Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries

Casmir Chidiebere Onyeneke; Effanga Okon Effanga

doi:doi:10.11648/j.ijtam.20160201.13

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Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries

Casmir Chidiebere Onyeneke, Effanga Okon Effanga

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 1)

Received: 25 July 2016 Accepted: 10 September 2016 Published: 17 October 2016

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Abstract

We are in the middle of an international financial crisis, which intensifies the demands on high quality, reliable and efficient solutions that optimize production processes, making production more efficient while minimizing cost, produce more with high quality, with few raw materials and less energy. It is these circumstances that necessitates the use of response surface methodology to search for the optimal conditions for improving grinding process in case of convex situations in paper producing industries. The uniqueness of this work focused on modeling and adopting the necessary assumptions and conditions to further reduced the formulated second order response surface model to obtain a more adequate model that best optimized the production process. The design was based on the use of central composite rotatable approach known as CCRD with the grinding fineness as the response. The conditions were subjected to experimental method, search method, graphical method and feasible region approach to generate the result which is not significantly different from each other using the reduced model. We could established nine grinding conditions which involves one center points with four factorial and four axial points. The reduced second order response surface model was optimized to obtain the best grinding at machine voltage of two hundred within fifty minutes. It is on this condition that the response variable gave the value of 1399.36 meshes.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 1)
DOI	10.11648/j.ijtam.20160201.13
Page(s)	13-23
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), 2016. Published by Science Publishing Group

Keywords

Optimization, Response Surface, Differentiable, Convexity, Models, Optimal Solution, Lack-of-Fit, Design, Experiment, Analysis, Maximization, Quadratic, Contour Plot

References

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APA Style

Casmir Chidiebere Onyeneke, Effanga Okon Effanga. (2016). Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries. International Journal of Theoretical and Applied Mathematics, 2(1), 13-23. https://doi.org/10.11648/j.ijtam.20160201.13

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ACS Style

Casmir Chidiebere Onyeneke; Effanga Okon Effanga. Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries. Int. J. Theor. Appl. Math. 2016, 2(1), 13-23. doi: 10.11648/j.ijtam.20160201.13

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AMA Style

Casmir Chidiebere Onyeneke, Effanga Okon Effanga. Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries. Int J Theor Appl Math. 2016;2(1):13-23. doi: 10.11648/j.ijtam.20160201.13

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@article{10.11648/j.ijtam.20160201.13,
  author = {Casmir Chidiebere Onyeneke and Effanga Okon Effanga},
  title = {Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {1},
  pages = {13-23},
  doi = {10.11648/j.ijtam.20160201.13},
  url = {https://doi.org/10.11648/j.ijtam.20160201.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160201.13},
  abstract = {We are in the middle of an international financial crisis, which intensifies the demands on high quality, reliable and efficient solutions that optimize production processes, making production more efficient while minimizing cost, produce more with high quality, with few raw materials and less energy. It is these circumstances that necessitates the use of response surface methodology to search for the optimal conditions for improving grinding process in case of convex situations in paper producing industries. The uniqueness of this work focused on modeling and adopting the necessary assumptions and conditions to further reduced the formulated second order response surface model to obtain a more adequate model that best optimized the production process. The design was based on the use of central composite rotatable approach known as CCRD with the grinding fineness as the response. The conditions were subjected to experimental method, search method, graphical method and feasible region approach to generate the result which is not significantly different from each other using the reduced model. We could established nine grinding conditions which involves one center points with four factorial and four axial points. The reduced second order response surface model was optimized to obtain the best grinding at machine voltage of two hundred within fifty minutes. It is on this condition that the response variable gave the value of 1399.36 meshes.},
 year = {2016}
}

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TY  - JOUR
T1  - Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries
AU  - Casmir Chidiebere Onyeneke
AU  - Effanga Okon Effanga
Y1  - 2016/10/17
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20160201.13
DO  - 10.11648/j.ijtam.20160201.13
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 13
EP  - 23
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160201.13
AB  - We are in the middle of an international financial crisis, which intensifies the demands on high quality, reliable and efficient solutions that optimize production processes, making production more efficient while minimizing cost, produce more with high quality, with few raw materials and less energy. It is these circumstances that necessitates the use of response surface methodology to search for the optimal conditions for improving grinding process in case of convex situations in paper producing industries. The uniqueness of this work focused on modeling and adopting the necessary assumptions and conditions to further reduced the formulated second order response surface model to obtain a more adequate model that best optimized the production process. The design was based on the use of central composite rotatable approach known as CCRD with the grinding fineness as the response. The conditions were subjected to experimental method, search method, graphical method and feasible region approach to generate the result which is not significantly different from each other using the reduced model. We could established nine grinding conditions which involves one center points with four factorial and four axial points. The reduced second order response surface model was optimized to obtain the best grinding at machine voltage of two hundred within fifty minutes. It is on this condition that the response variable gave the value of 1399.36 meshes.
VL  - 2
IS  - 1
ER  -

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Author Information

Casmir Chidiebere Onyeneke

Department of Mathematics/Statistics and Computer Science, University of Calabar, Calabar, Nigeria
Effanga Okon Effanga

Department of Mathematics/Statistics and Computer Science, University of Calabar, Calabar, Nigeria

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APA Style

Casmir Chidiebere Onyeneke, Effanga Okon Effanga. (2016). Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries. International Journal of Theoretical and Applied Mathematics, 2(1), 13-23. https://doi.org/10.11648/j.ijtam.20160201.13

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ACS Style

Casmir Chidiebere Onyeneke; Effanga Okon Effanga. Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries. Int. J. Theor. Appl. Math. 2016, 2(1), 13-23. doi: 10.11648/j.ijtam.20160201.13

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AMA Style

Casmir Chidiebere Onyeneke, Effanga Okon Effanga. Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries. Int J Theor Appl Math. 2016;2(1):13-23. doi: 10.11648/j.ijtam.20160201.13

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@article{10.11648/j.ijtam.20160201.13,
  author = {Casmir Chidiebere Onyeneke and Effanga Okon Effanga},
  title = {Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {1},
  pages = {13-23},
  doi = {10.11648/j.ijtam.20160201.13},
  url = {https://doi.org/10.11648/j.ijtam.20160201.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160201.13},
  abstract = {We are in the middle of an international financial crisis, which intensifies the demands on high quality, reliable and efficient solutions that optimize production processes, making production more efficient while minimizing cost, produce more with high quality, with few raw materials and less energy. It is these circumstances that necessitates the use of response surface methodology to search for the optimal conditions for improving grinding process in case of convex situations in paper producing industries. The uniqueness of this work focused on modeling and adopting the necessary assumptions and conditions to further reduced the formulated second order response surface model to obtain a more adequate model that best optimized the production process. The design was based on the use of central composite rotatable approach known as CCRD with the grinding fineness as the response. The conditions were subjected to experimental method, search method, graphical method and feasible region approach to generate the result which is not significantly different from each other using the reduced model. We could established nine grinding conditions which involves one center points with four factorial and four axial points. The reduced second order response surface model was optimized to obtain the best grinding at machine voltage of two hundred within fifty minutes. It is on this condition that the response variable gave the value of 1399.36 meshes.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Application of Reduced Second Order Response Surface Model of Convex Optimization in Paper Producing Industries
AU  - Casmir Chidiebere Onyeneke
AU  - Effanga Okon Effanga
Y1  - 2016/10/17
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20160201.13
DO  - 10.11648/j.ijtam.20160201.13
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 13
EP  - 23
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160201.13
AB  - We are in the middle of an international financial crisis, which intensifies the demands on high quality, reliable and efficient solutions that optimize production processes, making production more efficient while minimizing cost, produce more with high quality, with few raw materials and less energy. It is these circumstances that necessitates the use of response surface methodology to search for the optimal conditions for improving grinding process in case of convex situations in paper producing industries. The uniqueness of this work focused on modeling and adopting the necessary assumptions and conditions to further reduced the formulated second order response surface model to obtain a more adequate model that best optimized the production process. The design was based on the use of central composite rotatable approach known as CCRD with the grinding fineness as the response. The conditions were subjected to experimental method, search method, graphical method and feasible region approach to generate the result which is not significantly different from each other using the reduced model. We could established nine grinding conditions which involves one center points with four factorial and four axial points. The reduced second order response surface model was optimized to obtain the best grinding at machine voltage of two hundred within fifty minutes. It is on this condition that the response variable gave the value of 1399.36 meshes.
VL  - 2
IS  - 1
ER  -

Copy | Download