Araştırma Makalesi
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A Bayesian Parameter Estimation Approach to Response Surface Optimization in Quality Engineering

Yıl 2019, Cilt: 23 Sayı: 5, 767 - 774, 01.10.2019
https://doi.org/10.16984/saufenbilder.485785

Öz

ABSTRACT



In
recent years, Bayesian analyses have become increasingly popular for solving
industrial related problems. This paper illustrates the use of Bayesian methods
in response surface methodology (RSM) in the context of “off-line quality”
improvement. Bayesian linear regression uses the prior information in the high
uncertainty state of the response function to make more efficient and more
realistic inferences than can be obtained with classical regression. Several
different models of parameter estimation and uncertainty analysis will be
presented for comparative purposes. An example illustrates the findings.



 

Kaynakça

  • REFERENCES[1] T. Bayes, “An essay towards solving a problem in the doctrine of chances”, R soc Lond Philos Trans., vol.5, no.3, pp. 370–418, 1763.
  • [2] G.E.P. Box, “ Discussion of ‘off-Line quality control, parameter design, and the Taguchi methodby R.N. Kackar”, Journal of Quality Technology, vol.17, pp. 189-190, 1985.
  • [3] G.E.P. Box and K.B. Wilson, “On the experimental attainment of optimum conditions”, Journal of the Royal Statistical Society, vol.13, no.B ,pp. 1-45, 1951.
  • [4] M. Goldstein, “Bayesian analysis of regression problems”, Biometrika, vol. 63, no.1, pp. 51-58, 1976.
  • [5] S.G. Gilmour and R. Mead, “A Bayesian design criterion for locating the optimum point on a response surface”, Statistics & Probability Letters vol.64, no.3, pp. 235-242,2003.
  • [6] W.K. Hasting, “Monte Carlo sampling methods using Markov chains and their applications”, Biometrika vol.57, no.1, pp. 97-109, 1970.
  • [7] P.D Hoff., “A First Course in Bayesian Statistical Methods”, Springer, New York, 2009.
  • [8] H. Jeffreys, “Theory of Probability”, The Clarendon Press, Oxford, 1939.
  • [9] J.M. Keynes, “A Treatise on Probability”, St Martin’s, London, 1921.
  • [10] P.S Laplace, “Memoir on the probability of causes of events”, Mémoires de Mathématique et de Physique, Tome Sixième, English translation by S. M. Stigler 1986, Statist. Sci. vol.1, no.19, pp. 364–378, 1774.
  • [11] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H.Teller and E. Teller , “Equation of state calculations by fast computing machines,” Journal of Chemical Physics, vol.21, no.6, pp. 1087-1092,1953.
  • [12] D.C Montgomery, “Design and Analysis of Experiments (5th edition)”, John Willey & Sons, New York, 2001.
  • [13] I.Ntzoufras, “Bayesian Modeling Using WinBUGS”, John Wiley & Sons, New Jersey, 2009.
  • [14] F.P. Ramsey, “Truth and probability (1926), in Ramsey, F.P”,. The Foundations of Mathematics and Other Logical Essays, Harcourt, Brace and Company, New York, pp. 156-198,1931.
  • [15] L.J. Savage, “The theory of statistical decision”, Journal of the American Statistical Association, vol. 46,pp. 55–67,1951.
  • [16] G.G Vining and R.H. Myers, “Combining Taguchi and response surface philosophies: A dual response approach”, Journal of Quality Technology vol.22,no.1, pp. 38-45,1990.
  • [17] S.Vaseghi, “Advanced Digital Signal Processing and Noise Reduction”, John Wiley & Sons, New York, 2000.
Yıl 2019, Cilt: 23 Sayı: 5, 767 - 774, 01.10.2019
https://doi.org/10.16984/saufenbilder.485785

Öz

Kaynakça

  • REFERENCES[1] T. Bayes, “An essay towards solving a problem in the doctrine of chances”, R soc Lond Philos Trans., vol.5, no.3, pp. 370–418, 1763.
  • [2] G.E.P. Box, “ Discussion of ‘off-Line quality control, parameter design, and the Taguchi methodby R.N. Kackar”, Journal of Quality Technology, vol.17, pp. 189-190, 1985.
  • [3] G.E.P. Box and K.B. Wilson, “On the experimental attainment of optimum conditions”, Journal of the Royal Statistical Society, vol.13, no.B ,pp. 1-45, 1951.
  • [4] M. Goldstein, “Bayesian analysis of regression problems”, Biometrika, vol. 63, no.1, pp. 51-58, 1976.
  • [5] S.G. Gilmour and R. Mead, “A Bayesian design criterion for locating the optimum point on a response surface”, Statistics & Probability Letters vol.64, no.3, pp. 235-242,2003.
  • [6] W.K. Hasting, “Monte Carlo sampling methods using Markov chains and their applications”, Biometrika vol.57, no.1, pp. 97-109, 1970.
  • [7] P.D Hoff., “A First Course in Bayesian Statistical Methods”, Springer, New York, 2009.
  • [8] H. Jeffreys, “Theory of Probability”, The Clarendon Press, Oxford, 1939.
  • [9] J.M. Keynes, “A Treatise on Probability”, St Martin’s, London, 1921.
  • [10] P.S Laplace, “Memoir on the probability of causes of events”, Mémoires de Mathématique et de Physique, Tome Sixième, English translation by S. M. Stigler 1986, Statist. Sci. vol.1, no.19, pp. 364–378, 1774.
  • [11] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H.Teller and E. Teller , “Equation of state calculations by fast computing machines,” Journal of Chemical Physics, vol.21, no.6, pp. 1087-1092,1953.
  • [12] D.C Montgomery, “Design and Analysis of Experiments (5th edition)”, John Willey & Sons, New York, 2001.
  • [13] I.Ntzoufras, “Bayesian Modeling Using WinBUGS”, John Wiley & Sons, New Jersey, 2009.
  • [14] F.P. Ramsey, “Truth and probability (1926), in Ramsey, F.P”,. The Foundations of Mathematics and Other Logical Essays, Harcourt, Brace and Company, New York, pp. 156-198,1931.
  • [15] L.J. Savage, “The theory of statistical decision”, Journal of the American Statistical Association, vol. 46,pp. 55–67,1951.
  • [16] G.G Vining and R.H. Myers, “Combining Taguchi and response surface philosophies: A dual response approach”, Journal of Quality Technology vol.22,no.1, pp. 38-45,1990.
  • [17] S.Vaseghi, “Advanced Digital Signal Processing and Noise Reduction”, John Wiley & Sons, New York, 2000.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Elif Kozan 0000-0002-8267-074X

Onur Köksoy 0000-0003-2634-0794

Yayımlanma Tarihi 1 Ekim 2019
Gönderilme Tarihi 20 Kasım 2018
Kabul Tarihi 19 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 23 Sayı: 5

Kaynak Göster

APA Kozan, E., & Köksoy, O. (2019). A Bayesian Parameter Estimation Approach to Response Surface Optimization in Quality Engineering. Sakarya University Journal of Science, 23(5), 767-774. https://doi.org/10.16984/saufenbilder.485785
AMA Kozan E, Köksoy O. A Bayesian Parameter Estimation Approach to Response Surface Optimization in Quality Engineering. SAUJS. Ekim 2019;23(5):767-774. doi:10.16984/saufenbilder.485785
Chicago Kozan, Elif, ve Onur Köksoy. “A Bayesian Parameter Estimation Approach to Response Surface Optimization in Quality Engineering”. Sakarya University Journal of Science 23, sy. 5 (Ekim 2019): 767-74. https://doi.org/10.16984/saufenbilder.485785.
EndNote Kozan E, Köksoy O (01 Ekim 2019) A Bayesian Parameter Estimation Approach to Response Surface Optimization in Quality Engineering. Sakarya University Journal of Science 23 5 767–774.
IEEE E. Kozan ve O. Köksoy, “A Bayesian Parameter Estimation Approach to Response Surface Optimization in Quality Engineering”, SAUJS, c. 23, sy. 5, ss. 767–774, 2019, doi: 10.16984/saufenbilder.485785.
ISNAD Kozan, Elif - Köksoy, Onur. “A Bayesian Parameter Estimation Approach to Response Surface Optimization in Quality Engineering”. Sakarya University Journal of Science 23/5 (Ekim 2019), 767-774. https://doi.org/10.16984/saufenbilder.485785.
JAMA Kozan E, Köksoy O. A Bayesian Parameter Estimation Approach to Response Surface Optimization in Quality Engineering. SAUJS. 2019;23:767–774.
MLA Kozan, Elif ve Onur Köksoy. “A Bayesian Parameter Estimation Approach to Response Surface Optimization in Quality Engineering”. Sakarya University Journal of Science, c. 23, sy. 5, 2019, ss. 767-74, doi:10.16984/saufenbilder.485785.
Vancouver Kozan E, Köksoy O. A Bayesian Parameter Estimation Approach to Response Surface Optimization in Quality Engineering. SAUJS. 2019;23(5):767-74.

Sakarya University Journal of Science (SAUJS)