Multi-Objective Redundancy Allocation for Multi-State System Design Under Epistemic Uncertainty of Component States

Multi-state is a typical characteristic of engineered systems. Most existing studies of redundancy allocation problems (RAPs) for multi-state system (MSS) design assume that the state probabilities of redundant components are precisely known. However, due to lack of knowledge and/or ambiguous judgements from engineers/experts, the epistemic uncertainty associated with component states cannot be completely avoided and it is befitting to be represented as belief quantities. In this paper, a multi-objective RAP is developed for MSS design under the belief function theory. To address the epistemic uncertainty propagation from components to system reliability evaluation, an evidential network (EN) model is introduced to evaluate the reliability bounds of an MSS. The resulting multi-objective design optimization problem is resolved via a modified non-dominated sorting genetic algorithm II (NSGA-II), in which a set of new Pareto dominance criteria is put forth to compare any pair of feasible solutions under the belief function theory. A numerical case along with a SCADA system design is exemplified to demonstrate the efficiency of the EN model and the modified NSGA-II. As observed in our study, the EN model can properly handle the uncertainty propagation and achieve narrower reliability bounds than that of the existing methods. More importantly, the original nested design optimization formulation can be simplified into a one-stage optimization model by the proposed method.