Science Journal of Applied Mathematics and Statistics

| Peer-Reviewed |

Computer Simulation-Based Designs for Industrial Engineering Experiments

Received: Apr. 27, 2018    Accepted: May 19, 2018    Published: Jun. 07, 2018
Views:       Downloads:

Share This Article

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.

DOI 10.11648/j.sjams.20180603.12
Published in Science Journal of Applied Mathematics and Statistics ( Volume 6, Issue 3, June 2018 )
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), 2024. Published by Science Publishing Group

Keywords

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

References
[1] Zhang, Y. and Notz, W. I. (2015). Computer experiments with qualitative and quantitative variables: a review and reexamination. Quality Engineering, 27, 2-13.
[2] Huang, H. Z., Lin, D. K. J., Liu, M. Q. and Yang, J. F. (2016). Computer experiments with both qualitative and quantitative variables. Technometrics 58, 495-507.
[3] Nie, X., Huling, J. and Qian, P. Z. G. (2017). Accelerating large-scale statistical computation with the GOEM algorithm. Technometrics 59, 416-425.
[4] Pareek B., Ghosh, P., Wilson, H. N., Macdonald, E. K. and Baines, P. (2018). Tracking the Impact of Media on Voter Choice in Real Time: A Bayesian Dynamic Joint Model. Journal of the American Statistical Association, https://doi.org/10.1080/01621459.2017.1419134.
[5] Chen, J. K., Chen, RB, Fujii, A., Suda, R. and Wang, W. (2018). Surrogate-assisted tuning for computer experiments with qualitative and quantitative parameters. Statistica Sinica 28, 761-789.
[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.
[13] Currin, C., Mitchell, T. J., Morris, M. D. and Ylvisaker, D. (1991). Bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments. Journal of the American Statistical Association 86, 953-963.
[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.
Cite This Article
  • 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

    Copy | Download

    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

    Copy | Download

    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

    Copy | Download

  • @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://download.sciencepg.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  - 

    Copy | Download

Author Information
  • College of Mathematics and Statistics, Guangxi Normal University, Guilin, China

  • College of Mathematics and Statistics, Guangxi Normal University, Guilin, China

  • College of Mathematics and Statistics, Guangxi Normal University, Guilin, China

  • Section