Fitting Statistical Distribution Models to MOE and MOR in Mill-Run Spruce and Red Pine Lumber Populations

Abstract

It has been mathematically demonstrated that the distribution of modulus of rupture (MOR) in a graded lumber subpopulation does not have the same theoretical form as the distribution of the mill-run population from which the subpopulation is drawn. However, the distributional form of the graded lumber subpopulation does depend heavily on the distributional form of the full mill-run population, and thus it is important to characterize the distributions of full mill-run lumber populations. Previous studies presented evidence suggesting that commonly-used distributions such as normal, lognormal, and Weibull distributions might not be suitable for modeling mill-run modulus of  elasticity (MOE) and MOR; rather, nontraditional distributions such as skew-normal and mixed normal seem to be more appropriate models for the MOE and MOR of mill-run populations across mills and time.  Previous studies of this kind have been carried out using only southern pine ( Pinus spp.) lumber.  In this study, we extend this work by investigating whether the distributional forms found to adequately fit southern pine mill-run lumber populations also adequately fit other species (or species groups).  The objective of this study is to identify statistical models that fit MOE and MOR distributions in mill-run spruce ( Picea spp.) and red pine ( Pinus resinosa ) lumber populations. Mill-run samples of 200 spruce 2 × 4 specimens and 200 red pine 2 × 4 specimens (for a total of 400 test pieces) were collected, and the MOE and MOR for each specimen were assessed. Various distributions were fit to the MOE and MOR mill-run data and evaluated for goodness-of-fit. In addition to further demonstrating that traditional distributions such as normal, lognormal, and Weibull may not be adequate to model mill run MOE and MOR populations, the results suggested that mixed normal and skew normal distributions might perform well across species.