Dynamic analysis of a complex system under preemptive repeat repair discipline

Abstract

This paper considers a two-unit complex system, in which one of the components has priority with preemptive repeat repair disciplines, described by partial differential equations with integral boundary conditions. First, we prove that the system has a unique nonnegative time-dependent solution by using the strong continuous semigroup theory of linear operators. Then, we obtain the exponential convergence of the time-dependent solution to its steady-state solution by means of the spectral properties of the corresponding operator. We also provide the asymptotic behavior of some time-dependent reliability indices, a numerical illustration showing the effects of various parameters on the system, and the validity of the theoretical analysis.