Distribution of total uptime during a given time interval

The distribution of total uptime during a given time interval for a repairable system is obtained. The total uptime is the total amount of time the system is up (in operation) during the interval. It is assumed that: (1) the system starts to operate at the beginning of the interval and alternately takes only the two states, up and down (under repair); (2) repair restores the system to "like-new". A simple approximation to the distribution function of total uptime for a shorter interval is presented.<
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