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This paper attempts to integrate a derivative-free probability analysis method to Reliability-Based Robust Design Optimization (RBRDO). The Eigenvector Dimension Reduction (EDR) method is used for the probability analysis method. It has been demonstrated that the EDR method is more accurate and efficient than the Second-Order Reliability Method (SORM) for reliability and quality assessment. Moreover, it can simultaneously evaluate both reliability and quality without any extra expense. Two practical engineering problems (vehicle side impact and layered bonding plates) are used to demonstrate the effectiveness of the EDR method.

Researchers desire to evaluate system reliability uniquely and efficiently. Despite its strong technical demand, little progress has been made on system reliability analysis in the last two decades. Up to now, bound methods for system reliability prediction have been dominant. For system reliability bounds, the second order bound method gives fairly accurate prediction for system reliability assuming that the probabilities of second-order joint events are accurately obtained. Two primary challenges in system reliability analysis are evaluation of the probabilities of second-order joint events and no unique system reliability for design optimization. Firstly, the greatest technical demand is found in an accurate and efficient method to numerically evaluate the probability of a second-order joint event.

This paper presents an innovative approach for quality engineering using the Eigenvector Dimension Reduction (EDR) Method. Currently industry relies heavily upon the use of the Taguchi method and Signal to Noise (S/N) ratios as quality indices. However, some disadvantages of the Taguchi method exist such as, its reliance upon samples occurring at specified levels, results to be valid at only the current design point, and its expensiveness to maintain a certain level of confidence. Recently, it has been shown that the EDR method can accurately provide an analysis of variance, similar to that of the Taguchi method, but is not hindered by the aforementioned drawbacks of the Taguchi method. This is evident because the EDR method is based upon fundamental statistics, where the statistical information for each design parameter is used to estimate the uncertainty propagation through engineering systems.