Modeling of rose coco beans using twenty four points optimum second order rotatable design

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    The response surface methodology (RSM) is a collection of mathematical and statistical techniques useful for the modeling and analysis of problems in which a response of interest is influenced by several variables, and the objective is to optimize the response. The objective of the study was to model the rose coco beans (Phaseolus vulgaris) through an existing A-optimum and D-efficient second order rotatable design of twenty four points in three dimensions in a greenhouse setting using three inorganic fertilizers, namely, nitrogen, phosphorus and potassium. Thus, the objective of the study was accomplished using the calculus optimum value of the free/letter parameter f=1.1072569. This was done by estimating the parameters via least square's techniques, by making available for the yield response of rose coco beans at calculus optimum value design for the first time. The results showed that, the three factors: nitrogen, phosphorus, and potassium contributed significantly on the yield of rose coco beans (p<0.05). In GP3G, the second-order model was adequate for 1% level of significance with 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 and coefficient variation, CV was 10.30. This study demonstrated the importance of statistical methods in the optimal and efficient production of rose coco beans. We do recommend a randomize screening of all the fertilizer components with which it has influence on rose coco beans be done to ascertain the right initial amount of each fertilizer that could achieve maximum yield than this study realized.


  • Keywords


    Response Surface Methodology; Second Order Design; Optimality; Coded Levels; Natural Levels; Calculus Optimum Value; Rose Coco Beans.

  • References


      [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] 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.

      [6] 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.

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 Unpublished M.Phil.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

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

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

      [10] 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.


 

View

Download

Article ID: 8445
 
DOI: 10.14419/ijasp.v5i2.8445




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.