A novel non-heuristic search technique for constructing uniform designs with a mixture of two- and four-level factors: a simple industrial applicable approach.

Uniformly scatter the design points over the experimental domain is one of the most widely used techniques to construct optimal designs (called, uniform designs) for real-world high-dimensional experiments with limited resources and without model pre-specification. Uniform designs are robust to the underlying model assumption and thus experimenters do not need to specify the models of their experiments in advance before conducting them. A uniform design affords a good design space coverage that yields more accurate approximations globally using fewer experimental trials. The construction of uniform designs is a significant challenge due to the computational complexity. The existing techniques are extremely time-consuming (heuristic search techniques), difficult for non-mathematicians experimenters, and optimal results are not guaranteed. This paper tries to help non-mathematicians experimenters by providing a simple non-heuristic search technique for constructing uniform designs for experiments with a mixture of two- and four-level factors. The efficiency of the new technique is investigated theoretically and numerically. A comparison study between the new technique and the existing techniques is given. Furthermore, the applicability of the new technique for real-world applications is discussed and demonstrated by two real industrial experiments. The results show that the new designs that are generated by the new technique are better than the existing recommended designs. [ABSTRACT FROM AUTHOR]