Redundancy optimization problem with warm-standby redundancy

This paper describes and demonstrates a solution methodology that determines optimal design configurations that maximize the reliability of a wide range of non-repairable systems. The problem formulation considers the generic case of warm-standby redundancy and extends state-of-the-art reliability optimization techniques in several dimensions: (1) non-constant component hazard functions, (2) warm standby components including cold and hot standby situations, (3) imperfect switches, (4) k-out-of-n redundancy structures, (5) multiple component choices, and (6) redundancy strategy choices. The problem involves selection of components, redundancy strategies, and redundancy levels to maximize system reliability subject to constraints. Optimal solutions are determined based on an equivalent binary integer programming formulation. Compared to other available methods, the proposed methodology more accurately models many engineering design problems with both active and standby redundancies. Previously, it has been difficult to determine optimal solutions for this class of problems or to calculate system reliability efficiently. The methodology is successfully demonstrated on a large problem with 14 subsystems with arbitrary failure distributions.