Equiradial designs under changing axial distances, design sizes and varying center runs with their relationships to the central composite designs

  • Authors

    • Mary Iwundu University of Port Harcourt, Nigeria
    • Henry Onu Department of Mathematics and Statistics, University of Port Harcourt, Nigeria
    2017-07-13
    https://doi.org/10.14419/ijasp.v5i2.7701
  • Equiradial Design, Central Composite Design, Axial Distance, Design Size, Center Point, D-Absolute Deviation, G-Absolute Deviation.

  • Abstract

    In assessing the preferences of equiradial designs based on design size, axial distance and number of center points in relation to the central composite designs, D-absolute deviation (D-AD) and G-absolute deviation (G-AD) are proposed as new design measures of closeness of experimental designs. Each absolute deviation is positive or zero. The G-absolute deviation is zero or approximately zero at  equals 1 center point. For  greater than 1, G-absolute deviation decreases for increasing values of . On the other hand, the D-absolute deviation decreases as the design size increases. Designs having G-AD values of zero or approximately zero are identical or near identical in G-optimality properties. Also, designs having D-AD values of zero or approximately zero are identical or near identical in D-optimality properties. It is conjecturally hoped that at some increased design size, the equiradial designs and the central composite designs, having same axial or radial distance will coincide (be identical) in their properties, with D-AD value of zero or approximately zero.

  • References

    1. [1] Akram, M. (2002). Central composite designs robust to three missing observations. A Ph.D Thesis, The Islamic University, Bahawalpur.

      [2] Antille, G. and Weinberg, A. (2000). A Study of D-optimal Designs Efficiency for Polynomial Regression. Department of Econometrics, University of Geneva. http://www.unige.ch/ses/metri/.

      [3] Atkinson, A. C. and Donev, A. N. (1992). Optimum Experimental Designs, Oxford: Oxford University Press, (1992).

      [4] Box, G. E. P. & Wilson, K. B (1951). On the experimental attainment of optimum conditions. J. R. Stat. Soc., Ser B (13)1–45.

      [5] Iwundu M. P. (2016a). Useful Numerical Statistics of Some Response Surface Methodology Designs; Journal of Mathematics Research. Vol. 8, No. 4, pg. 40-67. doi:10.5539/jmr.v8n4p40 URL: https://doi.org/10.5539/jmr.v8n4p40.

      [6] Iwundu, M. P. (2016b). On the behaviour of second-order N-point equiradial designs under varying model parameters. International Journal of Statistics and Applications, Vol. 6. No. 5, pg. 276-292.

      [7] Iwundu, M. P. and Jaja, E. I. (2017) Precision of full polynomial response surface designs on models with missing coefficients. International Journal of Advanced Statistics and Probability. Vol. 5 (1), pg. 32-36. https://doi.org/10.14419/ijasp.v5i1.7491.

      [8] Iwundu, M. P. and Otaru, O. A. P. (2014). Imposing D-optimality criterion on the design regions of the Central Composite Designs (CCD). SCIENTIA AFRICANA Vol. 13, No. 1, pg.109-119.

      [9] Khuri, A. I. and Cornel, J. A. (1996) Response Surface: Design and Analysis. Second Edition. Marcel Dekker, Inc. New York.

      [10] Kinai, R. (2015). Effect of Dropout on the Efficiency of Ds-Optimal Designs for Linear Mixed Models. Master of Arts Thesis, University of Kansas.

      [11] Myers, R. H., Montgomery, D. C. and Anderson-Cook, C. M. (2009) Response Surface Methodology: Process and Product Optimization using designed experiments. 3rd Edition. John Wiley & Sons, Inc. New Jersey.

      [12] Rady, E. A., Abd El-Monsef, M. M. E. and Seyam, M. M. (2009). Relationship among several optimality criteria. interstat.statjournals.net>YEAR>articles.

      [13] Smucker, B. J., Jensen, W. Wu, Z. and Wang, B. (2016). Robustness of Classical and Optimal Designs to Missing Observations. Computational Statistics & Data Analysis. http://doi.org/10.1016/j.csda.2016.12.001. Available online January 2017, pg. 1-17.

      [14] Srisuradetchai, P. (2015). Robust response surface designs against missing observations. A Ph.D dissertation, Montana State University, Bozeman, Montana.

      [15] Yakubu, Y., Chukwu, A. U., Adebayo, B. T. and Nwanzo, A. G. (2014). Effects of missing observations on predictive capability of central composite designs. International Journal on Computational Sciences & Applications. Vol. 4, No. 6, pg. 1-18. DOI:10.5121/ijcsa.2014.4601

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  • Received date: 2017-05-02

    Accepted date: 2017-06-01

    Published date: 2017-07-13