| Summary: | 碩士 === 國立中興大學 === 統計學研究所 === 99 === This thesis studies the cost analysis of the M/G/1 machine repair problem with multiple imperfect coverage. When an operating machine fails, it may be immediately detected and located with a coverage probability. We first use a recursive method and supplementary variable technique to develop steady-state analytic solutions. Numerical results of various system performance measures are provided. Next, we construct a steady-state expected cost function per machine per unit time. We use the direct search method and the Newton-Quasi to determine the optimal number of operating machines Ν and the joint optimal values of the repair rate and the coverage probability с at minimum cost. Numerical examples are presented to illustrate the Newton-Quasi method. Finally, we perform a sensitivity analysis for changes in the optimal value (Ν*, μ*, с*) along with changes in specific values of the system parameters.
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