M/M/R機器修理問題含有備用機器及兩種故障模式之經濟分析

Abstract

在這篇論文中，我們討論的主題為機器修理問題。在這個系統中有M部操 作機器 (operating machine) 及S部備用機器 (spare machine) ，每部 機器都有兩種壞掉模式，而這些機器是由R個修理工人所維修的。備用機 器可以考慮是冷備 (cold standby) ，暖備 (warm standby)，或是熱備 (hot standby)}。兩種壞掉模式有相同的機率被修理，其壞掉的時間和修 理的時間都是指數分配。我們不僅推導出其穩態解，而且利用消費函數 (cost function) 決定在系統中有幾個修理工人及備用機器可以使系統消 費最少而且使系統可靠度 (system availability)達到一特定標準。 In this thesis, we deal with the machine repair problem where a group of M operating machines and S spare machines both have two failure modes and are maintained by R repairmen. Spares are considered to be either cold-standby, or warm-standby, or hot- standby. The two failure modes have equal probability of repair. Failure time of the machines and repair time of the repairmen are assumed to be negative exponentially distributed. A cost model is developed in order to determine the optimal values of the number of repairmen and spares simultaneously, while maintaining the system availability at a certain level. Numerical results are presented in which several system characteristics are evaluated for three types of standby under optimal operating conditions.