Statistical Models for the Distribution of Modulus of Elasticity and Modulus of Rupture in Lumber with Implications for Reliability Calculations

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 "pseudotruncation."The theoretical 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 Contents