求連續權重k-out-of-n:F系統可靠度之最佳演算法

Abstract

自1981年開始,計算連續k-out-of-n:F系統可靠度的問題就被大家廣泛地 討論,並提出了一個有效率的方法能在O(n)的時間內找到正確解.在此,我 們提出一個新的模組,它比原來的模組更一般化,我們將它定義為連續權重 k-out-of-n:F系統.首先,在原來的連續k-out-of-n:F系統上,我們另外在 每個單元加上正整數的價值.我們定義,只有當連續失敗單元總價值超過k 的時候,連續權重k-out-of-n:F系統才真正失敗.假若我們宣告每個單元的 價值為一,很明顯地,它是一個連續k-out-of-n:F系統.所以我們可以說,連 續k-out-of-n:F系統是連續權重k-out-of-n:F系統的一個特殊狀況.在這 篇論文中,我們提出了一個方法來計算連續權重k-out -of-n:F系統的可靠 度,此法只需O(n)的計算時間.我們確信這已是最短時間,因為整個系統至 少有k個單元需要撿查. Reliability evaluation of consecutive-k-out-of-n:F system is widely studied since 1981, and the most efficient algorithm requires O(n) computing time. In this thesis, we propose a more general model and an efficient algorithm to compute the reliability of consecutive-weighted-k-out-of-n:F system in O(n) time. Since the total nember of components is n,our algorithm is optimal. A consecutive-weighted-k-out-of-n:F system consists n components in a linear order, and each component has its own positive integer weight. A consecutive -weighted-k-out-of-n:F system fails if and only if the total weight of consecutive failed components is at least k.