Designing the optimal process mean vector for mixed multiple quality characteristics

Abstract

For the manufacturing community, determining the optimal process mean can often lead to a significant reduction in waste and increased opportunity for monetary gain. Given the process specification limits and associated rework or rejection costs, the traditional method for identifying the optimal process mean involves assuming values for each of the process distribution parameters prior to implementing an optimization scheme. In contrast, this article proposes integrating response surface methods into the framework of the problem, thus removing the need to make assumptions on the parameters. Furthermore, whereas researchers have studied models to investigate this research problem for a single quality characteristic and multiple nominal-the-best type characteristics, this article specifically examines the mixed multiple quality characteristic problem. A non-linear programming routine with economic considerations is established to facilitate the identification of the optimal process mean vector. An analysis of the sensitivity corresponding to the cost structure, tolerance, and quality loss settings is also provided to illustrate their effect on the solutions.

Keywords:

• Quality
• optimal process mean vector
• response surface methodology
• multivariate skew normal distribution

Acknowledgments

Paul Goethals is currently on the faculty of Mathematical Sciences at the United States Military Academy. He holds a B.A. in Chemistry from Indiana University, an M.S. in Applied Mathematics from Florida State University, and a Ph.D. in Industrial Engineering from Clemson University. His research interests include quality engineering, robust design, and operations research.

Byung Rae Cho is on the faculty of Industrial Engineering at Clemson University. He holds an M.S. degree in Industrial and Systems Engineering from Ohio State University and a Ph.D. in Industrial Engineering from the University of Oklahoma. His research interests include design of experiments, quality and reliability engineering, robust design, tolerance analysis, and Design for Six Sigma.