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: Statistical models for the distribution of modulus of elasticity and modulus of rupture in lumber with implications for reliability calculations

Source: Res. Pap. FPL-RP-692. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 51 p.

Author(s)Verrill, Steve P.; Owens, Frank C.; Kretschmann, David E.; Shmulsky, Rubin

Publication Year: 2017  View PDF »

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

Abstract: It is common practice to assume that a two-parameter Weibull probability distribution is suitable for modeling lumber properties. Verrill and co-workers demonstrated theoretically and empirically that the modulus of rupture (MOR) distribution of visually graded or machine stress rated (MSR) lumber is not distributed as a Weibull. Instead, the tails of the MOR distribution are thinned via “pseudo-truncation.” The theoretically portion of Verrill’s argument was based on the assumption of a bivariate normal—Weibull (Gaussian—Weibull) MOE—MOR distribution for the full population of lumber (as opposed to the bivariate distribution of visual or MSR grades of lumber). We felt that it was important to investigate this assumption. In the absence of data sets in the literature that were drawn from the full population at a mill, we determined to obtain such a sample for analysis. In this paper, we report the results from this analysis. From the current experiment on mill run lumber, we conclude that if reliability engineers are entertaining the idea of obtaining new efficiencies via careful probability modeling of strength properties, then additional experimental research must be done on the fundamental question of valid models for stiffness and strength distributions for full populations of lumber from a single mill on a single day. Further, we suspect that even if research determines that a simple model can characterize such a distribution, further research will determine that this simple model varies from day to day, mill to mill, and region to region so that an ever-changing mixture model is the correct model. In this case, to ensure that reliability goals are efficiently met, reliability engineers might need to develop detailed computer models that yield real-time, in-line estimates of lumber strength based on measurements of stiffness, specific gravity, knot size and location, slope of grain, and other strength predictors.

Keywords: normal distribution; mixed normal distribution; two-parameter Weibull distribution; three-parameter beta distribution; skew normal distribution; mixed bivariate normal distribution; bivariate Gaussian-Weibull distribution; pseudo-truncated Weibull distribution; machine stress rated data; MSR data; probability density functions; goodness-of-fit; mill run; thin tail; lumber property distribution

Publication Review Process: Informally Refereed (Peer-Reviewed)

File size: 1,024 kb(s)

Date posted: 12/07/2017

This publication is also viewable on Treesearch:  view
RITS Product ID: 89296
Current FPL Scientists associated with this product (listed alphabetically)
Kretschmann, David E.
Research General 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 »