Abstract
The paper presents new statistical approaches for modeling highly variable mechanical properties and screening specimens in development of new materials. Particularly, for steels, Charpy V-Notch (CVN) exhibits substantial scatter which complicates prediction of impact toughness. The paper proposes to use Conditional Value-at-Risk (CVaR) for screening specimens with respect to CVN. Two approaches to estimation of CVaR are discussed. The first approach is based on linear regression coming from the Mixed-Quantile Quadrangle, and the second approach builds CVN distribution with percentile regression, and then directly calculates CVaR. The accuracy of estimated CVaR is assessed with some variant of the coefficient of multiple determination. We estimated discrepancy between estimates derived by two approaches with the Mean Absolute Percentage error. We compared VaR and CVaR risk measures in the screening process. We proposed a modified procedure for ranking specimens, which takes into account the uncertainty in estimates of CVaR.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Golodnikov, A., Macheret, Y., Trindade, A., Uryasev, S., Zrazhevsky, G.: Statistical Modeling of Composition and Processing Parameters for Alloy Development. Model. Simul. Mater. Sci. Eng. 13, 633–644 (2005)
McClintock, F.A., Argon A.S.: Mechanical Behavior of Materials. Addison-Wesley, Reading, MA (1966)
Goldren, A.P., Cox, T.B.: AMAX Report, CPR-2, AMAX Materials Research Center, Ann Arbor, MI (1986)
Todinov, M.T.: Uncertainty and Risk Associated with the Charpy Impact Energy of Multi-run Welds. Nucl. Eng. Des. 231, 27–38 (2004)
Koenker, R., Bassett, G.: Regression Quantiles. Econometrica 46, 33–50 (1978)
Rockafellar, R.T., Uryasev, S.: The Fundamental Risk Quadrangle in Risk Management, Optimization, and Statistical Estimation. Surv. Oper. Res. Manag. Sci. 18, 33–53 (2013)
Koenker, R., Machado, J.A.F.: Goodness of Fit and Related Inference Processes for Quantile Regression. J. Am. Stat. Assoc. 94, 1296–1310 (1999)
Koenker, R., d’Orey, V.: Computing Regression Quantiles. Appl. Stat. 43, 410–414 (1994)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Zrazhevsky, G., Golodnikov, A., Uryasev, S., Zrazhevsky, A. (2015). Advanced Statistical Tools for Modelling of Composition and Processing Parameters for Alloy Development. In: Migdalas, A., Karakitsiou, A. (eds) Optimization, Control, and Applications in the Information Age. Springer Proceedings in Mathematics & Statistics, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-319-18567-5_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-18567-5_21
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18566-8
Online ISBN: 978-3-319-18567-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)