Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya

Wambua Alex Mwaniki; Koske Joseph; Mutiso John; Mulinge Wellington; Kibunja Catherine; Eboi Bramuel

doi:doi:10.11648/j.sjams.20170506.12

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Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya

Wambua Alex Mwaniki, Koske Joseph, Mutiso John, Mulinge Wellington, Kibunja Catherine, Eboi Bramuel

Published in Science Journal of Applied Mathematics and Statistics (Volume 5, Issue 6)

Received: 20 September 2017 Accepted: 8 October 2017 Published: 11 November 2017

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Abstract

The Agriculture sector is the main stay of the Kenyan economic development contributing over 70% of the Gross Domestic Product (GDP). The sector is faced with numerous challenges leading to frequent and recurrent food shortages. Declining maize grain yield is one among the major challenges that call for urgent interventions to address the looming food crisis in the country. Maize play a big role in the Kenyan food security and in most case lack of the same is taken to mean food insecurity. It is due the importance attached to the crop that a Long Term Agricultural Experiments (LTAE) was set up specifically to research on the Maize grain yield. Many paper published on the LTAE in the country are only single factors analysis and lack the application of Response Surface Methodology (RSM) approaches in solving challenges facing the low and declining maize grain yield (y₁), total microbe population (y₂) a crucial component of Soil Organic Matter (SOM) and their optimization. The focus of this paper therefore is the application of RSM in maize grain yield and total microbial population optimization. Specifically, the paper determined the most significant factors for maize grain yield and total microbial population (bacteria, fungi, actinomycetes, rhizobia), (screening phase of the paper), constructed of an efficient and appropriate experimental design for evaluating the optimal settings of maize yield and total microbial population count and determined univariate optimal settings for maize grain yield and total microbial population. The primary data was summarized from LTAE in National Agricultural Research Laboratories (NARL) in Kabete under the Kenya Agriculture and Livestock Research Organization (KALRO) and secondary data imputed for experimental points falling outside the set field experimental design points. Two treatment factors were identified as the most significant treatment factors (Farm Yard Manure (FYM) and Nitrogen and Phosphorus (NP)) at their low levels and Circumscribed Central Composite Design (CCCD) with two star points as the most efficient design. CCCD passed most optimal criteria of DAET. Univariately, optimal setting for maize grain yield was realized at 3.8x10³ kg/ha and that of the total microbial population at 3.6x10⁶ count. The study confirmed that it was possible to optimize the input treatment factor that lead to the optimization of both maize grain yield and maintaining maximal total microbial population count at its optimal levels.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 5, Issue 6)
DOI	10.11648/j.sjams.20170506.12
Page(s)	200-209
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

Response Surface Methodology, Long Term Agricultural Experiments, Univariate Optimization, Circumscribed Central Composite Design

References

[1]	Box, G., & Wilson, K. (1951). On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society, Series B, 13 (1), 1-45.
[2]	Cheng, S.-W., & Wu, C. F. (2001). Factor screening and response surface exploration. Statistica Sinaca, 553-604.
[3]	Cochran, W. G., & Cox, G. M. (1950). Experimental Designs. New York: Wiley.
[4]	Edmondson, R. N. (1991). Agricultural response surface experiments based on four level-factorial designs. Biometrics, 1435-1448.
[5]	Food and Agriculture Organization for United Nation. (2012). The state of food insecurity in the world. Rome: United Nations.
[6]	Food and Agriculture for United Nation. (2014). The state of food insecurity in the world. Rome: United Nation.
[7]	Food and Agriculture Organization for United Nation. (2013). The state of food and agriculture. Rome: United Nation.
[8]	Food and Agriculture Organization of the United Nation. (2015). The State of Food and Agriculture Report 2015: Social protection and agriculture: breaking the cycle of rural poverty. Rome: United Nation.
[9]	George, E. P., Hunter, J. S., & Hunter, W. G. (2005). Statistics for experinters: Design, innovation and discovery 2nd edition.
[10]	Greenland, D. (1994). Soil science and sustainable land management. Soil science and sustainable land management in the tropics, 1-15.
[11]	Hill, W. J., & Hunter, W. G. (1966). A review of response surface methodology-a literature survey. Techno Metric, 8, 571-590.
[12]	Kariuki, J. G. (2011). The future of agriculture in Africa (The Pardee Paper No. 15). Boston: Boston University.
[13]	Kenya National Bureau of Statistics. (2016). Economic survey. Nairobi: Government of Kenya.
[14]	Kibunja, C. N. (2007). Nutrient dynamics and soil microbial diversity (Unpublished PhD Thesis). Nairobi: University of Nairobi.
[15]	Koning, N., & Smaling, E. (2005). Environmental crisis or "lie of land?" The debate on soil degradation in Africa. Land Use Policy, 22, 3-11.
[16]	Lee, J.-K., Park, I., Choo, S., Kim, S., Choi, Y., & Choo, J. (2013). Optimization of medium composition for alpha-galactosidase production by Antarctica bacterial isolate, Bacillus sp. LX-1 using response surface methodology. African Journal of Microbiology Research, 7(27), 3494-3500.
[17]	Maat, H. (2011). The history and future of agricultural experiments. NJAS - WageningenJournal of Life Sciences, 57, 187-195.
[18]	Mead, R., & Pike, D. J. (1975). A review of response surface methodology from a biometric point of view. Biometric, 803-915.
[19]	Montgomery, D. C. (2009). In Design and anlysis of experiments. New York: John Wiley & Sons.
[20]	Montgomery, D. C. (2009). Design and analysis of experiments. New York: John Wiley & Sons.
[21]	Myer, R. H., & Montgomery, D. C. (2002). Response surface methodology: process and product optimization using designed experiments, second edn,. Boston: PSN-Kent.
[22]	Myer, R. H., Khuri, A. I., & Carter, W. H. (1989). Response surface methodology. Technometrics, 31(2), 137-157.
[23]	Raissi, S., & Farsani, R. (2009). Statistical Process Optimization Through Multi-Response Surface Methodology. World Academy of Science, Engineering and Technology, 267–271.
[24]	Richards, P. (1989). Farmers also experiment: a neglected intellectual resource in African science. Quality and Reliability Engineering International, 3, 227-240.
[25]	Su, C.-T., & Yeh, C.-J. (2011). Optimization of the CU wire bonding process for IC assembly using Taguchi methods. Microelectronics reliability, 53-59.
[26]	Wadsworth, H. M. (1997). Handbook of statistical methods for engineers and scientists. (2nd, Ed.) New York: McGraw - Hill Professional.
[27]	Wass, J. (2010). First steps in experimental design-the screening experiment. Journal of validation technology, 49-57.

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Wambua Alex Mwaniki, Koske Joseph, Mutiso John, Mulinge Wellington, Kibunja Catherine, et al. (2017). Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya. Science Journal of Applied Mathematics and Statistics, 5(6), 200-209. https://doi.org/10.11648/j.sjams.20170506.12

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ACS Style

Wambua Alex Mwaniki; Koske Joseph; Mutiso John; Mulinge Wellington; Kibunja Catherine, et al. Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya. Sci. J. Appl. Math. Stat. 2017, 5(6), 200-209. doi: 10.11648/j.sjams.20170506.12

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Wambua Alex Mwaniki, Koske Joseph, Mutiso John, Mulinge Wellington, Kibunja Catherine, et al. Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya. Sci J Appl Math Stat. 2017;5(6):200-209. doi: 10.11648/j.sjams.20170506.12

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@article{10.11648/j.sjams.20170506.12,
  author = {Wambua Alex Mwaniki and Koske Joseph and Mutiso John and Mulinge Wellington and Kibunja Catherine and Eboi Bramuel},
  title = {Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {5},
  number = {6},
  pages = {200-209},
  doi = {10.11648/j.sjams.20170506.12},
  url = {https://doi.org/10.11648/j.sjams.20170506.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20170506.12},
  abstract = {The Agriculture sector is the main stay of the Kenyan economic development contributing over 70% of the Gross Domestic Product (GDP). The sector is faced with numerous challenges leading to frequent and recurrent food shortages. Declining maize grain yield is one among the major challenges that call for urgent interventions to address the looming food crisis in the country. Maize play a big role in the Kenyan food security and in most case lack of the same is taken to mean food insecurity. It is due the importance attached to the crop that a Long Term Agricultural Experiments (LTAE) was set up specifically to research on the Maize grain yield. Many paper published on the LTAE in the country are only single factors analysis and lack the application of Response Surface Methodology (RSM) approaches in solving challenges facing the low and declining maize grain yield (y1), total microbe population (y2) a crucial component of Soil Organic Matter (SOM) and their optimization. The focus of this paper therefore is the application of RSM in maize grain yield and total microbial population optimization. Specifically, the paper determined the most significant factors for maize grain yield and total microbial population (bacteria, fungi, actinomycetes, rhizobia), (screening phase of the paper), constructed of an efficient and appropriate experimental design for evaluating the optimal settings of maize yield and total microbial population count and determined univariate optimal settings for maize grain yield and total microbial population. The primary data was summarized from LTAE in National Agricultural Research Laboratories (NARL) in Kabete under the Kenya Agriculture and Livestock Research Organization (KALRO) and secondary data imputed for experimental points falling outside the set field experimental design points. Two treatment factors were identified as the most significant treatment factors (Farm Yard Manure (FYM) and Nitrogen and Phosphorus (NP)) at their low levels and Circumscribed Central Composite Design (CCCD) with two star points as the most efficient design. CCCD passed most optimal criteria of DAET. Univariately, optimal setting for maize grain yield was realized at 3.8x103 kg/ha and that of the total microbial population at 3.6x106 count. The study confirmed that it was possible to optimize the input treatment factor that lead to the optimization of both maize grain yield and maintaining maximal total microbial population count at its optimal levels.},
 year = {2017}
}

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TY  - JOUR
T1  - Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya
AU  - Wambua Alex Mwaniki
AU  - Koske Joseph
AU  - Mutiso John
AU  - Mulinge Wellington
AU  - Kibunja Catherine
AU  - Eboi Bramuel
Y1  - 2017/11/11
PY  - 2017
N1  - https://doi.org/10.11648/j.sjams.20170506.12
DO  - 10.11648/j.sjams.20170506.12
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  - 200
EP  - 209
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20170506.12
AB  - The Agriculture sector is the main stay of the Kenyan economic development contributing over 70% of the Gross Domestic Product (GDP). The sector is faced with numerous challenges leading to frequent and recurrent food shortages. Declining maize grain yield is one among the major challenges that call for urgent interventions to address the looming food crisis in the country. Maize play a big role in the Kenyan food security and in most case lack of the same is taken to mean food insecurity. It is due the importance attached to the crop that a Long Term Agricultural Experiments (LTAE) was set up specifically to research on the Maize grain yield. Many paper published on the LTAE in the country are only single factors analysis and lack the application of Response Surface Methodology (RSM) approaches in solving challenges facing the low and declining maize grain yield (y1), total microbe population (y2) a crucial component of Soil Organic Matter (SOM) and their optimization. The focus of this paper therefore is the application of RSM in maize grain yield and total microbial population optimization. Specifically, the paper determined the most significant factors for maize grain yield and total microbial population (bacteria, fungi, actinomycetes, rhizobia), (screening phase of the paper), constructed of an efficient and appropriate experimental design for evaluating the optimal settings of maize yield and total microbial population count and determined univariate optimal settings for maize grain yield and total microbial population. The primary data was summarized from LTAE in National Agricultural Research Laboratories (NARL) in Kabete under the Kenya Agriculture and Livestock Research Organization (KALRO) and secondary data imputed for experimental points falling outside the set field experimental design points. Two treatment factors were identified as the most significant treatment factors (Farm Yard Manure (FYM) and Nitrogen and Phosphorus (NP)) at their low levels and Circumscribed Central Composite Design (CCCD) with two star points as the most efficient design. CCCD passed most optimal criteria of DAET. Univariately, optimal setting for maize grain yield was realized at 3.8x103 kg/ha and that of the total microbial population at 3.6x106 count. The study confirmed that it was possible to optimize the input treatment factor that lead to the optimization of both maize grain yield and maintaining maximal total microbial population count at its optimal levels.
VL  - 5
IS  - 6
ER  -

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Author Information

Wambua Alex Mwaniki

Department of Planning and Statistics, Ministry of Agriculture, Livestock and Fisheries, Nairobi, Kenya
Koske Joseph

Department of Mathematics and Computer Science, Moi University, Eldoret, Kenya
Mutiso John

Department of Mathematics and Computer Science, Moi University, Eldoret, Kenya
Mulinge Wellington

Kenya Agricultural and Livestock Research Organization, Nairobi, Kenya
Kibunja Catherine

Kenya Agricultural and Livestock Research Organization, Nairobi, Kenya
Eboi Bramuel

Department of Planning and Statistics, Ministry of Agriculture, Livestock and Fisheries, Nairobi, Kenya

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APA Style

Wambua Alex Mwaniki, Koske Joseph, Mutiso John, Mulinge Wellington, Kibunja Catherine, et al. (2017). Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya. Science Journal of Applied Mathematics and Statistics, 5(6), 200-209. https://doi.org/10.11648/j.sjams.20170506.12

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ACS Style

Wambua Alex Mwaniki; Koske Joseph; Mutiso John; Mulinge Wellington; Kibunja Catherine, et al. Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya. Sci. J. Appl. Math. Stat. 2017, 5(6), 200-209. doi: 10.11648/j.sjams.20170506.12

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AMA Style

Wambua Alex Mwaniki, Koske Joseph, Mutiso John, Mulinge Wellington, Kibunja Catherine, et al. Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya. Sci J Appl Math Stat. 2017;5(6):200-209. doi: 10.11648/j.sjams.20170506.12

Copy | Download

@article{10.11648/j.sjams.20170506.12,
  author = {Wambua Alex Mwaniki and Koske Joseph and Mutiso John and Mulinge Wellington and Kibunja Catherine and Eboi Bramuel},
  title = {Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {5},
  number = {6},
  pages = {200-209},
  doi = {10.11648/j.sjams.20170506.12},
  url = {https://doi.org/10.11648/j.sjams.20170506.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20170506.12},
  abstract = {The Agriculture sector is the main stay of the Kenyan economic development contributing over 70% of the Gross Domestic Product (GDP). The sector is faced with numerous challenges leading to frequent and recurrent food shortages. Declining maize grain yield is one among the major challenges that call for urgent interventions to address the looming food crisis in the country. Maize play a big role in the Kenyan food security and in most case lack of the same is taken to mean food insecurity. It is due the importance attached to the crop that a Long Term Agricultural Experiments (LTAE) was set up specifically to research on the Maize grain yield. Many paper published on the LTAE in the country are only single factors analysis and lack the application of Response Surface Methodology (RSM) approaches in solving challenges facing the low and declining maize grain yield (y1), total microbe population (y2) a crucial component of Soil Organic Matter (SOM) and their optimization. The focus of this paper therefore is the application of RSM in maize grain yield and total microbial population optimization. Specifically, the paper determined the most significant factors for maize grain yield and total microbial population (bacteria, fungi, actinomycetes, rhizobia), (screening phase of the paper), constructed of an efficient and appropriate experimental design for evaluating the optimal settings of maize yield and total microbial population count and determined univariate optimal settings for maize grain yield and total microbial population. The primary data was summarized from LTAE in National Agricultural Research Laboratories (NARL) in Kabete under the Kenya Agriculture and Livestock Research Organization (KALRO) and secondary data imputed for experimental points falling outside the set field experimental design points. Two treatment factors were identified as the most significant treatment factors (Farm Yard Manure (FYM) and Nitrogen and Phosphorus (NP)) at their low levels and Circumscribed Central Composite Design (CCCD) with two star points as the most efficient design. CCCD passed most optimal criteria of DAET. Univariately, optimal setting for maize grain yield was realized at 3.8x103 kg/ha and that of the total microbial population at 3.6x106 count. The study confirmed that it was possible to optimize the input treatment factor that lead to the optimization of both maize grain yield and maintaining maximal total microbial population count at its optimal levels.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Application of Response Surface Methodology for Determining Optimal Factors in Maximization of Maize Grain Yield and Total Microbial Count in Long Term Agricultural Experiment, Kenya
AU  - Wambua Alex Mwaniki
AU  - Koske Joseph
AU  - Mutiso John
AU  - Mulinge Wellington
AU  - Kibunja Catherine
AU  - Eboi Bramuel
Y1  - 2017/11/11
PY  - 2017
N1  - https://doi.org/10.11648/j.sjams.20170506.12
DO  - 10.11648/j.sjams.20170506.12
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  - 200
EP  - 209
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20170506.12
AB  - The Agriculture sector is the main stay of the Kenyan economic development contributing over 70% of the Gross Domestic Product (GDP). The sector is faced with numerous challenges leading to frequent and recurrent food shortages. Declining maize grain yield is one among the major challenges that call for urgent interventions to address the looming food crisis in the country. Maize play a big role in the Kenyan food security and in most case lack of the same is taken to mean food insecurity. It is due the importance attached to the crop that a Long Term Agricultural Experiments (LTAE) was set up specifically to research on the Maize grain yield. Many paper published on the LTAE in the country are only single factors analysis and lack the application of Response Surface Methodology (RSM) approaches in solving challenges facing the low and declining maize grain yield (y1), total microbe population (y2) a crucial component of Soil Organic Matter (SOM) and their optimization. The focus of this paper therefore is the application of RSM in maize grain yield and total microbial population optimization. Specifically, the paper determined the most significant factors for maize grain yield and total microbial population (bacteria, fungi, actinomycetes, rhizobia), (screening phase of the paper), constructed of an efficient and appropriate experimental design for evaluating the optimal settings of maize yield and total microbial population count and determined univariate optimal settings for maize grain yield and total microbial population. The primary data was summarized from LTAE in National Agricultural Research Laboratories (NARL) in Kabete under the Kenya Agriculture and Livestock Research Organization (KALRO) and secondary data imputed for experimental points falling outside the set field experimental design points. Two treatment factors were identified as the most significant treatment factors (Farm Yard Manure (FYM) and Nitrogen and Phosphorus (NP)) at their low levels and Circumscribed Central Composite Design (CCCD) with two star points as the most efficient design. CCCD passed most optimal criteria of DAET. Univariately, optimal setting for maize grain yield was realized at 3.8x103 kg/ha and that of the total microbial population at 3.6x106 count. The study confirmed that it was possible to optimize the input treatment factor that lead to the optimization of both maize grain yield and maintaining maximal total microbial population count at its optimal levels.
VL  - 5
IS  - 6
ER  -

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