一種適用於非同調系統的網路可靠度改良演算法則

An Improved Algorithm for Calculating the Network Reliability of the Noncoherent System

劉熙海(Hsi-Hai Liu) ； 林玉展(Yuh-Jann Lin) ； 柯秉昌(Bing-Chang Koh) ； 陳幼林(You-Lin Chen)

《華岡工程學報》 15期 (2001/06) Pp. 185-200

https://doi.org/10.29987/CCUHKJE.200106.0013

摘要

本文提出一種適用於二位元同調系統與非同調系統的網路可靠度演算法則，主要是利用向ALL(2)定理，將輸入路徑集表示成不相交的SDP型式，再經過布林代數法則1~5，即可得到最少SDP項數的布林函數。目前文獻中所提出的演算法則均只適用於同調系統，而本文所提出的演算法則，不只適用於同調系統，也適用於非同調系統，且經改良後，可得到比ALR&ALW演算法則更少項數的SDP型式，並且已經設計成一套程式。最後，先列舉五個二位元同調系統，再列舉五個二位元非同調系統，求其最少項數的SDP型式與可靠度。

並列摘要

This paper presents a new algorithm, for calculating the reliability of the binary coherent and noncoherent network system. The virtue of this algorithm lies in its ability to express the Boolean function in SDP form on the basis of ALL (2) algorithm, reducing the number of SDP terms to the nearly smallest. While the Abraham algorithm and it's successors obtain relatively short SDP forms of the Boolean functions of coherent network systems, this new method not only generates shorter disjoint product terms than any other known SDP methods, but also is applicable to the noncoherent network system. Example 1 to 5 illustrate how this new algorithm fares better than ALR&ALW algorithm in terms of the number of SDP terms and the computation process. Example 6 to 10 illustrate how this new algorithm generates the fewest number of SDP terms for the noncoherent network system.