Recursive method to calculate reliability of (M, N) systems with service facility and general vacation for repairman

A fast and memory efficient recursive method is proposed to calculate the steady state probabilities of M-out-of-N:G reliability model with vacation for repairman. It is assumed that the repair time is exponential, failure time has general distribution and vacation times are independently and identically distributed random variables with general distribution. Using the embedded Markov chain techniques steady state probabilities are computed at pre-arrival epochs and at random epochs. The distribution of waiting time of a unit before the service station (excluding the one with the service facility) has been derived.