A Nonlinear Integer Programming Approach to Solving the Robust Parameter Design Optimization Problem

Robust parameter design is a widely implemented design methodology for continuous quality improvement by identifying optimal factor level settings with minimum product variation. However, apparent flaws surrounding the original version of robust parameter design have resulted in alternative approaches, of which response surface methodology using the central composite design, in particular, has drawn a great deal of attention. There is a large number of practical situations in which some or all of variables must be integers; however, the design space associated with the traditional central composite design is typically a bounded convex feasible set involving real numbers. The purpose of this paper is twofold. First, we discuss why the Box–Behnken design may be preferred over the central composite design and other three‐level designs when maintaining constant or nearly constant prediction variance associated with a second‐order model is crucial to integer‐valued robust parameter design problems. Second, we lay out the foundation to show how the Box–Behnken design is transformed into a nonlinear integer programming framework. In this paper, we develop Box–Behnken design embedded nonlinear integer programming models, using the sequential quadratic integer programming and the Karush–Khun–Tucker conditions. Comparison studies of the proposed models and traditional counterparts are also conducted. It is believed that the proposed models have the potential to impact a wide range of engineering problems, ultimately leading to process and quality improvement.