Maximum entropy approach to machine repair problem

For an M/G/1 machine repair problem, the steady-state probability distributions of the number of down machines are usually found by using the supplementary variable technique and recursive method. We use in this paper the required steady-state availability and the expected number of down machines to compute the maximum entropy approximation for the steady-state probability distributions of the number of down machines in the system, thus avoiding the use of supplementary variable technique. In numerical examples, comparison of the steady-state probability distributions obtained by the exact approach and the approximation procedure are provided to illustrate the effectiveness of maximum entropy approach.