Int. J. Materials and Product Technology, Vol. 25, Nos. 1/2/3, 2006 99 Copyright © 2006 Inderscience Enterprises Ltd. Two-level approximation method for reliability-based design optimisation Hae Chang Gea* and Kunjal Oza Department of Mechanical and Aerospace Engineering Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA E-mail: gea@rci.rutgers.edu E-mail: kunjal@eden.rutgers.edu *Corresponding author Abstract: In order to model uncertainties and achieve the required reliability, Reliability-Based Design Optimisation (RBDO) has evolved as a dominant design tool. Many methods have been introduced to solve the RBDO problem. However, the computational expense associated with the probabilistic constraint evaluation still limits the applicability of the RBDO to practical engineering problems. In this paper, a Two-Level Approximation method (TLA) is proposed. At the first level, a reduced second order approximation is used for better optimisation solution; at the second level a linear approximation is used for faster reliability assessment. The optimal solution is obtained iteratively. The proposed method is tested on certain numerical examples, and results obtained are compared to evaluate the cost-effectiveness. Keywords: design with uncertainty; reliability-based design optimisation. Reference to this paper should be made as follows: Gea, H.C. and Oza, K. (2006) ‘Two-level approximation method for reliability-based design optimisation’, Int. J. Materials and Product Technology, Vol. 25, Nos. 1/2/3, pp.99–111. Biographical notes: Hae Chang Gea is a Professor at the Rutgers University. He received his MS degree from The University of Southern California in 1985 and PhD degree from The University of Michigan, Ann Arbour in 1993. Professor Gea has been awarded the Best Technical Paper Award in the ASME Design Technical Conference twice and the Lilly Fellowship Award. He specialises in the Automated Design Process, and works closely with automobile and aerospace industries. His current research interests are Topology Optimisation, Design with Uncertainty and Image-based CAD systems. Kunjal Oza is a Graduate Student in the Department of Mechanical and Aerospace Engineering, Rutgers University. His research area is on the Probabilistic Design Optimisation. 1 Introduction Optimisation techniques have been extensively used in order to diminish cost and augment quality. Traditionally, the optimisation problem is formulated as a deterministic