Probabilistic Design: Optimizing for Six Sigma Quality

Probabilistic design to address uncertainty and variability has been approached from many different angles, by different communities. While reliability methods focus on probability of constraint satisfaction or violation, robust design methods have focused primarily on the level of performance variation, the sensitivity of design objectives. “Six Sigma” quality concepts have arisen more recently from the manufacturing arena, focusing on measuring and controlling variation. All of these approaches deal with some aspect of modeling uncertainty or variability and measuring, improving, or controlling performance variation. For the case of six sigma, the term “Design for Six Sigma (DFSS)” has been coined and is the current push in industry; however, its implementation often does not involve design. In an engineering design context, the concepts and philosophy of Six Sigma can be combined with methods from structural reliability and robust design to formulate a strategy to “optimize for six sigma” quality. Such a strategy is presented in this paper, a six sigma based probabilistic design optimization formulation. Through combining these concepts and approaches, variability is incorporated within all elements of this probabilistic optimization formulation – input design variable bound formulation, output constraint formulation, and robust objective formulation. This six sigma based probabilistic design optimization formulation, as implemented within the iSIGHT design framework, is demonstrated in this paper for the structural design of a welded joint. Results presented illustrate the trade off between performance and quality when optimizing for six sigma quality.