Determining the discrete-time reliability of a repairable 2-out-of-(N+1):F system

A discrete-time reliability analysis of a repairable 2-out-of-(N+1):F system with active redundancy is presented. Upon failure of any one unit, system failure is avoided if the failed unit is repaired prior to any other unit failures. Starting with a Markov chain model, a novel technique involving the use of semi-absorbing states and an auxiliary coefficient matrix allows the derivation of a reliability function for this system.