System redundancy optimization with uncertain stress-based component reliability: Minimization of regret

System reliability design optimization models have been developed for systems exposed to changing and diverse stress and usage conditions. Uncertainty is addressed through defining a future operating environment where component stresses have shifted or changed for different future usage scenarios. Due to unplanned variations or changing environments and operating stresses, component and system reliability often cannot be predicted or estimated without uncertainty. Component reliability can vary due to a relative increase/decrease of stresses or operating conditions. The uncertain parameters of stresses have been incorporated directly into the new decision-making model. Risk analysis perspectives, including risk-neutral and risk-averse, are considered as system reliability objective functions. A regret function is defined, and minimization of the maximum regret provides an objective function based on random future usage stresses. This is an entirely new formulation of the redundancy allocation problem, but it is a relevant one for some problem domains. The redundancy allocation problem is solved to select the best design solution when there are multiple choices of components and system-level constraints. Nonlinear programming and a neighborhood search heuristic method are recommended to obtain the integer solutions for risk-based formulations.