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: Visual and MSR grades of lumber are not two-parameter Weibulls and why it matters (with a discussion of censored data fitting)

Source: Res Pap. FPL-RP-703. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 40 p.

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

Publication Year: 2019  View PDF »

Category: Research Papers

Abstract: It has been common practice to assume that a two-parameter Weibull probability distribution is suitable for modeling lumber strength properties. Verrill and others (papers published in 2012, 2013, 2014, and 2015) demonstrated theoretically and empirically that the modulus of rupture (MOR) distribution of a visual grade of lumber or of lumber that has been “binned” by modulus of elasticity (MOE) is not a two-parameter Weibull. Instead the tails of the MOR distribution are thinned via “pseudo-truncation.” Verrill and others (papers published in 2013 and 2014) performed simulations that established that fitting two-parameter Weibulls to pseudo-truncated data via either full or censored data methods can yield poor estimates of probabilities of failure. In this paper we support the 2013 and 2014 simulation results by analyzing large “In-Grade type” data sets and establishing that two-parameter Weibull fits yield inflated estimates of the probability of lumber failure when specimens are subjected to loads near allowable properties. We also discuss the censored data or “tail fitting” methods permitted under ASTM D5457, and we extend, via simulations, the empirical “In-Grade type” data results for individual pieces of lumber to a simple seven-member assembly.

Keywords: Two-parameter Weibull distribution; pseudotruncated Weibull distribution; machine stress rated lumber; MSR lumber; MOE binned lumber; visually graded lumber; thinned tail; lumber property distribution; lumber reliability; lumber assembly reliability; censored data two-parameter Weibull fits

Publication Review Process: Informally Refereed (Peer-Reviewed)

File size: 583 kb(s)

Date posted: 03/06/2020

This publication is also viewable on Treesearch:  view
RITS Product ID: 97196
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 »