Abstract
This thesis analyzes the M/M/R machine repair problem with second optional repair. Failure times of the operating machines follow an exponential distribution. Repair times of the first essential repair and the second optional repair are assumed to follow exponential distributions. A failed machine may leave the system either after the first essential repair with probability (1-theta) or at the completion of first essential repair may instantly select to repair for second optional repair with probability theta.We obtain the steady-state solutions through matrix-geometric method. A cost model is derived to determine the optimal number of the repairmen, and the optimal values of the first essential repair rate and the second optional repair rate simultaneously, while maintain the system availability at a specified level. We use the direct search method and the Newton-Quasi method to obtain the global minimum value until the system availability constraint is satisfied.
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