Reliability of ak-out-of-n system with repair and retrial of failed units

We consider ak-out-of-n system with repair. Life times of components are independent exponentially distributed random variables with parameter λ _i when the number of working units isi. Failed units are taken for repair to a station, manned by a single server, having no waiting room. The failed units are brought to an orbit, if the server is found to be busy, for retrial. Reliability of the system is computed in the following three situations: (i) Cold system (ii) Warm system and (iii) Hot system. Several other system characteristics are derived.