k-out-of-n-system with repair: The N-policy

We consider a k-out-of-n-system with repair under N-policy. Under this policy a server is hired on failure of N units. He is sent back as soon as these N and subsequent failed units are repaired. System state probabilities in finite time and long run are derived for (i) cold, (ii) warm and (iii) hot systems. Several characteristics of these systems are obtained. Optimal N value is investigated and numerical illustrations provided.