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İkinci Derece Yan ı t Yüzey Modellerinin Uygulaması ve Yorumlanması

Year 2001, Volume: 07 Issue: 04, 121 - 128, 01.11.2001
https://doi.org/10.1501/Tarimbil_0000000698

Abstract

İkinci derece yan ı t yüzey modellerinin uygulamas ı ve sonuçları n yorumlanmas ı için yapay olarak oluşturulan üç veri kümesi kullan ı lm ışt ı r. Verilerin 3x3 düzeninde tertiplenmi ş iki tekerrürlü bir denemeden topland ığı varsay ı lmışt ı r. Yapay olarak oluşturulan veriler için ikinci derece yan ı t yüzey modeli hesapland ığı zaman VERIMI 'deki toplam varyasyonun %95.52'sinin, VER İ M2'deki toplam varyasyonun %83.93'ünün ve VER İ M3'teki toplam varyasyonun %85.41'inin hesaplanan model taraf ı ndan aç ı kland ığı görülmüştür. İ kinci derece modelin uygunluk kontrolünden elde edilen sonuçlar hesaplanan modelin yan ı t yüzeyini tan ı mlamak için yeterli oldu ğunu göstermiştir. Yan ı t yüzeyinin yap ı s ı n ı incelemek için uygulanan kanonik analiz VERIMI için maksimum, VER İ M2 için minimum oldu ğunu göstermi ştir. Buna karşı n VER İ M3 için bir eyer saddle noktas ı hesaplanmışt ı r. Yapay veriler kullan ı ld ı ktan sonra şeker içeriğ ine ait toplanm ış veriler analiz edilmiştir. Şeker içeriği verileri için ikinci derece yan ı t yüzeyi modeli hesapland ığı zaman, şeker içeriğindeki toplam varyasyonun %68.9'unun hesaplanan model taraf ı ndan aç ı kland ığı görülmüştür. İ kinci derece modelin uygunluk kontrolünden elde edilen sonuçlar hesaplanan modelin şeker içeriği için yan ıt yüzeyini tan ı mlamak için yeterli olduğ unu göstermi ştir.Uygulanan kanonik analizde şeker içeri ği için bir eyer saddle nokta hesaplanm ışt ı r.

References

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An Application and Interpretation of the Second Order Response Surface Model

Year 2001, Volume: 07 Issue: 04, 121 - 128, 01.11.2001
https://doi.org/10.1501/Tarimbil_0000000698

Abstract

İn this study, three artificial data sets were used to explain the second order response surface model. It was assumed that the data were collected from a 3x3 experiment with two replications. Fitting the second order response surface model showed that 92.51%, 83.93% and 85.41% of the tatei variation in YIELD1, YIELD2 and YIELD3, respectively, accounted for by the fitted model. When the lack of fit test was applied, the results clarif ı ed that the second order model was adequately described the response surface for all the three sets of data. Application of the canonical analysis confı rmed that there was a stationary point of maximum response for YIELD1, a stationary point of minimum response for YIELD2 and a saddle point for YIELD3. After that, the data on the corrected sugar content of sugar beet were analyzed. The results showed that the fitted second order model accounted for 68.9% of the total variation in the sugar content. When the lack of fit test was applied, the results showed that the second order model adequately described the response surface of sugar content. The results of canonical analysis indicated that there was a saddle point for the sugar content.

References

  • Anonymous, 1987. SAS/STAT Guide for Personal Computers, Version 6 Edition. SAS lnstitute Inc., Cary, NC, USA.
  • Agarwal, M. C., S. C. Mohan, B. L. Dhyami, K. Nirmal and N. Kumar, 1994. Economising fertilizer use for rainfed sesame crop in Doon Valley. Fertiliser Marketing News 25: 12, 1, 3- 5, 7.
  • Castro, J. Tirapegui, R. S. F. Silva, I. Alves-Castro and R. S. Ferreira-Silva, 1998. Development of protein mixtures and evaluation of their sensory properties using the statistical response surface methodology. International J. Food Sci. and Nutrition, 49(6) 453-461.
  • Floros, J.,D. A. Ekanayake, G. P. Abide and P. E. Nelson, 1992. Optimization of a diced tomato calcification process. J. Food Sci., 57 (5) 1144-1148.
  • Kulshreshtha, M.,A. K. Pathak and B. C. Sarkar, 1988. Energy and peak force requirement in potato slicing. J. Sci. and Tech., India, 25 (5) 259-262.
  • Montgomery, D. C. 1997. Design and Analysis of Experiments. John Wiley & Sons, Inc. Canada, 704 p.
  • Myers, R. H. and D. C. Montgomery, 1995. Response Surface Methodology, Process and Product Optimization Using Designed Experiments. John Wiley & Sons, Inc. Canada, 700 p.
  • Pereira, G.V., L. A. F. Antunes and R. S. D. S. F. D. Silva, 1992. Development and characterization of a cheese analog containing aqueous soy extract (soy milk), whey and cow's milk. Aeqivos de Biologia e Tecnologia (Curitiba), 35 (1) 99-115.
  • Petersen, R. G. 1985. Design and Analysis of Experiments. Marcel Dekker, Inc. New York, USA, 429 p.
  • Prapulla, A. S. G., Z. Jacob, N. Chand, D. Rajalakshmi and N. G. Karanth, 1992. Maximization of lipid production by Rhodotorula gracilis CFR-1 using response surface methodology. Biotechnology and Bioengineering, 40 (8) 965-970
There are 10 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Zahide Kocabaş This is me

Publication Date November 1, 2001
Submission Date November 1, 2001
Published in Issue Year 2001 Volume: 07 Issue: 04

Cite

APA Kocabaş, Z. (2001). An Application and Interpretation of the Second Order Response Surface Model. Journal of Agricultural Sciences, 07(04), 121-128. https://doi.org/10.1501/Tarimbil_0000000698

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