Distributions of MOE and MOR in Eight Mill-Run Lumber Populations (Four Mills at Two Times)

Abstract

To evaluate the reliability of lumber structures, good models for the strength and stiffness distributions of visual and machine stress-rated (MSR) grades of lumber are necessary. Verrill and coworkers established theoretically and empirically that the strength properties of visual and MSR grades of lumber are not distributed as 2-parameter Weibulls. Instead, strength properties of grades of lumber must have “pseudo-truncated” distributions. To properly implement the pseudo-truncation theory (to correctly estimate the MOR and MOE distributions of graded subpopulations), one must know the MOE and MOR distributions of full (“mill-run”) lumber populations. Owens and coworkers investigated the mill-run distributions of MOE and MOR at each of four mills. They found that univariate mill-run MOE and MOR distributions are well-modeled by skew normal distributions or mixtures of normal distributions but not so well modeled by normal, lognormal, 2-parameter Weibull, or 3-parameter Weibull distributions. They noted that it was important to investigate whether these results were stable over time. In this article, to investigate stability over time, the authors extend the analyses of “summer” data sets performed by Owens et al to new mill-run “winter” data sets. The results show that normal, lognormal, 2-parameter Weibull and 3-parameter Weibull distributions continue to perform relatively poorly, and that skew normal distributions and mixtures of normal distributions continue to perform relatively well.