中文摘要：

建立四个串—并联冗余系统的可靠性数学模型,为每个数学模型分别建立一个线性约束,模型Ⅰ和Ⅱ是传统的串—并联冗余系统数学模型,模型Ⅲ和Ⅳ是考虑共因失效的串—并联冗余系统数学模型;应用基于泛函描述的Fenchel对偶定理,求出所建可靠性模型每级所用冗余数的最优值;与Sharma-Venkateswarn启发式算法进行比较。以系统可靠性分配问题为背景,将Fenchel对偶定理应用于可靠性最优化,为可靠性最优化提出一种新的数学方法,此方法可以使某些可靠性最优化问题得到简化。

英文摘要：

Four series-parallel system reliability models,and related linear constraint conditions as well,are developed.The equations are solved with duality theorem to obtain the optimal values.Model Ⅰ and Ⅱ are conventional independent series-parallel system reliability models.Model Ⅲ and Ⅳ are dependent series-parallel system reliability models.Duality theorem algorithm is compared with Sharma-Venkateswarn heuristic algorithm.Taking system reliability allocation as the background,Fenchel dual theorem applied to re...