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    Author(s): Steve P. Verrill; Frank C. Owens; David E. Kretschmann; Rubin Shmulsky; Linda S. Brown
    Date: 2019
    Source: Res Pap. FPL-RP-703. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 40 p.
    Publication Series: Research Paper (RP)
    Station: Forest Products Laboratory
    PDF: Download Publication  (583.0 KB)


    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.

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    • This article was written and prepared by U.S. Government employees on official time, and is therefore in the public domain.


    Verrill, Steve P.; Owens, Frank C.; Kretschmann, David E.; Shmulsky, Rubin; Brown, Linda S. 2019. Visual and MSR grades of lumber are not two-parameter Weibulls and why it matters (with a discussion of censored data fitting). Res Pap. FPL-RP-703. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 40 p.


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    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

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