinary to substitute the steady-state reliability indices for dynamic ones because the time-dependent solution is difficult to get. But this replacement should be based on some conditions in general. Therefore it is important to study the unique existence and the expression of the dynamic solution and it is the same with its stability. This paper is devoted to studying the unique existence of the dynamic solution of the system by C₀-semigroup theory and discussing its exponential stability by analyzing the spectra distribution of the system operator and its quasi-compactness. Some reliability indices of the system are discussed with a different method from traditional one, which is simpler when considering the steady-state indices.