Computer Simulation-Based Designs for Industrial Engineering Experiments

Dongyu Zhou; Weihua Guo; Hengzhen Huang

doi:doi:10.11648/j.sjams.20180603.12

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Computer Simulation-Based Designs for Industrial Engineering Experiments

Dongyu Zhou, Weihua Guo, Hengzhen Huang

Published in Science Journal of Applied Mathematics and Statistics (Volume 6, Issue 3)

Received: 27 April 2018 Accepted: 19 May 2018 Published: 7 June 2018

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Abstract

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.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 6, Issue 3)
DOI	10.11648/j.sjams.20180603.12
Page(s)	74-80
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Computer Experiments, Design of Experiments, Gaussian Process Model, Kriging, Latin Hypercube Design

References

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[6]	Santner, T. J., Williams, B. J. and Notz, W. I. (2003). The design and analysis of computer experiments. New York: Springer.
[7]	Fang, K. T., Li, R. and Sudjianto, A. (2006). Design and modeling for computer experiments. New York: CRC Press.
[8]	McKay, M. D., Beckman, R. J. and Conover, W. J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21, 239-245
[9]	Wang, L., Yang, J. F., Lin, D. K. J. and Liu, M. Q. (2015). Nearly orthogonal Latin hypercube designs for many design columns. Statistica Sinica 25, 1599-1612.
[10]	Yang, X., Yang, J. F., Lin, D. K. J. and Liu, M. Q. (2016). A new class of nested orthogonal Latin hypercube designs. Statistica Sinica 26, 1249-1267.
[11]	Chen, H., Huang, H. Z., Lin, D. K. J. and Liu, M. Q. (2016). Uniform sliced Latin hypercube designs. Applied Stochastic Models in Business and Industry 32, 574-584.
[12]	Wang, X. L., Zhao, Y. N., Yang, J. F. and Liu, M. Q. (2017). Construction of (nearly) orthogonal sliced Latin hypercube designs. Statistics and Probability Letters 125, 174-180.
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[14]	Joseph, V. R., Hung, Y. and Sudjianto, A. (2008). Blind kriging: A new method for developing metamodels. ASME Journal of Mechanical Design 130, 031102-1-8.
[15]	Kennedy, M. C and O'Hagan, A. (2000). Predicting the output from a complex computer code when fast approximations are available. Biometrika 87, 1-13.
[16]	Fang, K. T., Liu, M. Q., Qin, H. and Zhou, Y. D. (2018). Theory and application of uniform experimental designs. New York: Springer.

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APA Style

Dongyu Zhou, Weihua Guo, Hengzhen Huang. (2018). Computer Simulation-Based Designs for Industrial Engineering Experiments. Science Journal of Applied Mathematics and Statistics, 6(3), 74-80. https://doi.org/10.11648/j.sjams.20180603.12

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ACS Style

Dongyu Zhou; Weihua Guo; Hengzhen Huang. Computer Simulation-Based Designs for Industrial Engineering Experiments. Sci. J. Appl. Math. Stat. 2018, 6(3), 74-80. doi: 10.11648/j.sjams.20180603.12

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AMA Style

Dongyu Zhou, Weihua Guo, Hengzhen Huang. Computer Simulation-Based Designs for Industrial Engineering Experiments. Sci J Appl Math Stat. 2018;6(3):74-80. doi: 10.11648/j.sjams.20180603.12

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@article{10.11648/j.sjams.20180603.12,
  author = {Dongyu Zhou and Weihua Guo and Hengzhen Huang},
  title = {Computer Simulation-Based Designs for Industrial Engineering Experiments},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {6},
  number = {3},
  pages = {74-80},
  doi = {10.11648/j.sjams.20180603.12},
  url = {https://doi.org/10.11648/j.sjams.20180603.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20180603.12},
  abstract = {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.},
 year = {2018}
}

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TY  - JOUR
T1  - Computer Simulation-Based Designs for Industrial Engineering Experiments
AU  - Dongyu Zhou
AU  - Weihua Guo
AU  - Hengzhen Huang
Y1  - 2018/06/07
PY  - 2018
N1  - https://doi.org/10.11648/j.sjams.20180603.12
DO  - 10.11648/j.sjams.20180603.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 74
EP  - 80
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20180603.12
AB  - 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.
VL  - 6
IS  - 3
ER  -

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Author Information

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

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Dongyu Zhou, Weihua Guo, Hengzhen Huang. (2018). Computer Simulation-Based Designs for Industrial Engineering Experiments. Science Journal of Applied Mathematics and Statistics, 6(3), 74-80. https://doi.org/10.11648/j.sjams.20180603.12

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ACS Style

Dongyu Zhou; Weihua Guo; Hengzhen Huang. Computer Simulation-Based Designs for Industrial Engineering Experiments. Sci. J. Appl. Math. Stat. 2018, 6(3), 74-80. doi: 10.11648/j.sjams.20180603.12

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AMA Style

Dongyu Zhou, Weihua Guo, Hengzhen Huang. Computer Simulation-Based Designs for Industrial Engineering Experiments. Sci J Appl Math Stat. 2018;6(3):74-80. doi: 10.11648/j.sjams.20180603.12

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@article{10.11648/j.sjams.20180603.12,
  author = {Dongyu Zhou and Weihua Guo and Hengzhen Huang},
  title = {Computer Simulation-Based Designs for Industrial Engineering Experiments},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {6},
  number = {3},
  pages = {74-80},
  doi = {10.11648/j.sjams.20180603.12},
  url = {https://doi.org/10.11648/j.sjams.20180603.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20180603.12},
  abstract = {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.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Computer Simulation-Based Designs for Industrial Engineering Experiments
AU  - Dongyu Zhou
AU  - Weihua Guo
AU  - Hengzhen Huang
Y1  - 2018/06/07
PY  - 2018
N1  - https://doi.org/10.11648/j.sjams.20180603.12
DO  - 10.11648/j.sjams.20180603.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 74
EP  - 80
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20180603.12
AB  - 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.
VL  - 6
IS  - 3
ER  -

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