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    Author(s): Richard A. Johnson; James W. Evans; David W. Green
    Source: (Research paper FPL ; RP-575):11 p. : ill. ; 28 cm.
    Publication Series: Research Paper (RP)
    Station: Forest Products Laboratory
    PDF: View PDF  (148 KB)

    Description

    Accurate modeling of the joint stochastic nature of the strength properties of dimension lumber is essential to the determination of reliability-based design safety factors. This report reviews the major techniques for obtaining bivariate distributions and then discusses bivariate distributions whose marginal distributions suggest they might be useful for modeling the joint distribution of two strength properties. Finally, we pick a bivariate Weibull distribution and show that we can write its likelihood function under a proof loading scheme, offering the possibility that it can be used to model the joint distribution of two properties that must each be measured using a destructive test.

    Publication Notes

    • We recommend that you also print this page and attach it to the printout of the article, to retain the full citation information.
    • This article was written and prepared by U.S. Government employees on official time, and is therefore in the public domain.

    Citation

    Johnson, Richard A.; Evans, James W.; Green, David W. Some bivariate distributions for modeling the strength properties of lumber. (Research paper FPL ; RP-575):11 p. : ill. ; 28 cm.

    Keywords

    Lumber, Strength, Models, Variance, Distribution, Weibull distribution

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https://www.fs.usda.gov/treesearch/pubs/5800