The response surface-based robust parameter design, with its extensive use of optimization techniques and statistical tools, is known as an effective engineering design methodology for improving production processes, when input variables are quantitative on a continuous scale. In many engineering settings, however, there are situations where both qualitative and quantitative variables are considered. In such situations, traditional response surface designs may not be effective. To rectify this problem, this article lays out a foundation by embedding those input variables into a factorial design with pseudo-centre points. A 0–1 mixed-integer nonlinear programming model is then developed and the solutions found using three optimization tools, namely the outer approximation method, the branch-and-bound technique and the hybrid branch-and-cut algorithm, are compared with traditional counterparts. The numerical example shows that the proposed models result in better robust parameter design solutions than the traditional models.

Finding optimum conditions for process factors in an engineering optimization problem with response surface functions requires structured data collection using experimental design. When the experimental design space is constrained owing to external factors, its design space may form an asymmetrical and irregular shape and thus standard experimental design methods become ineffective. Computer-generated optimal designs, such as D-optimal designs, provide alternatives. While several iterative exchange algorithms for D-optimal designs are available for a linearly constrained irregular design space, it has not been clearly understood how D-optimal design points need to be generated when the design space is nonlinearly constrained and how response surface models are optimized. This article proposes an algorithm for generating the D-optimal design points that satisfy both feasibility and optimality conditions by using piecewise linear functions on the design space. The D-optimality-based response surface design models are proposed and optimization procedures are then analysed.

Optimal experimental designs are effective offline quality improvement techniques used to enhance existing products and develop new products for a constrained design region. For some practical situations, I-optimal experimental designs may be the most suitable way to construct optimal experimental design points, by addressing prediction variance to generate a measure of prediction performance over the non-standard experimental design region. The purpose of this article is three-fold: (1) the I-optimality criterion is selected for minimizing the average prediction variance; (2) fitted mean and variance response models are found; and (3) a nonlinear lexicographic goal programming model incorporating an I-optimal experimental design is proposed to find the optimum settings of controllable design factors. Comparison studies and a numerical example are provided to illustrate the effectiveness of the proposed methodology for improvement of the quality of products.