Robust design modeling and optimization for dealing with a non-convex design space

•An inner approximation-based exchange algorithm is proposed.•The fitted response functions are obtained where the design space is non-convex.•A selected optimal design concept-based robust design model is introduced.•A numerical example with the Industry 4.0 concept is given for the removal process. Classic experimental designs effectively generate experimental design points under standard design spaces such as a circle, a cube, or a sphere. However, for non-convex design spaces, traditional experimental designs are not appropriate due to nonstandard experimental design conditions. No attention has been given to developing an algorithm to generate design points for a non-convex design space in the literature. This paper is three-fold. One, this paper presents a novel exchange algorithm based on an inner approximation approach in order to construct optimal design points where the design space is non-convex. Besides, the proposed algorithm efficiently produces experimental design points for non-convex design space. In addition, it is provided a fair comparison of the proposed algorithm performance. Two, the fitted response functions of the mean, standard deviation, and variance are found using the proposed regression model construction technique where the design space is non-convex. Three, a selected optimal design concept-based robust design optimization model is developed to find Pareto optimal solution settings of chosen design factors for the non-convex design space. Finally, an Industry 4.0 concept-based numerical example is provided to illustrate how to apply the proposed methodology effectively for the non-convex design space.