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Estimating the Probability Distributions of Alloy Impact Toughness: a Constrained Quantile Regression Approach

In: Cooperative Systems

Author

Listed:
  • Alexandr Golodnikov

    (University of Florida)

  • Yevgeny Macheret

    (Institute for Defense Analysis)

  • A. Alexandre Trindade

    (University of Florida)

  • Stan Uryasev

    (University of Florida)

  • Grigoriy Zrazhevsky

    (University of Florida)

Abstract

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.

Suggested Citation

  • Alexandr Golodnikov & Yevgeny Macheret & A. Alexandre Trindade & Stan Uryasev & Grigoriy Zrazhevsky, 2007. "Estimating the Probability Distributions of Alloy Impact Toughness: a Constrained Quantile Regression Approach," Lecture Notes in Economics and Mathematical Systems, in: Don Grundel & Robert Murphey & Panos Pardalos & Oleg Prokopyev (ed.), Cooperative Systems, pages 269-283, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-48271-0_16
    DOI: 10.1007/978-3-540-48271-0_16
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