Analysis of a two-unit standby redundant system with three states of units

Abstract

A cold-standby redundant system with two identical units and one repair facility is considered. Units can be in three states> good (I), degraded (II), and failed (III). We suppose that only the following state-transitions of a unit are possible: $I\rightarrow II, II\rightarrow III, II\rightarrow I, III\rightarrow I$. The repair of a unit of the type $II \rightarrow I$ can be interpreted as a preventive maintenance. Its realization depends on the states of both units. Several characteristics of the system (probabilities, distribution functions or their Laplace-Stieltjes transforms and mathematical expectations) are derived, e.g. time to system failure, time of non-operating period of the system and stationary-state probabilities of the couple of units of the system.