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標題: 包含暖備備用機器與一般分配修理時間之序列結構的效益性之最佳化多餘
Optimal Redundancies for Availability of Series Systems with Warm Standby Components and General Repair Times
作者: 劉怡均
關鍵字: availability;效益性;cost-benefit;series system;general distribution;recursive method;supplementary variable technique;成本與利益之比;序列系統;一般分配;遞迴方法;輔助變數技巧
出版社: 應用數學系
摘 要
我們研究包含暖備備用機器與一般分配在三種不同序列系統結構的修理時間。主要機器與暖備備用機器的故障時間都為指數分配,其參數分別為 λ 和 α。服務者的修理時間為一般分配。
在本論文中,我們使用了遞迴方法以及利用輔助變數的技巧,在三種不同序列系統結構中,推導出在穩態模式下的效益性 At(∞)。我們取一些特別的數值代入系統之參數與機器之單位成本來比較其 At(∞),最後比較其成本與利益之比值 cost/At(∞)。

In this thesis, we study the availability analysis of three different series system configurations with warm standby components and general repair times. The time-to-failure for each of the primary and warm standby components is assumed to be exponentially distributed with respective parameter λ and α. This thesis presents a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining repair time, to develop the steady-state probability distribution of the number of working components in the system. We develop the explicit expressions for the steady-state availability, for three configurations and perform comparisons. For all three configurations, comparisons are made for specific values of distribution parameters and of the cost of the components. The configurations are ranked based on availability and cost∕benefit ratio, for three various repair time distributions: exponential, 3-stage Erlang, and deterministic, where benefit is availability.
Keywords: availability, cost-benefit, series system, general distribution, recursive method, supplementary variable technique.
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