INVESTIGATION OF ALTERNATIVE STATISTICAL DISTRIBUTION MODELS FOR EXPLAINING AND PREDICTING THE PHYSICAL PROPERTIES OF LUMBER

• Sponsoring Institution: National Institute of Food and Agriculture
• Project Status: COMPLETE
• Funding Source: MCINTIRE-STENNIS
• Reporting Frequency: Annual
• Accession No.: 1015681
• Project Start Date: Jul 1, 2018
• Project End Date: Jun 30, 2022
• Program Code: [(N/A)]- (N/A)

Recipient Organization
MISSISSIPPI STATE UNIV
(N/A)
MISSISSIPPI STATE,MS 39762

Performing Department
Forest Products

Non Technical Summary
Scientists and engineers use mathematical models called distributions to estimate the probability lumber will break under particular conditions. Historically, they have relied on a few common distributions to model the stiffness and strength of lumber: for example, the normal distribution (a bell curve) and the Weibull distribution. Lumber grading agencies can use these distribution models to determine design values for each lumber grade - that is, how stiff the material is on average and what its "near minimum strength" might be. Because these design values are used by engineers to estimate how heavy a load a particular grade of lumber can support without breaking, they have important safety implications as well as market implications (that is, the lower the design value is for a particular grade and species of lumber, the less that lumber is worth on the market). If the mathematical models that scientists and engineers use are not correct, one may underestimate or overestimate the probability that lumber will fail. Underestimating that probability could result in safety issues. Overestimating that probability could result in over-engineering and wasteful consumption of valuable forest resources.Recent statistical research by Dr. Steve P. Verrill from the USDA Forest Products Laboratory and his coauthors questions the appropriateness of the Weibull distribution as a model for strength in graded lumber. They highlight the importance of understanding the full population of lumber (comprised of lumber of all qualities regardless of grade) as a prerequisite to understanding the subpopulations of graded lumber. They demonstrate with mathematical proofs that, even if the strength distribution of a full lumber population is, for example, a Weibull distribution, the resulting distribution for lumber of any particular grade will not be Weibull. These results already cast doubt on the traditional assumption that strength of graded lumber can be adequately modeled with a Weibull distribution. However, an important question remains: what is the appropriate model for the full lumber population from which graded lumber is selected? If this question can be answered, it might be possible to derive a better, alternative model for stiffness and strength properties in individual lumber grades.Other researchers have examined the distribution of stiffness and strength in particular lumber grades, but it seems no one has yet investigated the distribution of stiffness and strength in a full lumber population. This research project seeks to fill that gap. If the distributions of stiffness and strength in full lumber populations can be correctly characterized, it might be possible to formulate alternative distributional models that would more accurately predict and explain the performance of graded lumber. Improved understanding of full distributions could facilitate the development of better grading technologies that offer good reliability and also the highest possible value recovery from this valuable forest resource. As lumber production is a sizable industry, nationally representing billions of dollars in annual product sales and hundreds of thousands of jobs in primarily rural areas, the benefit to the public would be substantial.This research will attempt to model several "full lumber populations" at the sawmill level. From each of several sawmills, 200 pieces of mill run pine lumber will be sampled. ("Mill run" refers to every piece of lumber that is produced during a particular timeframe, regardless of grade - in other words, the full lumber population of that mill on a given day.) Each board will be evaluated with specialized testing machines to measure its stiffness and strength values. Those values will then be analyzed with statistical software to find a good fitting distribution model for the stiffness and strength properties of each mill's full (mill run) population. The results among mills will be compared. If the distributions exhibit similarities or patterns, it might be possible to propose a general characterization of mill run populations from these mills. This, in turn, might make it possible to derive alternative distributional models that would more accurately predict and explain the stiffness and strength of graded lumber. Results from this research will be published in the form of academic journal articles, theses and dissertations. Results will also be presented at academic and forest products industry conferences.

Animal Health Component

10%

Research Effort Categories

Basic

80%

Applied

10%

Developmental

10%

Classification

Knowledge Area (KA)	Subject of Investigation (SOI)	Field of Science (FOS)	Percent
123	0650	2090	100%

Knowledge Area
123 - Management and Sustainability of Forest Resources;

Subject Of Investigation
0650 - Wood and wood products;

Field Of Science
2090 - Statistics, econometrics, and biometrics;

Keywords

lumber

mechanical properties

modulus of elasticity

modulus of rupture

statistical distributions

weibull

normal distribution

Goals / Objectives
Statistical distributions are instrumental to the determination of allowable properties in dimension lumber. Applying statistical distributions to empirical data allows researchers to estimate near-minimum strength properties and the likelihood of failure in service. The reliability of those estimates is predicated on fitting a distribution to the data that is representative of the underlying population.While it has been common for researchers to model stiffness (modulus of elasticity, or MOE) as a normal distribution and strength (modulus of rupture, or MOR) as a normal, lognormal, or Weibull distribution (Green and Evans 1987, Evans et al. 1997, ASTM 2010, ASTM 2015a,), recent studies have suggested major inconsistencies with respect to how appropriate those distributional models might be for graded lumber. Verrill et al. (2014, 2015) demonstrate with mathematical proofs that, even if the strength distribution of an underlying full (i.e. mill run) lumber population is, for example, a Weibull distribution, the resulting distribution for the subpopulation after visual or MSR grading will not be Weibull.Verrill et al. (2014, 2015) have emphasized the role distributions of full (i.e. mill run) lumber populations might play in affecting the distributions of in-grade subpopulations. Instead of merely trying to fit a distribution model to in-grade data, Verrill et al. (2014, 2015) attempt to explain how the distribution of in-grade strength data might be derived from something more fundamental. Their theory starts with the basic assumption of a full population of lumber comprised not only of in-grade pieces but also of every other piece of lumber that is produced when logs are sawn. (Colloquially, one might refer to this as a "mill run" population.) Belonging to this full lumber population is an MOE-MOR bivariate distribution comprised of a marginal MOE and marginal MOR univariate distribution. They demonstrate how strength distributions of in-grade subpopulations can be derived from the MOE-MOR bivariate distribution of the full population by using predictors - MOE cutoffs in the case of MSR grading or visual grading cues in the case of visual grading.For the purpose of theoretical analysis, Verrill et al. (2014, 2015) made the assumption that the underlying marginal (mill run) distributions for MOE and MOR of a full lumber population were normal and Weibull, respectively, but this was no more than an educated guess based on assumptions made in the body of existing research. While there are numerous examples in the literature where distributions of in-grade populations have been assessed, noticeably absent are any cases where distributions have been fitted to full populations. The goal of this research proposal is to fill that gap.A recent pilot study by Verrill et al. (2017) showed early indication that the marginal strength distribution of a full lumber population sampled from a single mill on a single day was neither Weibull, normal nor log-normal. This research will expand on that initial study to include samples from multiple mills and perform statistical analyses on both the univariate and bivariate level.Specific project objectives are as follows.Measure the MOR (destructively) and MOE (destructively and nondestructively) of full-size mill run lumber samples acquired from multiple southern pine lumber mills.Fit both univariate marginal and bivariate distributions to each dataset and identify the best fitting models for MOE and MOR.Assess whether or not the best fitting models exhibit an overall pattern that could lead to new hypotheses of generalization.If the data suggest that generalization is not possible, consider other ways to use predictors to predict or explain the relationships among physical properties.Disseminate the results in academic publications.

Project Methods
A mill run sampling of 800-1600 kiln-dried, rough-sawn southern yellow pine (Pinus spp.) lumber specimens (sizes to be determined) will be taken from 4-8 sawmills (200 pieces each). At each mill, a stickered kiln pack will be chosen at random based on weekly kiln output. From the chosen kiln pack, the single top row of pieces will be set aside. (These pieces generally contain the most warp and account for only a very small percentage, on the order of 2%, of production. Warped pieces are difficult to mechanically test and warpage causes downgrade that otherwise would not be influential with respect to the strength/stiffness relationship.) Then, the next consecutive 200 pieces will be removed for testing. The sampled material will be brought to Mississippi State University, where it will be planed on all four sides to final dressed dimensions of 1.5 x 3.5 inches (3.81 x 8.89 cm). After planing, the mill run lumber will be visually graded by a certified inspector to provide additional data for future analyses.Nondestructive tests of dynamic MOE (using both transverse and longitudinal vibration) will be administered per the operating instructions of each device manufacturer.Destructive testing for static MOE and MOR procedures will be performed in accordance with ASTM D 198-15 per the Flexure Test Method (ASTM 2015). Maximum likelihood estimations will be used to fit statistical distributions to the data and estimate parameters.Anderson-Darling, Cramer-von Mises, Shapiro-Wilk, likelihood ratio tests, and chi-squared tests (for bivariate data) will be used to test for goodness-of-fit.The possibility that the mechanical properties of a full lumber population might be a mixture of distributions will also be investigated using similar methods.

Progress 10/01/19 to 09/30/20

Outputs
Target Audience:Our target audience for this reporting period was the attendees at the 2020 Forest Products Society Virtual International Conference, which was held online due to COVID-19. These attendees included individuals from both academia and industry. Panel attendees were engineers, researchers and students interested in lumber standards, reliability analyses, and lumber design values. At the 2020 Forest Products Society International Conference, we reported the correlations found between Metriguard's grain angle meter (Model 511) readings and bending properties of the 1,400 kiln-dried 2 × 4 specimens of southern pine (Pinus spp.) lumber used in this study. These findings suggest that the Metriguard Model 511 might have potential, in an industrial setting, to provide supplementary nondestructive data that could be more useful for assessing bending strength in lower-grade lumber. Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided?This project provided the PhD student with the following training and professional development. Through hands-on testing of the lumber specimens, learned how to operate an Instron universal testing machine, an acoustic velocity meter, a transverse vibration meter, and a grain angle meter. To perform statistical analyses using IBM Corporation's SPSS statistical software package. Gained experience making online presentations at the 2020 Forest Products Society Virtual Conference. Engaged in consultation and collaboration with the Drs. Robert J. Ross and Steve P. Verrill at the USDA Forest Products Laboratory in Madison, Wisconsin. How have the results been disseminated to communities of interest?At the 2020 Forest Products Society International Conference, we reported the correlations found between Metriguard's grain angle meter (Model 511) readings and bending properties of the 1,400 kiln-dried 2 × 4 specimens of southern pine (Pinus spp.) lumber used in this study. We also disseminated the grain angle meter reading correlations and the results of the univariate goodness-of-fit tests in the following print publications, respectively. Anderson, G. C., F. C. Owens, F. Franca, R. J. Ross, R. Shmulsky. 2020. Correlations between grain angle meter readings and bending properties of mill-run southern pine lumber. Forest Products Journal 70(3)275-278. Owens, F. C., S. P. Verrill, R. Shmulsky, R. J. Ross. 2020. Distributions of MOE and MOR in eight mill-run lumber populations (four mills at two times). Wood and Fiber Science 52(2): 165-177. Finally, we published two papers presenting evidence that visual and MSR grades are not two-parameter Weibull distributions and why that matters. What do you plan to do during the next reporting period to accomplish the goals?In the current period, we fit univariate distributions to the data (fulfilling the first half of Objective 2). In the next reporting period, we intend to fit bivariate statistical distributions to the MOE and MOR datasets and assess their goodness of fit (fulfilling the second half of Objective 2). Based on those results and the results from the univariate analysis in the current reporting period, we intend to assess whether or not the best fitting models exhibit an overall pattern that could lead to new hypotheses of generalization (Objective 3).

Impacts
What was accomplished under these goals? Per the schedule in the initial proposal, we fit univariate statistical distributions to the mill-run MOE and MOR datasets and evaluated them for goodness-of-fit, thereby fulfilling the first half of Objective 2. We fit normal, lognormal, two- and three-parameter Weibull, skew normal and mixed normal distributions to MOE and MOR for both "summer" and "winter" datasets. The results showed that normal, lognormal, two-parameter Weibull, and three-parameter Weibull distributions performed relatively poorly (i.e. their goodness-of-fit tests frequently rejected the null hypothesis at a 0.05 significance level). In contrast, skew normal distributions and mixtures of normal distributions performed relatively well (i.e. their goodness-of-fit tests frequently failed to reject the null hypothesis at a 0.05 significance level). These results suggest that perhaps none of the traditional distributions of normal, lognormal, or Weibull is adequate to model mill-run MOE or MOR across mills and at different times of year; rather, MOE and MOR in full lumber populations might be better modeled by skew normal or mixed normal distributions.

Publications

• Type: Journal Articles Status: Published Year Published: 2020 Citation: Anderson, G. C., F. C. Owens, F. Franca, R. J. Ross, R. Shmulsky. 2020. Correlations between grain angle meter readings and bending properties of mill-run southern pine lumber. Forest Products Journal 70(3)275-278.
• Type: Journal Articles Status: Published Year Published: 2020 Citation: Owens, F. C., S. P. Verrill, R. Shmulsky, R. J. Ross. 2020. Distributions of MOE and MOR in eight mill-run lumber populations (four mills at two times). Wood and Fiber Science 52(2): 165-177.
• Type: Journal Articles Status: Published Year Published: 2020 Citation: Verrill, S. P., F. C. Owens, D. E. Kretschmann, R. Shmulsky, L. S. Brown. 2020. Visual and MSR grades of lumber are not 2-parameter Weibulls and why this may matter. Journal of Testing and Evaluation 48(5):3946-3962.
• Type: Other Status: Published Year Published: 2019 Citation: Verrill, S. P., F. C. Owens, D. E. Kretschmann, R. Shmulsky, L. S. Brown. 2019. Visual and MSR grades of lumber are not two-parameter Weibulls and why it matters (with a discussion of censored data fitting). USDA Forest Service, Forest Products Laboratory, Madison, WI. FPL-RP-703. 40 pp.
• Type: Conference Papers and Presentations Status: Other Year Published: 2020 Citation: Anderson, G. C., F. C. Owens, R. J. Ross, R. Shmulsky. 2020. Correlations between grain angle meter readings and bending properties of mill-run southern pine lumber. Presentation at 2020 Forest Products Society International Conference, June 2020.

Progress 10/01/18 to 09/30/19

Outputs
Target Audience:Our target audience for this reporting period was the attendees at the 73rd Forest Products Society International Convention in Atlanta, Georgia. These attendees included individuals from both academia and industry. Panel attendees were engineers, researchers and students interested in lumber standards, reliability analyses, and lumber design values. We communicated the preliminary descriptive statistical data (means and variances) of the results of the mechanical testing in the form of a presentation at the 73rd Forest Products Society International Convention in Atlanta, Georgia. Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided?Through hands-on testing of the lumber specimens, PhD student Guangmei Anderson learned how to operate an Instron universal testing machine, an acoustic velocity meter, a transverse vibration meter, and a grain angle meter. She also performed statistical analyses using IBM Corporation's SPSS statistical software package. How have the results been disseminated to communities of interest?We communicated preliminary descriptive statistical data (means and variances) of the results of the mechanical testing in the form of a presentation at the 73rd Forest Products Society International Convention in Atlanta, Georgia. We taught a lab session of FP 4123/6123 Lumber Manufacturing during fall semester of 2019 at Mississippi State University in which we demonstrated in front of the students, the destructive testing methods used on this project thereby communicating the content and value of our research as it relates to strength and stiffness of lumber populations. What do you plan to do during the next reporting period to accomplish the goals?We intend to fit statistical distributions to the MOE and MOR datasets to determine which distribution models perform the best.

Impacts
What was accomplished under these goals? Per the schedule in the initial proposal, we prepped, planed and tested (both destructively and non-destructively) the 1400 mill run southern pine (Pinus spp.) lumber specimens we procured in the previous reporting period from the four Mississippi sawmills, thereby completing Objective 1. We recorded MOR, static MOE and dynamic MOE measured by both acoustic velocity and transverse vibration. We performed a preliminary analysis on the descriptive statistics of those measurements 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 at different times of year. We compared the means and variances of bending MOE and MOR of the summer and winter samplings from each mill. We found no significant differences between the mean mill-run MOE or mean mill-run MOR of the summer and winter samples from Mills 2 and 4, which suggests that the average strength and stiffness of the raw material at these two mills was consistent between the summer and winter samplings. On the other hand, we found significant differences in mean mill-run MOE and/or MOR between the summer and winter samples from Mills 1 and 3. In addition, we found that the Levene's test for the MOR of Mill 1 showed significant differences in the variance between summer and winter. These findings suggest that the raw material at these two mills changed somehow over time. We also discovered 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 notable differences in strength between the summer and winter samples both around the median and at the lowest (near-minimum) percentiles within each grade. This lends further support to 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.

Publications

• Type: Conference Papers and Presentations Status: Other Year Published: 2019 Citation: Anderson G.C., Owens F.C., Shmulsky R., Ross, R.J., 2019, Mean and Variance Comparisons of MOE and MOR between summer and winter samples of mill run lumber from four sawmills, (Presentation) Forest Products Society 73nd International Convention, Atlanta, GA, June 2019.
• Type: Journal Articles Status: Published Year Published: 2019 Citation: Anderson, G.C., Owens, F.C., Shmulsky, R., Ross, R.J., 2019, WITHIN-MILL VARIATION IN THE MEANS AND VARIANCES OF MOE AND MOR OF MILL-RUN LUMBER OVER TIME, Wood and Fiber Science, 51(4), 2019, pp. 387-401 https://doi.org/10.22382/wfs-2019-037 � 2019 by the Society of Wood Science and Technology

Progress 07/01/18 to 09/30/18

Outputs
Target Audience:Our target audience for this reporting period was the attendees at the Mississippi Lumber Manufactures Association Convention. We communicated the content and value of our research by providing static bending test demonstrations at our booth at the 2018 Mississippi Lumber Manufacturers Association Convention. We transported one of our universal testing machines to the exhibition hall in Biloxi, MS and provided demonstrations of how we gather strength and stiffness data. Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided?A PhD student and a Msc student enrolled in the graduate course FP 6123 Lumber Manufacturing. This course will provide with some of the technical knowhow needed to participate in this project - specifically, how the testing material is produced. How have the results been disseminated to communities of interest?We communicated the content and value of our research by providing static bending test demonstrations at our booth at the 2018 Mississippi Lumber Manufacturers Association Convention. We transported one of our universal testing machines to the exhibition hall in Biloxi, MS and provided demonstrations of how we gather strength and stiffness data. What do you plan to do during the next reporting period to accomplish the goals?We intend to plane the lumber specimens on four sides, labeled them, and prep them for both destructive and nondestructive testing.

Impacts
What was accomplished under these goals? Per the schedule in the initial proposal, we procured 1400 mill run southern pine (Pinus spp.) lumber specimens from four sawmills in the state of Mississippi. At each mill, a stickered kiln pack was chosen at random based on weekly kiln output. From the chosen kiln pack, the single top row of pieces was set aside. Then, the next consecutive 200 pieces were removed for testing. From three of the four mills, we obtained two separate samples. The material was transported to Mississippi State University. These actions satisfy the 2018 portion of the first objective indicated in the timetable in the initial proposal. As testing is forthcoming, there are no results or findings to report.

Publications