The Bootstrap Method As A Tool To Improve The Design Of Experiments

Renata Dwornicka; Norbert Radek; Jacek Pietraszek

doi:10.2478/czoto-2019-0092

.blurhash-client-img { display: none !important; }

The Bootstrap Method As A Tool To Improve The Design Of Experiments

System Safety: Human - Technical Facility - Environment

Volume 1 (2019): Issue 1 (March 2019)

By: Renata Dwornicka, Norbert Radek and Jacek Pietraszek

Open Access

|Mar 2019

Abstract

The paper considers the use of the bootstrap method to improve the determination of confidence intervals identified by the DOE (design of experiment) procedure. Two different approaches have been used: one that is appropriate for factorial designs and the other one relevant to the methodology of the response surface. Both approaches were tested on the real experiment datasets and compared with the results obtained from the classical statistical expressions based on well-known asymptotic formulas derived from the t distribution.

References

Box, G.E.P., Cox, D., 1964. An analysis of transformations. J. R. Stat. Soc. Ser. B-Stat. Methodol. B, 26, 211-246.
Search in Google Scholar Back to article
Box, G.E.P., Wilson, K.B., 1951. On the Experimental Attainment of Optimum Conditions. J. Roy. Stat. Soc. B, 13, 1-45.
Search in Google Scholar Back to article
Czerwiński, E., Gądek-Moszczak, A., Konopka, T., Latała, Z., Petryniak, R., Tabor, Z., Wojnar, L., Pietraszek, J., 2012. Development and optimization of diagnosis methods for estimation risk of fractures in osteoporosis based on a three-dimensional images of trabecular bones obtained in vivo. [in Polish]. Cracow University of Technology, Kraków, Poland.
Search in Google Scholar Back to article
Efron, B., 1979. Bootstrap Methods: Another Look at the Jackknife. Ann. Statist., 7(1), 1-26.
Search in Google Scholar Back to article
Fisher, R.A., 1925. Statistical Methods for Research Workers. Oliver and Boyd Press, Edinburgh, UK.
Search in Google Scholar Back to article
Fisher, R.A., 1935. The Design of Experiments. Oliver and Boyd Press, Edinburgh.
Search in Google Scholar Back to article
Gadek-Moszczak, A., 2017. History of stereology. Image Anal. Stereol., 36, 151-152.
Search in Google Scholar Back to article
Gadek-Moszczak, A., Pietraszek, J., Jasiewicz, B., Sikorska, S., Wojnar, L., 2015. The bootstrap approach to the comparison of two methods applied to the evaluation of the growth index in the analysis of the digital x-ray image of a bone regenerate. New Trends in Comput. Collective Intelligence, 572, 127-136.
Search in Google Scholar Back to article
Gadek-Moszczak, A., Matusiewicz, P., 2017. Polish Stereology – a Historical Review. Image Anal. Stereol., 36, 207-221.
Search in Google Scholar Back to article
Guzowski A, Sobczyk A., 2014. Reconstruction of Hydrostatic Drive and Control System Dedicated for Small Mobile Platform. ASME – Fluid Power Systems Technology, 8th FPNI Ph.D Symposium on Fluid Power, art.V001T05A012.
Search in Google Scholar Back to article
Kiefer, J., Wolfowitz, J., 1959. Optimum Designs in Regression Problems. Ann. Math. Stat., 30, 271-294.
Search in Google Scholar Back to article
Maszke, A., Dwornicka, R., Ulewicz, R., 2018. Problems in the implementation of the lean concept at a steel works – Case study. MATEC Web Conf., 183, art. 01014.
Search in Google Scholar Back to article
Montgomery, D.C., 2008. Design and analysis of experiments. Wiley, Hoboken.
Search in Google Scholar Back to article
Owen, A.B., 2001. Empirical Likelihood. Chapman & Hall/CRC, Boca Raton.
Search in Google Scholar Back to article
Pietraszek, J., Dwornicka, R., Szczotok, A., 2016. The Bootstrap Approach to the Statistical Significance of Parameters in the Fixed Effects Model. ECCOMAS Congress 2016 – Proc. 7^th European Congress on Computational Methods in Applied Sciences and Engineering, Vol.3, 6061-6068.
Search in Google Scholar Back to article
Pietraszek, J., Wojnar, L., 2016. The Bootstrap Approach to the Statistical Significance of Parameters in RSM Model. ECCOMAS Congress 2016 – Proc. 7^th European Congress on Computational Methods in Applied Sciences and Engineering, Vol.1, 2003-2009.
Search in Google Scholar Back to article
Scheffé, H., 1958. Experiments with Mixtures. J. Roy. Stat. Soc. B, 20, 344-360.
Search in Google Scholar Back to article
Shao, J., Tu, D., 1995. The Jackknife and Bootstrap. Springer, New York.
Search in Google Scholar Back to article
Skrzypczak-Pietraszek, E., 2016. High production of flavonoids and phenolic acids for pharmaceutical purposes in Vitex agnus castus L. shoot culture. New Biotechnol., 33, S155-S155.
Search in Google Scholar Back to article
Skrzypczak-Pietraszek, E; Hensel, A., 2000. Polysaccharides from Melittis melissophyllum L. herb and callus. Pharmazie, 55, 768-771.
Search in Google Scholar Back to article
Skrzypczak-Pietraszek, E., Pietraszek, J., 2009. Phenolic acids in in vitro cultures of Exacum affine Balf. f. Acta Biol. Cracov. Bot., 51, 62-62.
Search in Google Scholar Back to article
Skrzypczak-Pietraszek, E., Reiss, K., Zmudzki, P., Pietraszek, J., 2018. Enhanced accumulation of harpagide and 8-O-acetyl-harpagide in Melittis melissophyllum L. agitated shoot cultures analyzed by UPLC-MS/MS. PLoS ONE 13, e0202556.
Search in Google Scholar Back to article
Sygut, P., Klimecka-Tatar, D., Borkowski, S., 2016. Theoretical analysis of the influence of longitudinal stress changes on band dimensions during continuous rolling process. Arch. Metall. Mater., 61, 183-188.
Search in Google Scholar Back to article
Szczotok, A., Nawrocki, J., Gądek-Moszczak, A., Kołomycki, M., 2015. The Bootstrap Analysis of One-Way ANOVA Stability in the Case of the Ceramic Shell Mould of Airfoil Blade Casting. Solid State Phenomena, 235, 24-30.
Search in Google Scholar Back to article
Ulewicz, R.; Novy, F. R., 2016. The influence of the surface condition on the fatigue properties of structural steel. Journal of the Balkan Tribological Association, 22, 1147-1155.
Search in Google Scholar Back to article
Walczak, P., Sobczyk A., 2014. Simulation of water hydraulic control system of francis turbine. ASME – Fluid Power Systems Technology, 8th FPNI Ph.D Symposium on Fluid Power, art. V001T04A001.
Search in Google Scholar Back to article
Weglowski, B., Osocha, P., 2009. Modelling of creep for Y pipe from ferriticmartensitic P91 steel. Rynek Energii, 6, 140-145.
Search in Google Scholar Back to article
Wolfberg, J., 2006. Data Analysis Using the Method of Least Squares. Extracting the Most Information from Experiments. Springer, Berlin-Heidelberg.
Search in Google Scholar Back to article
Yates, F., 1935. Complex experiments. J. Roy. Statist. Soc., Suppl.2, 181-247.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/czoto-2019-0092 | Journal eISSN: 2657-5450

Journal RSS Feed

Language: English

Page range: 724 - 729

Submitted on: Nov 30, 2018

Accepted on: Feb 5, 2019

Published on: Mar 28, 2019

Published by: Quality and Production Managers Association

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

bootstrap,

statistics,

design of experiments,

numerical simulation

Related subjects:

Business and economics,

Business management,

Business management, other,

Engineering,

Mechanical engineering,

Production technology,

Social sciences,

Sociology,

Sociology of science, technology, and environment,

Communication science,

Interpersonal communication

© 2019 Renata Dwornicka, Norbert Radek, Jacek Pietraszek, published by Quality and Production Managers Association
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 1 (2019): Issue 1 (March 2019)