Design for six sigma through robust optimization

Abstract

The current push in industry is focused on ensuring not only that a product performs as desired but also that the product consistently performs as desired. To ensure consistency in product performance, "quality" is measured, improved, and controlled. Most quality initiatives have originated and been implemented in the product manufacturing stages. More recently, however, it has been observed that much of a product's performance and quality is determined by early design decisions, by the design choices made early in the product design cycle. Consequently, quality pushes have made their way into the design cycle, and "design for quality" is the primary objective. How is this objective measured and met? The most recent quality philosophy, also originating in a manufacturing setting, is six sigma. The concepts of six sigma quality can be defined in an engineering design context through relation to the concepts of design reliability and robustness --- probabilistic design approaches. Within this context, design quality is measured with respect to probability of constraint satisfaction and sensitivity of performance objectives, both of which can be related to a design "sigma level". In this paper, we define six sigma in an engineering design context and present an implementation of design for six sigma --- a robust optimization formulation that incorporates approaches from structural reliability and robust design with the concepts and philosophy of six sigma. This formulation is demonstrated using a complex automotive application: vehicle side impact crash simulation. Results presented illustrate the tradeoff between performance and quality when optimizing for six sigma reliability and robustness.