Assume that we have a system with two units. For each unit, its failure frequency follows an exponential distribution with mean $\lambda_1$ and its repair time follows an exponential distribution with mean $\lambda_2$. In addition, we assume that these units fail indendently. My question is: how do i calculate the average (and ideally the distribution of) time spent in double outage conditions (i.e. both units have failed)?
Thank you in advance for your replies.