Science Journal of Applied Mathematics and Statistics
Volume 6, Issue 3, June 2018, Pages: 74-80
Received: Apr. 27, 2018;
Accepted: May 19, 2018;
Published: Jun. 7, 2018
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Dongyu Zhou, College of Mathematics and Statistics, Guangxi Normal University, Guilin, China
Weihua Guo, College of Mathematics and Statistics, Guangxi Normal University, Guilin, China
Hengzhen Huang, College of Mathematics and Statistics, Guangxi Normal University, Guilin, China
Computer simulations have been receiving a lot of attention in industrial engineering as the rapid growth in computer power and numerical techniques. In contrast to physical experiments which are usually carried out in factories, laboratories or fields, computer simulations can save considerable time and cost. From the statistical perspective, the current research work about computer simulations is mostly focusing on modeling the relationship between the output variable from the simulator and the input variables set by the experimenter. However, an experimental design with careful selection of the values of the input variables can significantly affect the quality of the statistical model. Specifically, prediction on the edge area of the experimental domain, which is extremely critical for an industrial engineering experiment often suffers from inadequate data information because the design points usually do not well cover the edge area of the experimental domain. To address this issue, a new type of design, called semi-LHD is proposed in this paper. Such a design type has the following appealing properties: (1) it encompasses a Latin hypercube design as a sub-design so that the design points are uniformly scattered over the interior of the design region; and (2) it possesses some extra marginal design points which are close to the edge so that the prediction accuracy on the edge area of the experimental domain is fully taken into account. Detailed algorithms for finding the marginal design points and how to construct the proposed semi-LHDs are given. Numerical comparisons between the proposed semi-LHDs with the commonly-used Latin hypercube designs, in terms of prediction accuracy, are illustrated through simulation studies. It turns out that the proposed semi-LHDs yield desirable prediction accuracy not only in the interior but also on the edge area of the experimental domain, so they are recommended as the experimental designs for simulation-based industrial engineering experiments.
Computer Simulation-Based Designs for Industrial Engineering Experiments, Science Journal of Applied Mathematics and Statistics.
Vol. 6, No. 3,
2018, pp. 74-80.
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