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，主要是利用向農展開定理，將輸入路徑集表示成不相SDP型式，再徑過適當的選取Xi或Xi變數，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，且經發改良後，可得到比SLR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，比較本文的演算法則與SLR演算法則的SDP項數，再列舉五個二元非同調系統，求其最少項數的SDP型式與可靠度。
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 Shannon's expansion theorem, and reduces the number of SDP terms to the nearly smallest by choosing the most appropriate variable Xi and Xi. While the Abraham algorithm and its successors obtain relatively abort 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. Examples 1 to 5 illustrate how this new algorithm fares better than SLR algorithm in terms of the number of SDP terms and the computation process, Examples 6 to 10 illustrate how this new algorithm generates the fewest number of SDP terms for the noncoherent network system.
