Search

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]

Suppose that an experimenter begins the experimentation using three-level uniform designs. After the experiment is over or during the experimentation, some additional resources become available and the experimenter can afford more runs to the design. The full design obtained by augmenting the additional runs to those of the original design is called as extended design. The extended designs have been applied into computer experiments, microarray experiments and numerical integration. How does the experimenter pick the additional runs and augment the original design so as to get an optimal extended design? The main objective of the present paper is to provide an answer to this question. [ABSTRACT FROM AUTHOR]

Nonregular fractional factorial designs can provide economical designs in screening experiments. In this paper, two criteria are proposed for evaluating the projectivity and uniformity properties of projections onto active factors in two-level nonregular fractional factorial designs. Moreover, two-level nonregular fractional factorial designs derived from binary nonlinear codes with 12, 24, 32 and 40 codewords and various lengths are evaluated using the new criteria. Such designs are also evaluated under the known E ( s 2 ) criterion for optimal designs in screening experiments, and are compared to Plackett–Burman designs or to projections of Plackett–Burman designs. Results show that some binary nonlinear codes can provide useful two-level nonregular fractional factorial designs in screening experiments. A search method is proposed for finding good designs with a large number of factors, starting from a good design with the same number of runs but with a smaller number of factors. [ABSTRACT FROM AUTHOR]