Banner for LabNotes
From Lab Notes
Contact Information
Forest Products Laboratory
One Gifford Pinchot Drive
Madison, WI 53726-2398
Phone: (608) 231-9200
Fax: (608) 231-9592


You are here: FPL Home  / Information Products & Services  / Publications

Requested Product

Title: Estimated probability of breakage of lumber of a fixed “grade” can vary greatly from mill to mill and time to time

Source: Res. Pap. FPL-RP-705. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 47 p.

Author(s)Verrill, Steve P.; Owens, Frank C.; Arvanitis, Matthew A.; Kretschmann, David E.; Shmulsky, Rubin ; Ross, Robert J.; Lebow, Patricia

Publication Year: 2020  View PDF »

Category: Research Papers
Associated Research Project(s):   FPL-4714-1B  FPL-4851-2B

Abstract: To evaluate the reliability of lumber structures, we need (among many other things) good models for the strength and stiffness distributions of visual and machine-stressrated (MSR) grades of lumber. Verrill et al. established theoretically and empirically that the strength properties of visual and MSR grades of lumber are not distributed as twoparameter Weibulls. Instead, strength properties of grades of lumber must have (at least to a first approximation) “pseudo-truncated” distributions. To properly implement Verrill et al.’s pseudo-truncation theory, we must know the true mill run modulus of elasticity (MOE) and modulus of rupture (MOR) distributions. Owens et al. investigated the mill run distributions of MOE and MOR at two times for each of four mills. They found that univariate mill run MOE and MOR distributions are well-modeled by skewnormal distributions or mixtures of normal distributions, but not so well-modeled by normal, lognormal, two-parameter Weibull, or three-parameter Weibull distributions. Verrill et al. investigated a mixture of two bivariate normals model for the mill run bivariate MOE–MOR population at a single time at a single mill. (Some possible sources of two-component mixture relationships include a mixture of trees from a fast-grown plantation stand and a suppressed stand, trees of two separate species, small-diameter trees and large-diameter trees, and lumber from the pith region versus lumber from the bark region.) They found that a mixture of two bivariate normals model performed well. In this paper, we apply this model to all eight of the Owens et al. lumber samples. We find that the model continues to yield good fits. However, we also find that the fits differ from mill to mill and time to time. Some variability is, of course, to be expected. However, we find that the fitted models differ to such an extent that the calculated probability that a piece of lumber randomly drawn from a fixed “grade” breaks at a fixed load can vary by a factor as large as 35 when we permit both season and mill to vary, and as large as 15 when we permit only mill to vary. Similar factors were found when we replaced fixed loads with loads randomly drawn from fixed load distributions.

Keywords: Machine-stress-rated lumber; MSR lumber; MOE binned lumber; visually graded lumber; lumber property distribution; lumber reliability; bivariate normal; mixture of bivariate normals

Publication Review Process: Informally Refereed (Peer-Reviewed)

File size: 1,024 kb(s)

Date posted: 08/21/2020

This publication is also viewable on Treesearch:  view
RITS Product ID: 98657
Current FPL Scientists associated with this product (listed alphabetically)
Arvanitis, Matthew
Mathematical Statistician
Kretschmann, David E.
Research General Engineer
Lebow, Patricia K.
Mathematical Statistician
Ross, Robert J.
Supervisory Research Gen. Engineer
Verrill, Steve P.
Mathematical Statistician

Additional items that might interest you
View the video celebrating FPL's 100 years of public service in 2010, from the producers of the Greatest Good....view

Research Highlights from FPL....view

Termite Eradication: A search for the Holy Grail.... view

Moisture Management in Residential Construction Series videos...view

Wood Floor Systems in Residential Construction Series videos....view
- FPL's Mission and Strategic Plan -

FPL's mission is to identify and conduct innovative wood and fiber utilization research that contributes to conservation and productivity of the forest resource, thereby sustaining forests, the economy, and quality of life. ... ..more »

- FPL Research Emphasis Areas -
Advanced Composites

As an integral part of the FPL mission, we improve the long-term sustainability of our Nation's forests by creating valuable composite products from biobased materials ... ..more »

Advanced Structures

The FPL has been in the forefront of wood-frame housing research since 1910 and has long been recognized as a world leader in such housing-related areas as engineered wood ... ..more »

Forest Biorefinery

We all know the compelling reasons that the United States needs to reduce its dependence on fossil fuels. Historically, the greatest increases in energy demand have been for transportation fuels ... ..more »


A leader in wood products research for over a century, the FPL is positioning itself to become the lead Federal research facility for the application of nanotechnology in forest products ... more »

Woody Biomass Utilization

Forests in the United States contain a substantial amount of small-diameter, overstocked, and underutilized material.FPL research projects are exploring the potential of the small-diameter ... ..more »