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A design is robust when the performance targets have been achieved and the effects of variation have been minimized without eliminating the causes of the variation such as manufacturing tolerances, material properties, environmental temperature, humidity, operational wear etc. In recent years several robust design concepts have been introduced in an effort to obtain optimum designs and minimize the variation in the product characteristics [1,2]. In this study, a probabilistic design analysis was performed on a catalytic converter substrate in order to determine the required manufacturing tolerance that results in a robust design. Variation in circularity (roundness) and the ultimate shear stress of the substrate material were considered. The required manufacturing tolerance for a robust design with 1,2 and 3 sigma quality levels was determined. The same manufacturing tolerance for a reliability based design with reliability levels of 85%, 90% and 95% was also determined and compared.

A methodology for topology and performance redesign of complex structures by LargE Admissible Perturbations (LEAP) has been developed since 1983 in the Department of Naval Architecture and Marine Engineering, the University of Michigan. LEAP theory has successfully solved various redesign problems for performance and simultaneous topological and performance changes. The redesign problem is defined as a two-state problem that consists of two structural states, States S1 and S2. State S1 has undesirable characteristics or performance which does not satisfy designer specifications. The unknown State S2 has the desired structural response and/or performance. The relation between State S1 and State S2 is highly nonlinear with respect to its response or topology. So far, LEAP algorithms have solved various redesign problems for large structural changes (on the order of 100%–500%) of State S1 with only one finite element analysis.