Optimal and efficient production of rose coco beans through the twenty-four points second order rotatable design

  • Authors

    • Isaac Tum Statistics Lecturer Moi University Kenya
    • Joseph Koske Statistics Lecturer Moi University Kenya
    • John Mutiso Statistics Lecturer Moi University Kenya
    2017-12-15
    https://doi.org/10.14419/ijasp.v6i1.8552
  • Response Surface Methodology, Second Order Design, Optimality, Coded Levels, Natural Levels, Calculus Optimum Value, Rose Coco Beans.

  • The yield results of the twenty four points response surface methodology (RSM) design permitted a response surface to be fitted easily and provided spherical information contours besides the realizations of an optimum combination of the fertilizers in rose coco beans, which resulted in economic use of scarce resources for optimal production of rose coco beans. In this study an existing A-optimum and D-efficient second order rotatable design in three dimensions was used to produce rose coco beans optimally and efficiently. The general objective of the study was to produce rose coco beans (Phaseolus vulgaris) optimally and efficiently using an existing A-optimum and D-efficient twenty four points second order rotatable design in three dimensions in a greenhouse setting using three inorganic fertilizers, namely, nitrogen, phosphorus and potassium. Thus the study was accomplished using the calculus optimum value of the free/letter parameter f=1.1072569. The specific objectives were to estimate the linear parameters, thereby making available for the yield response of rose coco beans at calculus optimum value design for the first time, fitted and tested the model adequacy via lack of fit test, and then found the setting of the experimental factors that produces optimal response using contour plots to assist visualizes the response surfaces. This study demonstrated the importance of statistical methods in the optimal and efficient production of rose coco beans. The results showed that the three factors: nitrogen, phosphorus, and potassium contributed significantly on the yield of rose coco beans (p<0.05). The regression coefficients were determined by employing least square's techniques to predict quadratic polynomial model for group 3 greenhouse (GP3G) for the three fertilizer combinations. In GP3G, the second-order model was adequate at 1% level of significance with a p-value of 0.0034. The analysis of variance (ANOVA) of response surface for rose coco yield showed that this design was adequate due to satisfactory level of a coefficient of determination, R2, 0.8066 (GP3G) and coefficient variation, CV was 10.30. The canonical analysis showed that there was the saddle point for GP3G, meaning there was no unique optimum; therefore, ridge analysis was used to overcome the saddle problem. The result from ridge analysis provided the maximum yield of 70.25grams for the three fertilizer combinations at radii of one. We, therefore, recommend the use of GP3G design since it gave the required coefficient of determination (R2=80.66) and the maximum yield (70. 25grams) was achieved.

  • References

    1. [1] Bose, R. C. and Draper, N.R. (1959). Second order rotatable designs in three dimensions.Ann. Math. Stat., Vol. 30, (1959): pp. 1097-1112.https://doi.org/10.1214/aoms/1177706093.

      [2] Box, G.E.P. (1952). Multi-factor designs of the first order. Journal of Biometrika: 39, 49-57.https://doi.org/10.1093/biomet/39.1-2.49.

      [3] Box, G.E.P, Wilson, K.B. (1951). On the Experimental Attainment of Optimum Conditions. Journal of the Royal Statistical Society B: 13, 1–45.

      [4] Draper, N.R. (1960). Second order rotatable designs in four or more dimension. Ann. Math. Stat., Vol. 31, pp. 23-33.https://doi.org/10.1214/aoms/1177705984.

      [5] Khuri, A. I., and Cornell, J. A. (1996). Response Surfaces: Designs and Analysis. Marcel Dekker, New York.

      [6] Koske, J.K., Mutiso J.M., &Kosgei, M.K. (2008). A specific optimum second order rotatable design of twenty four points with a practical example. East African Journal of pure and applied science, school of science, Moi University, Eldoret Kenya.

      [7] Koske, J.K., Mutiso J.M., & Tum, I.K. (2012). Construction of a Practical Optimum Second Order Rotatable Designs in the Three Dimensions. Advances and Applications in Statistics. Vol. 30, No. 1, 2012 pp 31-43, ISSN 0972-3617.

      [8] Koech, F. (2016). Relative efficiency and DT- optimality criteria for the six specific second order rotatable designs. Unpublished M. Phil. Thesis, Moi University.

      [9] Little, T.M., and Hills, F.J. (1978).Agricultural experimental design and analysis. New York: John Wiley.

      [10] Montgomery D. C. (2005). Design and Analysis of Experiments response surface methods and design. John Willey and Sons Inc. New Jersey.

      [11] Mutiso, J. M. (1998). Second and Third Order Specific and Sequential Rotatable Designs in K Dimensions. D.Phil. Thesis, Moi University.

      [12] Myers, R. H., and Montgomery, D. C. (2002). Response Surface Methodology: Process and Product Optimization Using Designed Experiments 2nd ed. J. Wiley, New York.

      [13] Myers, R. H, Montgomery D.C, Adweson-Cook C.M. (2008). Response surface methodology: Process and product optimization using designed experiments [M]. New York: John Wiley and Sons, Inc.

      [14] SAS Institute (2013): SAS User’s Guide, SAS Institute Inc. Cary, NC, USA.

      [15] Tum, I.K (2017). Optimal and efficient production of rose coco beans through the twenty four points second order rotatable design. Unpublished Ph.D Thesis, Moi University.

  • Downloads