| The modern competitive market requires optimal, inexpensive, and reliable products ranging from simple components to complex systems with the presence of uncertainties. Probabilistic design, such as robust design and reliability-based design, offers tools for making rational design decisions with the consideration of uncertainty associated with design variables and simulation models. However, its wide applications have been hindered by its costly computation and limited capabilities. The computational inefficiency results from both the expensive probabilistic analysis (robustness assessment or reliability analysis) and the nested structure of probabilistic analysis and optimization. The aim of this dissertation is to develop efficient probabilistic analysis tools as well as design frameworks.; The contributions of this dissertation include the following: (1) two efficient robustness assessment methods using the variable transformation, dimension reduction, and numerical integration techniques; (2) three saddlepoint approximation-based methods for reliability analysis, and the generation of cumulative distribution function and probability density function curves; (3) the application of the proposed robustness assessment methods in robust design; (4) a general sequential framework of reliability-based design; and (5) the application of saddlepoint approximation in probabilistic linear programming. The effectiveness of all the proposed methods is illustrated with mathematical and engineering examples and then compared with existing methods. |
