Analysis and optimization of an M/G/1 machine repair problem with multiple imperfect coverage

This paper examines an M/G/1 machine repair problem with multiple imperfect coverage. When an operating machine fails, it is immediately detected and located with coverage probability c. We first use a recursive method and supplementary variable technique to develop steady-state analytic solutions. Various system performance measures are developed based on the steady-state probability distributions. We then construct the expected cost function per machine per unit time and formulate an optimization problem to determine the minimum cost. Direct search and Quasi-Newton methods are implemented to search for the optimal number of operating machines, the optimal repair rate, and the optimal coverage factor. Sensitivity analysis and numerical illustrations are also provided.