summary:A two-unit cold-standby redundant system with one repair facility is considered. Each unit can be in three states: good (I), degraded (II), and failed (III). We suppose that only the following state-transitions af a unit are possible: $I\rightarrow II, II\rightarrow III, II\rightarrow I, III\rightarrow I$. The paper is devoted to the problems which arise only provided that the units of the redundant system can be in more than two states (i.e. in operating and failed states). The following characteristics dealing with a single operating period of the system are studied under the condition that at its starting instant both units are new: the whole time of operation of units in state $I$ (or $II$), the whole time of repairs of units of the type $II\rightarrow I$ (or $III\rightarrow I$) and the number of finished repairs of units of the type $II\rightarrow I$ (or $III\rightarrow I$)
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