Summary
We extend our earlier work, Golodnikov et al [3] and Golodnikov et al [4], by estimating the entire probability distributions for the impact toughness characteristic of steels, as measured by Charpy V-Notch (CVN) at −84°C. Quantile regression, constrained to produce monotone quantile function and unimodal density function estimates, is used to construct the empirical quantiles as a function of various alloy chemical composition and processing variables. The estimated quantiles are used to produce an estimate of the underlying probability density function, rendered in the form of a histogram. The resulting CVN distributions are much more informative for alloy design than singular test data. Using the distributions to make decisions for selecting better alloys should lead to a more effective and comprehensive approach than the one based on the minimum value from a multiple of the three test, as is commonly practiced in the industry.
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Golodnikov, A., Macheret, Y., Trindade, A.A., Uryasev, S., Zrazhevsky, G. (2007). Estimating the Probability Distributions of Alloy Impact Toughness: a Constrained Quantile Regression Approach. In: Grundel, D., Murphey, R., Pardalos, P., Prokopyev, O. (eds) Cooperative Systems. Lecture Notes in Economics and Mathematical Systems, vol 588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48271-0_16
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DOI: https://doi.org/10.1007/978-3-540-48271-0_16
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