Performance moment integration (PMI) method for quality assessment in reliability-based robust design optimization

The reliability-based robust design optimization deals with two objectives of structural design methodologies subject to various uncertainties: reliability and robustness. The reliability constraints deal with the probability of failures, while the robustness minimizes the product quality loss. In general, the product quality loss is described by using the. first two statistical moments: mean and standard deviation. In this paper, a performance moment integration ( PMI) method is proposed by using a three-level numerical integration on the output range to estimate the product quality loss. For the reliability part of the reliability-based robust design optimization, the enriched performance measure approach ( PMA+) and its numerical method, enhanced hybrid-mean value ( HMV+) method, are used. New formulations of reliability-based robust design optimization are presented for three different types of robustness objectives, such as smaller-the-better, larger-the-better, and nominal-the-best types. Examples that include an engine rubber gasket are used to demonstrate the effectiveness of reliability-based robust design optimization using the proposed PMI method for different types of robust objective.