k-out-of-n system with repair: the max(N,T) policy

We consider a k-out-of-n system with repair under the max(N,T) policy. Under this policy, the repair facility is activated for repair of failed units whenever the maximum of an exponentially distributed time duration T and the sum of N (1≤N≤n−k) random variables is realized. The repair times and lifetimes of components are assumed to be independent exponentially distributed random variables. The repaired units are assumed to be as good as new. Failed units are repaired one at a time. The repair facility is switched off the moment all failed units are back to operation. System state probabilities in the long run are derived for (a) cold (b) warm and (c) hot systems. System reliability, the distribution of time during which the server is continuously engaged and its expected duration are computed. Several other system characteristics are also obtained. Determination of the optimal values of N and α is discussed and some numerical illustrations are provided.