The Heuristic Approach to the Selection of Experimental Design, Model and Valid Pre-Processing Transformation of DoE Outcome

Abstract:

The typical problem in design of experiments methodology is to avoid risk of obtaining predictions outside of ranges with technological or physical sense. Such situation occurs very often if a simple linear regression or other unbounded is involved as a predictive model. The possible solution is to provide mappings of the outcome from the range of interest into the full range from negative to plus infinity before the linear regression is applied. The intermediate values obtained from unbounded predictive model is re-transformed into the physical domain by the inverse transformation. The key issue is to decide if the mapping is required and subsequently what mapping is necessary. Author proposed a simple heuristic supporting this decision and tested such solution in some examples described in this paper.

• Periodical: Advanced Materials Research (Volume 874)
• Pages: 145-149
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.874.145
• Online since: January 2014
• Authors: Jacek Pietraszek*, Andrii Goroshko
• Keywords: Design of Experiment (DOE), Experimental Design, Fractional Factorials, Heuristic Decision, Logistics Regression, Response Surface

References

[1] R.A. Fisher, Statistical Methods for Research Workers, Oliver and Boyd Press, Edinburgh (1925).

[2] R.A. Fisher, The Arrangement of Field Experiments, J. Roy. Statist. Soc. 33 (1926) 503-513.

[3] R.A. Fisher, The Design of Experiments, Oliver and Boyd Press, Edinburgh (1935).

[4] F. Yates, Complex experiments, J. Roy. Statist. Soc. Suppl. 2 (1935) 181-247.

[5] R.L. Plackett, J.P. Burman, The design of optimum multifactorial experiments, Biometrika 33 (1946) 305-325.

DOI: 10.1093/biomet/33.4.305

[6] G.E.P. Box, K.B. Wilson, On the Experimental Attainment of Optimum Conditions, J. Roy. Stat. Soc. B 13 (1951) (1) 1-45.

[7] G. Elfving, Optimum Allocation in Linear Regression Theory, Ann. Math. Stat. 23 (1952) (2) 255-262.

DOI: 10.1214/aoms/1177729442

[8] J. Kiefer, J. Wolfowitz, Optimum Designs in Regression Problems, Ann. Math. Stat. 30 (1959) (2) 271-294.

DOI: 10.1214/aoms/1177706252

[9] V.V. Fedorov, Theory of Optimal Experiments, Elsevier, (1972).

[10] H. Chernoff, Sequential Analysis and Optimal Design, Harvard University, Cambridge, Massachusetts, (1972).

[11] J. McElroy, Taguchi - Japans Secret Weapon, Automot. Ind. 164 (1984) (8) 18.

[12] M.S. Phadke, Quality Engineering Using Robust Design, Prentice Hall International, Inc., London (1989).

[13] O. Kempthorne, K. Hinkelmann, Design and analysis of experiments. Vol. 1. Introduction to experimental design, John Wiley & Sons, Hoboken, NJ, USA (1994).

[14] O. Kempthorne, K. Hinkelmann, Design and analysis of experiments. Vol. 2. Advanced experimental design, John Wiley & Sons, Hoboken, NJ, USA (1994).

[15] K. Hinkelmann, Editor, Design and analysis of experiments. Vol. 3. Special Designs and Applications, John Wiley & Sons, Hoboken, NJ, USA (2012).

[16] ISO 3534-3: 2013, Statistics - Vocabulary and symbols - Part 3: Design of experiments, (2013).

[17] R.L. Mason, R.F. Gunst, J.L. Hess, Statistical Design and Analysis of Experiments, John Wiley & Sons, Hoboken (1989).

[18] S.S. Stevens, On the theory of scales of measurements, 103 (1946) 677-680.

[19] W. Grzegożek, J. Szczygieł, M. Król, An Attempt of an Employment of a Continuous Wavelet Transform for Evaluation of Temporary Comfort Disturbance, J. KONES 16 (2009) 165-172.

[20] J. Pietraszek, W. Grzegożek, J. Szczygieł, Forecasting of Subjective Comfort in Tram Using Ordinal Logistic Regression and Manifold Learning, 19 (2012) (2) 403-410.

DOI: 10.5604/12314005.1138238

[21] A. Agresti, Categorical Data Analysis, John Wiley & Sons, Hoboken (2002).

[22] J.M. Hilbe, Logistc Regression Models, CRC Press, Boca Raton (2009).

[23] D.W. Hosmer, S. Lemeshow, Applied Logistic Regression, John Wiley & Sons, Hoboken (2000).

[24] I.T. Jolliffe, Principal Component Analysis, Springer, New York (2002).

[25] E. Skrzypczak-Pietraszek, J. Pietraszek, Chemical profile and seasonal variation of phenolic acid content in bastard balm (Melittis melissophyllum L., Lamiaceae), J Pharmaceut Biomed 66 (2012) 154-161.

DOI: 10.1016/j.jpba.2012.03.037

[26] J. Pietraszek, Fuzzy Regression Compared to Classical Experimental Design in the Case of Flywheel Assembly, Lect Notes Artif Int 7267 (2012) 310-317.

DOI: 10.1007/978-3-642-29347-4_36

[27] J. Pietraszek, N. Radek, DoE-based model for tribology of laser textured surfaces of silicon carbide, in: T. Łodygowski, J. Rakowski, T. Garbowski and W. Sumelka, (Eds. ), CMM-2013 - Computer Methods in Mechanics, 27-31. 08. 2013, Poznań, Poland, Poznań University of Technology (2013).

[28] D.C. Montgomery, Design and Analysis of Experiments, John Wiley & Sons, Inc., Hoboken (2008).

[29] J. Pietraszek, M. Kołomycki, E. Kocyłowska, The impact of CUDA technology on the efficiency of Blender renderer program, Czasopismo Techniczne 110 (2013) (1-M) 317-324.

[30] P. Osocha, P. Duda, B. Weglowski, Determining temperature and stress changes in thick-walled elements of steam lines, Inz Chem Procesowa 25 (2004) (4) 2249-2256.

[31] T. Styrylska, J. Pietraszek, Numerical Modeling of Non-Steady-State Temperature-Fields with Supplementary Data, Z Angew Math Mech 72 (1992) (6) T537-T539.

[32] J. Pietraszek, A. Gądek-Moszczak, N. Radek, The Estimation of Accuracy for the Neural Network Approximation in the Case of Sintered Metal Properties, in: A. Badica, (Ed. ), Recent Developments in Computational Collective Intelligence., Studies in Computational Intelligence 513, Springer (2014).

DOI: 10.1007/978-3-319-01787-7_12

[33] A. Gadek, S. Kuciel, L. Wojnar, W. Dziadur, Application of computer-aided analysis of an image for assessment of reinforced polymers structures, Polimery-W 51 (2006) (3) 206-211.

DOI: 10.14314/polimery.2006.206

[34] A. Gadek-Moszczak, L. Wojnar, Objective, Quantitative and Automatic X-Ray Image. Analysis of the Bone Regenerate in the Ilizarov Method, (2009) 453-458.

[35] A. Gadek-Moszczak, S. Zmudka, Description of 3D microstructure of the composites with polypropylene (PP) matrix and Tuf particles fillers, Solid State Phenom. 197 (2013) 186-191.

DOI: 10.4028/www.scientific.net/ssp.197.186

[36] A. Szczotok, R. Przeliorz, Phase transformations in CMSX-4 nickel-base superalloy, IOP Conf. Ser. -Mat. Sci. 35 (2012).

DOI: 10.1088/1757-899x/35/1/012005

[37] A. Szczotok, M. Sozanska, A Comparison of Grain Quantitative Evaluation Performed with Standard Method of Imaging with Light Microscopy and EBSD Analysis, Prakt Metallogr-Pr M 46 (2009) (9) 454-468.

DOI: 10.3139/147.110043