A New Approach for Solving Bi-Objective Redundancy Allocation Problem Using DOE, Simulation and ε-Constraint Method

The redundancy allocation problem (RAP) has been studied for many different system structures, objective functions, and distribution assumptions. In this paper, we present a problem formulation and a solution methodology to maximize the system steady-state availability and minimize the system cost for the repairable series-parallel system designs. In the proposed approach, the components’ time-to-failure (TTF) and time-to-repair (TTR) can follow any distribution such as the Gamma, Normal, Weibull, etc. We estimate an approximation of the steady-state availability of each subsystem in the series-parallel system with an individual meta-model. Design of experiment (DOE), simulation and the stepwise regression are used to build these meta-models. Face centred design, which is a type of central composite design is used to design experiments. According to a max–min approach, obtained meta-models are utilized for modelling the problem alongside the cost function of the system. We use the augmented ε-constraint method to reformulate the problem and solve the model. An illustrative example which uses the Gamma distribution for TTF and TTR is explained to represent the performance of the proposed approach. The results of the example show that the proposed approach has a good performance to obtain Pareto (near-Pareto) optimal solutions (system configurations).