Computer experiments are constructed to simulate the behavior of complex physical systems. Uniform designs have good performance in computer experiments from several aspects. In practical use, the experimenter needs to choose a small size uniform design at the beginning of an experiment due to a limit of time, budget, resources, and so on, and later conduct a follow up experiment to obtain precious information about the system, that is, a sequential experiment. The Lee distance has been widely used in coding theory and its corresponding discrepancy is an important measure for constructing uniform designs. This paper proves that all the follow up designs of a uniform design are uniform and at least two of them can be used as optimal follow up experimental designs. Thus, it is not necessary that the union of any two uniform designs yields a uniform sequential design. Therefore, this article presents a theoretical justification for choosing the best follow up design of a uniform design to construct a uniform sequential design that involves a mixture of ω ≥ 1 factors with βk ≥ 2, 1 ≤ k ≤ ω levels. For illustration of the usage of the proposed results, a closer look is given at using these results for the most extensively used six particular cases, three symmetric and three asymmetric designs, which are often met in practice.
Computer experiment Lee discrepancy Lee distance lower bound sequential design uniform design
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Ji Y B, Alaerts G, Xu C J, et al., Sequential uniform designs for fingerprints development of Ginkgo biloba extracts by capillary electrophoresis, J. Chromatography, 2006, A1128: 273–281.Google Scholar
Tong C, Refinement strategies for stratified sampling methods, Reliability Engineering and System Safety, 2006, 91: 1257–1265.CrossRefGoogle Scholar
Cheong K T W, Htay K, Tan R H C, et al., Identifying combinatorial growth inhibitory effects of various plant extracts on leukemia cells through systematic experimental design, Amer. J. Plant Sci., 2012, 3: 1390–1398.CrossRefGoogle Scholar
Elsawah A M, Constructing optimal router bit life sequential experimental designs: New results with a case study, Commun. Stat. Simulat. Comput., 2017, http://dx.doi.org/10.1080/03610918.2017.1397164.Google Scholar
Bullington K E, Hool J N, and Maghsoodloo S, A simple method for obtaining resolution IV designs for use with Taguchi orthogonal arrays, J. Qual. Technol., 1990, 22(4): 260–264.Google Scholar
Wang B, Robert G M, and John F B, A note on the selection of optimal foldover plans for 16- and 32-run fractional factorial designs, J. Stat. Plan. Inference, 2010, 140: 1497–1500.CrossRefzbMATHGoogle Scholar
Elsawah A M and Qin H, An efficient methodology for constructing optimal foldover designs in terms of mixture discrepancy, J. Korean Statist. Soc., 2016, 45: 77–88.MathSciNetCrossRefzbMATHGoogle Scholar