The Bootstrap Analysis of One-Way ANOVA Stability in the Case of the Ceramic Shell Mould of Airfoil Blade Casting

Abstract:

The analysis of variance (ANOVA) is a classic tool for an identification of discreet factors impact on the measurable output by a specific decomposition on a total variance according to the scheme proposed by R.A Fisher in the 1920s. There are many explicit and implicit assumptions required as a preliminary of ANOVA computations. The ANOVA computations scheme is well known and implemented in many types of software but all estimations are provided with the assumption of a normal and homoscedasticity distribution of the noise disturbing the output. Computation procedures produce a single number output (e.g. F statistics, p-Value) without any analysis of their own dispersion. This paper analyzes the ANOVA output using the bootstrap approach. It seems to be the most convenient as a data-driven procedure. The source raw data are taken from the image analysis conducted during the investigation of the impact of the ceramic layer thickness on the wax pattern assembly of a turbine blade on the (γ+γ’) eutectic in the IN713C superalloy.

• Periodical: Solid State Phenomena (Volume 235)
• Pages: 24-30
• DOI: https://doi.org/10.4028/www.scientific.net/SSP.235.24
• Online since: July 2015
• Authors: Agnieszka Szczotok*, Jacek Nawrocki, Aneta Gądek-Moszczak, Maciej Kołomycki
• Keywords: Analysis of Variance, Bootstrap, One-Way ANOVA, Parametric Factorial Model, Stability Analysis, Statistical Analysis

References

[1] L. Davies, U. Gather, Analysis of Variance, in: J.E. Gentle, W.K. Härdle and Y. Mori, (Eds. ), Handbook of Computational Statistics, Springer Verlag, Berlin Heidelberg, 2012, pp.742-745.

[2] A. Rutherford, Introducing ANOVA and ANCOVA - A GLM Approach, SAGE Publications Ltd., London, Thousand Oaks, New Delhi, (2001).

[3] J.J. Buckley, Fuzzy statistics: hypothesis testing, Soft Comput. 9/7 (2005) 512-518.

[4] J.J. Buckley, Fuzzy probability and Statistics, Springer, Heidelberg, (2006).

[5] J. Shao, D. Tu, The Jackknife and Bootstrap, Springer, New York, (1995).

[6] M.J. Chernick, Bootstrap Methods: A Guide for Practitioners and Researchers, John Wiley & Sons, Inc., Hoboken, New Jersey, (2008).

[7] A. Szczotok, R. Przeliorz, Phase transformations in CMSX-4 nickel-base superalloy, IOP Conf. Ser. Mat. Sci. Eng. 35 012005 (2012).

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

[8] Y. Huang, L. Wang, Y. Liu, S. Fu, J. Fu, P. Yan, Microstructure evolution of a new directionally solidified Ni-based superalloy after long-term aging at 950°C up to 1000h, Trans. Nonferrous Met. Soc. China 21 (2011) 2199-2204.

DOI: 10.1016/s1003-6326(11)60995-3

[9] J. Safari, S. Nategh, On the heat treatment of Rene 80 nickel-base superalloy, J. Mater. Process. Technol. 176 (2006) 240-250.

DOI: 10.1016/j.jmatprotec.2006.03.165

[10] Springer Handbook of Engineering Statistics, H. Pham (Ed. ), Springer Verlag, London, (2006).

[11] 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

[12] P. Grzegorzewski, Decision support in uncertain conditions. Statistical methods for imprecise data [in Polish], AOW EXIT, Warszawa, (2006).

[13] J. Pietraszek, A. Gadek-Moszczak, The smooth bootstrap approach to the distribution of a shape in the ferritic stainless steel AISI 434L powders, Solid State Phenom. 197 (2013) 162-167.

DOI: 10.4028/www.scientific.net/ssp.197.162

[14] J. Pietraszek, N. Radek, K. Bartkowiak, Advanced statistical refinement of surface layer's discretization in the case of electro-spark deposited carbide-ceramic coatings modified by a laser beam, Solid State Phenom. 197 (2013) 198-202.

DOI: 10.4028/www.scientific.net/ssp.197.198

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

DOI: 10.14314/polimery.2006.206

[16] A. Gadek-Moszczak, L. Wojnar, Objective, quantitative and automatic X-ray image. Analysis of the bone regenerate in the Ilizarov method, in: V. Capasso, G. Aletti, A. Micheletti (Eds. ), Stereology and Image Analysis, The 10th European Congress of ISS Proceedings, Bologna, 2009, pp.453-458.

[17] M. Scendo, J. Trela, N. Radek, Purine as an effective corrosion inhibitor for stainless steel in chloride acid solutions, Corros. Rev. 30 (2012) (1-2) 33-45.

DOI: 10.1515/corrrev-2011-0039

[18] A. Szymanska, D. Oleszak, A. Grabias, M. Rosinski, K. Sikorski, J. Kazior, A. Michalski, K.J. Kurzydlowski, Phase transformations in ball milled AISI 316L stainless steel powder and the microstructure of the steel obtained by its sintering, Rev. Adv. Mater. Sci. 8/2 (2004).

[19] R. Ulewicz, F. Novy, J. Selejdak, Fatigue strength of ductile iron in ultra-high cycle regime, Adv. Mater. Res. -Switz. 874 (2014) 43-48.

DOI: 10.4028/www.scientific.net/amr.874.43

[20] R. Ulewicz, J. Selejdak, S. Borkowski, M. Jagusiak-Kocik, Process management in the cast iron foundry, in: METAL 2013. 22nd International Conference on Metallurgy and Materials. Conference Proceedings, Brno, Czech Republic, 2013, p.1926-(1931).

[21] E. Skrzypczak-Pietraszek, A. Hensel, Polysaccharides from melittis melissophyllum L. herb and callus, Pharmazie 55 (2000) (10) 768-771.

[22] E. Skrzypczak-Pietraszek, J. Pietraszek, Seasonal changes of flavonoid content in melittis melissophyllum L. (Lamiaceae), Chem. Biodivers. 11/4 (2014) 562-570.

DOI: 10.1002/cbdv.201300148

[23] E. Skrzypczak-Pietraszek, J. Slota, J. Pietraszek, The influence of L-phenylalanine, methyl jasmonate and sucrose concentration on the accumulation of phenolic acids in Exacum affine Balf. f. ex Regel shoot culture, Acta Biochim. Pol. 61/1 (2014).

DOI: 10.18388/abp.2014_1922