Probability Constrained Optimization as a Tool for Functional Design for Six Sigma

ABSTRACT

An important up-stream activity in the overall design of a system is the so-called functional design wherein the means and tolerances of the design variables are determined with respect to the competing demands of quality and cost. In this article probability constrained optimization is invoked to produce a functional design that focuses on the goal of design for Six Sigma (i.e., improved customer satisfaction, robustness, and predictable cost levels). Herein, a maximum system probability of nonconformance is obtained from a prescribed defect rate that in turn provides the primary design constraint. The production cost provides the objective function to be minimized in order to allocate the design parameters. All three quality metrics (e.g., target/larger/smaller-is-best) and robustness are inherent in the approach. The design of an electro-mechanical servo system serves as a case study wherein three responses are related to three control variables and two noise variables by mechanistic models. Designs for selected defect rates show the practicality and potential of the approach.

KEYWORDS:

• costs
• defect rate
• mean and tolerance design
• probability
• Six Sigma

ACKNOWLEDGMENT

I thank Kwan Ryoo and Young-Kap Son for providing instructive comments on the manuscript. This work was partially funded by the National Science and Engineering Research Council of Canada (NSERC).