M/M/R 機器修理問題含有冷備機器及多種故障模式之經濟分析

Abstract

在本文中,我們研究穩態狀況下,含有冷備機器(cold-standby)之機器修理 問題,其中可操作機器(operating machine)含有K種故障模式.每一種壞掉 模式可被一個或多個修理工人修理且具有相同的被修理機率.機器之壞掉 時間及修理工人之修理時間均假設呈指數分配.壞掉的機器由R個修理工人 採先到先服務的方式來修理,我們不僅推導出其穩態解,更建立一個成本函 數,在維持系統效益 (system availability)於一定標準下,決定冷備機器 數及修理工人數的最佳解,以達到最低成本.在最佳操作之狀況下,我們估 計一些系統特性 (system characteristics)之數值結果.

This thesis studies the cold-standby M/M/R machine repair problem with K failure modes under steady-state conditions. It is assumed that any one mode of failure is served by one or more repairmen, and the K failure modes have equal probability of repair. Failure times of the machines and repair times of the repairmen are assumed to be follow a negative exponential distribution. A cost model is developed in order to determine the optimal values of the number of cold standbys and the number of repairmen simultaneously and maintain the system availability at a certain level. Under the optimal operating conditions, numerical results of sevsral system characteristics are presented for three and four failure modes.