Multi-class decision procedures for the inspection operation.

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: $I \to I I, I I \to I I I, I I \to I, I I I \to I$ . The repair of a unit of the type $I I \to I$ 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...