Reliability optimization through robust redundancy allocation models with choice of component type under fuzziness

Due to the inherent uncertainty associated with various factors in the designing stage, considering uncertainty is important in system designs. In this article, a redundancy allocation problem with active strategy and choice of component type is studied where the system engineer faces with insufficient knowledge about exact values of some characteristics of components such as reliability and cost. The impreciseness is considered in terms of fuzzy numbers with triangular and trapezoidal membership functions. To achieve a robust design under different realizations of uncertain parameters, robust models are developed, which is the first attempt in the area of redundancy allocation problems under fuzziness. In worst case, extreme values of uncertain parameters are considered. In the realistic case, the uncertain parameters are dealt with the help of the credibilistic approach of fuzzy programming and the expected value of fuzzy numbers. In other words, the robust model makes a trade-off between the expected value of system reliability as a performance measure, the deviation of system reliability, and the constraint violation where the penultimate one assures the optimality robustness and the last one preserves the feasibility robustness. The proposed models can help system/product designers and managers who are risk-averse to easily deal with the inherent uncertainty in the designing stage. At the end, numerical examples are presented and the results are analyzed.