A Single-Loop Approach for System Reliability-Based Design Optimization

An efficient single-loop approach for series system reliability-based design optimization problems is presented in this paper. The approach enables the optimizer to apportion the system reliability among the failure modes in an optimal way by increasing the reliability of those failure modes whose reliability can be increased at low cost. Furthermore, it identifies the critical failure modes that contribute the most to the overall system reliability. A previously reported methodology uses a sequential optimization and reliability approach. It also uses a linear extrapolation to determine the coordinates of the most probable points of the failure modes as the design changes. As a result, the approach can be slow and may not converge if the location of the most probable failure point changes significantly. This paper proposes an alternative system RBDO approach that overcomes the above difficulties by using a single-loop approach where the searches for the optimum design and for the most probable failure points proceed simultaneously. An easy to implement active set strategy is used. The maximum allowable failure probabilities of the failure modes are considered as design variables. The efficiency and robustness of the method is demonstrated on three design examples involving a beam, an internal combustion engine and a vehicle side impact. The results are compared with deterministic optimization and the conventional component RBDO formulation.