k-out-of-n 系統及 K 端點網路上之可靠度分析

Abstract

本論文研究在 k-out-of-n 系統及 K 端點網路上之可靠度分析。從 1981 年起，在 k-out-of-n 系統上可靠度的研究，有三大系統被廣泛地 討論： (1) k-out-of-n:G 系統，(2) 連續 k-out-of-n:F系統，及 (3) 環形連續 k-out-of-n:F 系統。在本論文中，我們提出一個更一般化的模 組：權重 k-out-of-n 系統，產生在以下三個系統上之可靠度評估問題 ： (1) 權重 k-out-of-n:G系統，(2) 連續權重 k-out-of-n:F系統， 及(3) 環形連續權重 k-out-of-n:F系統。我們設計出有效率的演算法來 計算這三個系統可靠度，並且得到和原來系統的演算法相同的時間複雜度 。在 K 端點網路上之可靠度的分析，早期的研究只考慮邊線會折損而結 點不會折損的新模組。在本論文中，我們提出一個邊線和結點均會折損的 新模組。並且設計出有一個可利用多邊形行程鏈形化簡法的演算法，來計 算當邊線和結點均折損時， K 端點網路上的可靠度。 In this dissertation, we study reliability analyses on both k- out-of-n systems and K-terminals networks. For k-out-of-n systems, computing reliabilities of k-out-of-n:G system, consecutive-k-out-of-n:F system, and circular-consecutive-out- of-n:F system has been widely discussed since 1981. Here, we propose a more general model of :weighted k-out-of-n systems, which lead to new reliability evaluation problems on three systems: (1) weighted-k-out-of-n:G system, (2) consecutive- weighted-k-out-of-n:F system, and (3) circular consecutive- weighted-k-out-of-n:F system. To compute these system reliabilities, we design efficient algorithms with the same time complexities as the algorithms for the original model. For K-terminal networks reliability, the early studies consider that only edges may fail while vertices always function. In this dissertation, we propose a new model: both edges and vertices may fail. An algorithm using polygon-to-chain reductions is constructed for computing the K-terminal networks reliability with both edge and vertex failures.