Analysis of intermittently used 2-unit redundant systems with a single repair facility

We deal with a two-unit warm standby system which is used intermittently with need and no-need periods alternating in a Markovian manner. The standby unit is kept under perpetual vigil. The life time and repair time of the two units are assumed to possess independent but distinct distributions. Explicit expressions are obtained for the following quantities: 1. 1. The probability density of the time to the first detection of the system's down state (disappointment). 2. 2. The first two moments of the number of disappointments over an arbitrary time interval. 3. 3. Expected value of the cumulative duration of the disappointment. © 1979.