WITHIN-MILL VARIATION IN THE MEANS AND VARIANCES OF MOE AND MOR OF MILL-RUN LUMBER OVER TIME
Keywords:
mill run, full lumber population, modulus of rupture, modulus of elasticity, mean, variance, seasonal difference, mixed normal distributionAbstract
The literature related to the phenomenon of pseudo-truncation has emphasized that the mechanical property distributions of graded lumber subpopulations are determined by the mechanical property distributions of the mill-run (or full) lumber populations from which the subpopulations are formed. Whereas previous studies have shown that the means and variances of mechanical properties in the same visual grade of lumber can vary from mill to mill, there have been no studies on the stability of the means and variances of MOE and modulus of rupture (MOR) in mill-run lumber populations at the same mill over time. The objective of this study was to investigate if statistically significant differences between the means and variances of MOE and MOR in mill-run lumber populations at the same mill could be observed across samples taken several months apart. Two mill-run samples of 200 pieces of rough, dry 2x4 southern pine lumber were taken from each of four Mississippi sawmills: one in the summer and one in the winter. For each mill, the summer and winter means and variances of flexural MOR and MOE were compared. Whereas no significant differences were found between the mean MOE and/or mean MOR of the summer and winter samples from Mills 2 and 4, significant differences in mean MOE and/or MOR were found between the summer and winter samples from Mills 1 and 3. In addition, a Levene’s test on the MOR of Mill 1 showed significant differences in the variance between the summer and winter samples. Further analysis revealed that in addition to the fact that the winter mill-run sample from Mill 3 was made up of a larger percentage of lower grade material than the summer sample, there were pronounced strength differences between the summer and winter samples both around the median and at the lowest (near-minimum) percentiles within each grade. This reinforces the notion that changes in mill-run MOR distributions over time can have an important effect on the overall strength of a given mill’s visual grades over time. A theory of mixed distributions could account for these differences.
References
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 in-grade tests of full-size specimens. D1990-16. Annual book of ASTM standards. ASTM, West Conshohocken, PA.
Bender D, Woeste F (2012) Effect of variability on lumber design values. Frame Build News 24(4):34-39.
Galligan WL, Snodgrass DV (1970) Machine stress rated lumber: Challenge to design. J StructDiv 96(12):2639-2651.
IBM Corp. (2017) IBM SPSS statistics for windows, version 25.0 [computer software]. IBM Corp., Armonk, NY.
Minitab, Inc. (2017) Minitab 18 statistical software [computer software]. Minitab, Inc., State College, PA. www.minitab.com.
Owens FC, Verrill SP, Shmulsky R, Kretschmann DE (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.
Ross RJ, Pellerin RF (1994) Nondestructive testing for assessing wood members in structures: A review. General Technical Report FPL-GTR-70. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, Madison, WI. 40 pp.
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 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 (2018) A fit of mixture of bivariate normals to lumber stiffness strength data. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory Research Paper FPL-RP-696, Madison, WI. 44 pp.
Verrill SP, Owens FC, Kretschmann DE, Shmulsky R, Brown LS (2019) Visual and MSR grades of lumber are not 2-parameter Weibulls and why this may matter. J Test Eval 48 doi: 10.1520/JTE20180472 (In press). Epub 24April 2019.
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.
