DISTRIBUTIONS OF MOE AND MOR IN A FULL LUMBER POPULATION
Keywords:lumber property, distribution, normal, mixed normal, Weibull, beta, skew normal, bivariate, Gaussian–Weibull, pseudo-truncated Weibull, MSR
Reliability calculations for lumber products ultimately depend on the statistical distributions that we use to model lumber stiffness and strength. Fits of statistical distributions to empirical data allow researchers to estimate the probability of failure in service. For these fits to be useful, the theoretical statistical distributions must be good matches for the empirical lumber property populations. It has been common practice to assume that the MOE of a grade of lumber is well-fit by a normal distribution, and the MOR of a grade of lumber is well-fit by a normal, lognormal, or two-parameter Weibull distribution. Recent theoretical results and empirical tests have cast significant doubt on these assumptions. The exact implications of the theoretical results depend on the distributions of full (mill-run) MOE and MOR populations. Mill-run data have not yet appeared in the literature. Instead, studies have focused on subpopulations formed by visual or machine stress rated (MSR) grades of lumber. To better understand the implications of the recent theoretical results, we have investigated the statistical distributions of mill-run MOE and MOR data. An ungraded mill-run sample of 200 southern pine 24 s produced at a single mill on a single day was subjected to both nondestructive (transverse vibration and longitudinal stress wave) evaluation and static bending tests to determine its MOE and MOR values. Various distributions were fit to the MOE and MOR data and evaluated for goodness-of-fit. The results suggest that mill-run MOE might be adequately modeled by a normal distribution or a mixture of two normal distributions, mill-run MOR might be adequately modeled by a skew normal distribution or a mixture of two normals, and neither mill-run MOE nor mill-run MOR is well-fit by a Weibull distribution.
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