Optimal reliability design (ORD) problem is challenging and fundamental to the study of system reliability. For a system with u components/stages where each of them can be set in m possible reliability levels, state-of-the-art linear reformulation models of ORD problem require O(um) binary variables, O(mn) continuous variables together with either O(mn) inequality constraints or O(um) equality constraints. Using the special property of prime factorization and adopting the logarithmic expression technique, in this article, we propose a novel linear reformulation model of the ORD problem requiring O(um) binary variables, O(mn n! ) continuous variables, and very few linear constraints. This theoretic reduction in variables and constraints can lead to significant savings in computational efforts. Our numerical experiments further confirm the drastic reduction in computational time for solving ORD problems in large size.

中文翻译：

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最优可靠性设计的素对数法


最优可靠性设计（ORD）问题是系统可靠性研究的一个具有挑战性和基础的问题。对于具有 u 个组件/级的系统，其中每个组件/级都可以设置为 m 个可能的可靠性级别，ORD 问题的最先进的线性重构模型需要 O(um) 个二元变量、O(mn) 个连续变量以及O(mn) 不等式约束或 O(um) 等式约束。利用质因数分解的特殊性质并采用对数表达技术，在本文中，我们提出了一种新颖的 ORD 问题线性重构模型，该模型需要 O(um) 二元变量、O(mn n! ) 连续变量和很少的线性变量限制。理论上变量和约束的减少可以显着节省计算量。我们的数值实验进一步证实了解决大尺寸 ORD 问题的计算时间大幅减少。