DISTRIBUTIONS OF MOE AND MOR IN EIGHT MILL-RUN LUMBER POPULATIONS (FOUR MILLS AT TWO TIMES)
Keywords:
full lumber population, mill run, modulus of elasticity, modulus of rupture, normal distribution, Weibull, pseudo-truncated, machine stress rated lumber, MSR, visually graded lumber, lumber property distribution, reliabilityAbstract
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.
References
American Society of Civil Engineers (ASCE) (1988) Load and resistance factor design for engineered wood construction: A pre-standard report. Task Committee on Load and Resistance Factor Design for Engineered Wood Construction, American Society of Civil Engineers, New York, NY.
Anderson GC, Owens FC, Shmulsky R, Ross RJ (2019) Within-mill variation in the means and variances of MOE and MOR of mill-run lumber over time. Wood Fiber Sci 51(4):387-401.
ASTM (2015) Standard test methods of static tests of lumber in structural sizes. D198-15. Annual book of ASTM standards. ASTM, West Conshohocken, PA.
ASTM (2016) Standard practice for establishing allowable properties for visually graded dimension lumber from ingrade tests of full-size specimens. D1990-16. Annual book of ASTM standards. ASTM, West Conshohocken, PA.
ASTM (2017a) Standard practice for evaluating allowable properties for grades of structural lumber. D2915-17. Annual book of ASTM standards. ASTM, West Conshohocken, PA.
ASTM (2017b) Standard specification for computing reference resistance of wood-based materials and structural connections for load and resistance factor design. D5457-17. Annual book of ASTM standards. ASTM, West Conshohocken, PA.
D’Agostino RB, Stephens MA (1986) Goodness-of-fit techniques. Marcel Dekker, New York, NY.
Evans JW, Johnson RA, Green DW (1997) Goodness-of-fit tests for two-parameter and three-parameter Weibull distributions. Pages 159-178 in NL Johnson, N Balakrishnan, eds. Advances in the theory and practice of statistics: A volume in honor of Samuel Kotz. Wiley, New York, NY.
Galligan WL, Hoyle RJ, Pellerin RF, Haskell JH, Taylor JR (1986) Characterizing the properties of 2-inch softwood dimension lumber with regressions and probability distributions: Project completion report. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, Madison, WI.
Green DW, Evans JW (1987) Mechanical properties of visually graded lumber, Vol. 1-8. U.S. Department of Commerce. National Technical Information Service, Springfield, VA.
Gross J, Ligges U (2015) nortest: Tests for Normality. R package version 1.0-4. https://CRAN.R-project.org/package. nortest. Accessed September 13, 2019.
Krit M (2017) EWGoF: Goodness-of-fit tests for the exponential and two-parameter Weibull distributions. R package version 2.2.1. https://CRAN.R-project.org/package.EWGoF. https://CRAN.R-project.org/package. nortest. Accessed September 13, 2019.
Owens FC, Verrill SP, Kretschmann DE, Shmulsky R (2018) Distributions of MOE and MOR in a full lumber population. Wood Fiber Sci 50(3):265-279.
Owens FC, Verrill SP, Shmulsky R, Ross RJ (2019) Distributions of modulus of elasticity and modulus of rupture in four mill-run lumber populations. Wood Fiber Sci 51(2): 183-192.
R Core Team (2018) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/,https://CRAN.R-project.org/package.nortest. Accessed September 13, 2019.
Ross RJ (ed) (2015) Nondestructive evaluation of wood, 2nd edition. General Technical Report FPL-GTR-238. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, Madison, WI. 169 pp.
Shapiro SS, Wilk MB (1965) An analysis of variance test for normality (complete sample). Biometrika 52(3-4):591-611.
Verrill SP, Evans JW, Kretschmann DE, Hatfield CA (2012) Asymptotically efficient estimation of a bivariate Gaussian-Weibull distribution and an introduction to the associated pseudo-truncated Weibull. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory Research Paper FPL-RP-666, Madison, WI. 76 pp.
Verrill SP, Evans JW, Kretschmann DE, Hatfield CA (2013) An evaluation of a proposed revision of the ASTM D 1990 grouping procedure. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory Research Paper FPL-RP-671, Madison, WI. 34 pp.
Verrill SP, Evans JW, Kretschmann DE, Hatfield CA (2014) Reliability implications in wood systems of a bivariate Gaussian-Weibull distribution and the associated univariate pseudo-truncated Weibull. J Test Eval 42(2):412-419.
Verrill SP, Evans JW, Kretschmann DE, Hatfield CA (2015) Asymptotically efficient estimation of a bivariate Gaussian-Weibull distribution and an introduction to the associated pseudo-truncated Weibull. Commun Stat Theory Methods 44:2957-2975.
Verrill SP, Owens FC, Kretschmann DE, Shmulsky R (2017) Statistical models for the distribution of modulus of elasticity and modulus of rupture in lumber with implications for reliability calculations. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory Research Paper FPL-RP-692, Madison, WI. 51 pp.
Verrill SP, Owens FC, Kretschmann DE, Shmulsky R, Brown L (2020) Visual and MSR grades of lumber are not 2-parameter Weibulls and why this may matter. J Test Eval 48(5).
Downloads
Published
Issue
Section
License
The copyright of an article published in Wood and Fiber Science is transferred to the Society of Wood Science and Technology (for U. S. Government employees: to the extent transferable), effective if and when the article is accepted for publication. This transfer grants the Society of Wood Science and Technology permission to republish all or any part of the article in any form, e.g., reprints for sale, microfiche, proceedings, etc. However, the authors reserve the following as set forth in the Copyright Law:
1. All proprietary rights other than copyright, such as patent rights.
2. The right to grant or refuse permission to third parties to republish all or part of the article or translations thereof. In the case of whole articles, such third parties must obtain Society of Wood Science and Technology written permission as well. However, the Society may grant rights with respect to Journal issues as a whole.
3. The right to use all or part of this article in future works of their own, such as lectures, press releases, reviews, text books, or reprint books.
