Some bivariate distributions for modeling the strength properties of lumber

Richard A. Johnson; James W. Evans; David W. Green

Treesearch

Some bivariate distributions for modeling the strength properties of lumber

Informally Refereed

Authors:

Richard A. Johnson, James W. Evans, David W. Green

Type:

Research Paper

Station:

Forest Products Laboratory

Source:

(Research paper FPL ; RP-575):11 p. : ill. ; 28 cm.

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Download (PDF 152 KB): https://research.fs.usda.gov/download/treesearch/5800.pdf

Abstract

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.

Keywords

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

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.