FPL Statistics Unit

Research Work Unit Description

  1. Number


  2. Station

    Forest Products Laboratory

  3. Unit Location

    Madison, WI 53705-2398

  4. Research Work Unit Title

    Statistical Methods in Wood and Fiber Research

  5. Project Leader

    James W. Evans, Project Leader, Forest Products Laboratory
    One Gifford Pinchot Drive, Madison, WI 53705-2398

  6. Area of Research Applicability


  7. Estimated Duration

    Five Years

  8. Mission

    To enhance the integrity and efficiency of the Forest Products Laboratory's research efforts through the development, evaluation, and promotion of modern statistical methods

  9. Justification and Problem Selection

    Our nation will continue to be faced with increasing demand for wood products and decreasing supplies. At the Forest Products Laboratory (FPL), we are supporting the active management of our nation's forests in meeting this demand in a way that achieves healthy ecosystems, protects watersheds and contributes to rural economic vitality. To this end, we are active in six strategic emphasis areas of research: sustainable ecosystems, conservation of forest resources, environmental technologies, fundamental research, public service, and social and economic vitality. To succeed in each of these strategic emphasis areas, powerful and efficient statistical tools must be available. Innovative experimental designs in FPL's bioremediation program are critical to FPL's environmental technology efforts. The advent of computer-intensive statistical methodologies such as bootstrapping offer opportunities to better understand the possible variation in predictions of future demands for resources from our national forests, thus helping in FPL's research in support of social and economic vitality. Statistical modeling of the effects of temperature and moisture changes on lumber properties influence FPL's fundamental research program by providing researchers with the capability of simulating environmental effects on end-use performance of wood-based systems.

    To continue supporting the FPL research program, the Statistics Unit needs to maintain a collaborative relationship with FPL research staff that enhances the quality of wood utilization research and economic assessments (Problem 1). This mission problem has been a critical part of the Statistics Unit since the unit was first formally created. Numerous FPL studies have been enhanced through professional assistance to scientists in designing experiments, analyzing data, mathematical modeling, and summarizing experimental results in tables and graphical displays. FPL's research program in major areas, such as composite research, requires the expertise of multidisciplinary teams to attack critical problems. Members of the Statistics Unit are integral parts of these research teams. They help the team identify research objectives, determine the best research approach, and design experiments that effectively and efficiently test research hypotheses.

    Conservation of forest resources is a cornerstone of sustainability. More efficient engineering designs can help conserve the resource by reducing the amount of wood in end products. Wood design has progressed from deterministic design methods to reliability-based design methods, which are more dependent on statistical methods. Characterizing the wood properties of new species or mixed species enhance economic value for wood fiber whose removal from the national forests can reduce fuel load and thus help sustain ecosystems. Characterization of properties no longer starts with an assumption that the strength properties of lumber specimens under load are normally distributed and independent from each other. Instead, wood properties are now regularly assumed to follow two- and three-parameter Weibull distributions or are characterized through nonparametric estimates. Other distributional forms, such as the Sb distribution, may further our capability to characterize wood properties. To obtain the best use of fiber from the national forests, we must be able to characterize wood properties as mixtures of distributions. Modeling multidimensional dependencies among wood properties requires the development of the bivariate Weibull distribution for use in wood property estimation. As our options for characterizing wood properties increase, we need to know how to choose which distributional form best represents the data or whether to use methods that don't assume a distributional form. We must be able to model relationships between properties in a way that allows us to predict performance when the material is under a combination of stresses. We need to be able to predict how processing affects performance through the development of models that help us understand the statistical uncertainty of our predictions. Thus we need improved statistical modeling of properties, processing and performance of wood, fiber and composites (Problem 2). Advances developed at FPL in characterizing wood properties and relationships between wood properties have been and will continue to be added to consensus performance standards, such as American Society of Testing and Materials (ASTM) standards. Such activities support FPL's public service role and have resulted in the use of FPL-produced computer programs and methods to estimate lumber properties in all recent submissions of new species' properties to the Board of Review (BOR) of the American Lumber Standards Committee (ALSC).

  10. Approach to Problem Solution

    Mission Problem (Problem Area 1). Enhancing the Quality of Wood Utilization Research and Economic Assessments.

    This mission problem focuses on enhancing FPL research activities through collaborative research with other FPL scientists, through professional support to scientists and through the transfer of research-derived technology in the form of user-friendly computer programs that provide new capabilities to FPL scientists. These programs will (1) allow scientists to fit complex distributions to their data and estimate properties based on the distributions, (2) provide the capability to calculate the power of tests in proposed research using new statistical tests developed by the Statistics Unit, and (3) transfer technology developed as part of the collaborative research efforts of members of the unit (such as programs to estimate drying schedules of wood species based on specific gravity or programs to estimate changes in strength properties of dimension lumber that occur with changes in moisture content). Professional support includes assistance to scientists in designing experiments, analyzing data, mathematically modeling results, and summarizing experimental results in tables and graphical displays. Collaborative research occurs when the research has a substantial statistical component and is conducted with members of the Statistics Unit as a part of research teams addressing Forest Service goals. The forest resource is changing. Small-diameter and underutilized species are a forest component that needs to be removed on public lands to restore ecosystem health. Material characterization is fundamental to the development of optimized and efficient use of the wood resource. In support of the Wood Engineering Research (WER) Strategic Plan at FPL, the statistics unit has an important role in the material characterization. Anticipated activities within the next 5 years are as follow:

    A. Evaluating the physical properties of traditional and underutilized species for structural applications

    The Statistics Unit is involved in helping to better understand the relationship between wood microstructure and mechanical and physical properties. In conjunction with RWU 4701 and RWU 4714, the Statistics Unit is looking at the problem of x-ray determination of microfibril angle. Microfibril angle (MFA) is believed to be highly correlated with wood properties. However, in the past, microfibril angle determinations have been time-consuming measurements made by microscopic examination of dyed specimens. This has restricted the usefulness of MFA as a strength property predictor. However, recently an x-ray diffraction technique has been proposed that would greatly simplify the task of obtaining MFA values. The collaborative research effort is aimed at converting the diffraction data to MFA estimates and comparing these x-ray diffraction estimates with those from a dye-based approach.

    B. In conjunction with RWU 4714, modeling properties and predicting performance of dimension lumber

    This collaborative research effort spans several studies. Following are a few highlights: Work is being done to (1) develop improved analytical models to predict the changes in dimension lumber properties that occur with changes in moisture content, (2) establish a better fundamental basis for predicting lumber strength properties using the In-Grade data bank and new studies planned to help develop improved models and (3) develop a better understanding of how to monitor for changes in lumber properties that might occur over time.

    C. Developing a knowledge base needed to use wood composites as a structural building material

    Members of the Statistics Unit are part of a large collaborative effort to connect raw materials and processing to end-use performance. Today's composites incorporate a variety of wood-based raw materials including fibers, flakes, strands, veneers, particulates and even dimension lumber. Composites are influenced by a number of processing variables. The three-step approach to understanding composites includes (1) understanding how use of different raw materials under constant processing affects composite performance, (2) understanding how processing variables using a basic raw material affect composite performance, and (3) optimizing processing parameters for a range of raw material. The Statistics Unit will play a strong supporting role in steps 1 and 2 and have lead responsibility in step 3.

    D. In conjunction with RWU 4723, extending the service-life of wood by abbreviating the time necessary to predict long-term performance of wood preservatives and by better evaluating the environmental impact of preservatives

    We need to explore time-to-failure approaches that could allow us to move away from the current "meet or beat" strategy to a "will this preservative system meet some end-use specification" approach. Use of time-to-failure has the potential advantage of allowing redesign of standards to be more end-use oriented (e.g., this product is designed to meet this lifetime with this degree of confidence). We need to look at other degradation measures and methods over time such as use of nondestructive evaluation (NDE) or fungal cellars, and develop approaches like a comprehensive (cumulative) index of condition for each stake that could be compared. With visual (ordinal) measurements, Markov models (which model probabilities of transitions from one state to another, say a 10 to a 9) are becoming more useful but require large amounts of data to test assumptions. With NDE and fungal cellar tests, many possibilities could and should be investigated, such as rates, area under curves, and time from maximum to minimum. Finally, field test data needs to be evaluated to determine ways of minimizing the cost of field trials and to develop data that can be used to calibrate lab and field measurements.

    E. Understanding the composition and molecular architecture of wood cell walls and intermolecular interactions of cell wall chemical components

    In conjunction with RWU 4709, the Statistics Unit is looking at the problem of underdetermined regressions that often occurs with Raman spectroscopy. In a standard regression, there are more observations than parameters to be estimated in a prediction model. In this case the parameters are usually estimated using standard least squares regression. However, given computerized data collection and situations in which the number of specimens to be measured is small (often due to cost or time constraints), scientists are increasingly confronted with underdetermined fitting problems (i.e., experiments that yield values on many "properties" for each of a relatively few specimens). For example, Raman spectroscopy on 10 specimens can result in a spectrum consisting of over 1,000 frequency-amplitude pairs for each specimen. If each of the amplitudes were used as a predictor, the standard least squares regression would be faced with 10 equations to estimate 1,000 parameters. This is an underdetermined problem. Not enough information is available to obtain unique estimates of all the parameters. One could try restricting attention to only a few of the possible predictors. However, this is not optimal because information is being discarded. In recent years, statisticians and chemometricians have proposed methods such as principal component regression, partial least squares, or ridge regression as ways of extracting as much information as possible from the data. Controversy exists as to the relative merits of these approaches. This collaborative research effort is aimed at evaluating the merits of different approaches to handling the underdetermined regression problem.

    F. In conjunction with RWU 4851, evaluating and improving the Price Endogenous Linear Programming System (PELPS) for use in long-term projections for the pulp and paper market and the lumber and panel markets

    PELPS is a modeling framework and computer program used by Forest Service scientists for economic modeling of the North American pulp and paper industry (NAPAP) and the North American solid wood sector (NASAW), both of which influence key policy decisions. In addition, it allows users to predict consumption, production, and capacity by technology and trade within or among regions for any sector. Collaborative research is aimed at enhancing predictions made from the economic models through mathematical and programmatic improvements. These include greater flexibility in modeling capacity expansion, constraining trade, improved by-product modeling, and modeling influences of resource changes on supply.

    Anticipated accomplishments for the next 5 years:

    1. Assistance to U.S. industry in developing methods to monitor changes in lumber properties that might occur over time

    2. Development of analytical models for predicting the effect of moisture content on the mechanical properties of dimension lumber

    3. Documentation of In-grade results of tests on Douglas Fir-Larch, Hem-Fir, and Southern Pine

    4. Documentation of results on 25 other commercially important species

    5. Development of improved analytical models to better predict the effect of growth features on properties of lumber

    6. Revision of PELPS modeling framework including publication of detailed user documentation

    7. Evaluation of by-product processing and capital investment in economic estimates

    8. Evaluation of methods for solving underdetermined fitting problems and the development of a public domain computer program that implements these methods

    9. Determination of the capability of x-ray diffraction to replace microscopy techniques and the development of a computer program that calculates microfibril angle estimates from x-ray diffraction measurements

    10. Evaluation of existing models of composite performance to identify differences, regions of similarity and compatibility with other models

    Problem Area 2. Improved statistical modeling of properties, processing and performance of wood, fiber and composites

    Innovative research efforts of FPL scientists to address critical issues often violate standard statistical assumptions and thus are hampered by the lack of appropriate statistical methodology. Research efforts in this problem area will focus on developing the improved statistical modeling methodology needed by FPL's research programs. In some situations, the research effort will focus on the evaluation of existing statistical methods. In other situations, it will be necessary to develop new methods or extend the capability of existing methods. The breadth of this research is as broad as FPL's research program. Research in this problem area will very likely be published in both statistical journals and journals appropriate to areas of FPL's research program. As an example, in the In-Grade research program, it was necessary to develop cheaper and more efficient procedures for testing lumber. The new procedure for testing lumber in compression parallel-to-the-grain utilized a short specimen cut from a full-length board and supported by a rigid sleeve. This procedure allowed testing without the expense of testing full-size specimens. Studying the relationship of full-size tests and small-specimen tests required development of a statistical procedure that would allow estimation of the correlation between the two tests. Since the full-size test and small-specimen test could not be performed on the same piece because each is a destructive test, classical correlation analysis could not be used because we could not meet the fundamental assumption that both properties are measured on the same specimen. Instead we had to develop a new "concomitance" procedure. Since we introduced the concept in the statistical literature, other researchers have developed and proposed alternative procedures.

    Anticipated activities within the next 5 years are as follow:

    A. Improved material characterization under combined loading

    We need to know how best to model the performance of wood-based materials under combined stresses where the strength properties under each stress requires a separate destructive test. We must also extend the procedures to situations in which strength properties do not have a bivariate normal distribution in order to more realistically model two or more related material characteristics in end-use performance.

    B. Improved estimation of material properties

    After data have been collected in an experiment, material characterization often requires that a distribution be fit to the data to estimate properties or to use in simulations. This may seem to be a relatively simple problem, but often it is not: (1) In some cases the best estimation method is unknown. For distributions used in FPL research, like the Weibull distribution, there are many different ways to estimate the parameters of the distribution from data. Comparisons among various types of estimators are needed, particularly when dealing with censored data sets (e.g., from proofloading specimens or from test equipment having a limited range of measurement). These comparisons are important to understanding the reliability of our fitted distribution in any use of the distribution. (2) Even if we can estimate all the distributional forms we are considering for the data, it is often not clear what distributional form best fits the data. Measures of goodness-of-fit of distributions can help if they exist. However, they may not exist for censored data sets. Also, they may not exist for some types of estimation (e.g., the regression estimators of Weibull parameters that are part of current reliability-based design procedures). We need to develop measures that help us evaluate the fit of a distribution for censored data and when nontraditional estimators (like the regression estimates) are used. (3) Existing distributional forms used in FPL research may limit our capability to effectively represent data. Introducing new distributional forms, such as bivariate Weibull distributions and Sb distributions, requires us to develop new estimation and goodness-of-fit procedures. However, they offer potentially better distributional forms to use in simulations of performance of materials. Mixtures of distributions also are needed to model performance of composite mixtures or material from multiple sources. The capability of fitting mixtures of distributions and evaluating their fit could be critical to composite modeling research at FPL.

    C. Improved ways of measuring the effectiveness of FPL research efforts

    The dwindling timber resource has increased the need to evaluate wood material to determine its best use. This often involves sorting the material into categories. The need for evaluation of the efficiency of a sorting procedure occurs as part of developing a new lumber grading system or as part of a comparison of existing grading systems. This need arises in the development and comparison of methods to sort logs. This need occurs in assessing long term expected performance of some material as part of evaluation, assessment and repair of wood components. In each case above the specimens are sorted into categories of predicted performance. When tested, the same specimen has a true category of performance. Determining how well we were able to sort specimens into the proper categories is an important part of research. A preliminary search of the statistical literature has revealed more then 14 potential measures of the effectiveness of a sorting procedure. A comparison of the procedures is needed to determine what statistical and practical properties they might possess as a measure of how well specimens were sorted into categories. The promising procedures then need to be evaluated for incorporating weighted measures of misclassification. This latter problem arises because errors in sorting are not all equal. If we under-grade a specimen and it is stronger than we say, it does not have the same effect or potential loss as if we over-grade a specimen. Incorporating weighting into measures of sorting efficiency will allow us to better reflect the asymmetric consequences of misclassification.

    D. Improved modeling of the performance of engineered assemblies

    Developing new types of engineered assemblies to use the new forest mix of materials, achieving sustainability, and restoring ecosystems require us first to have a thorough knowledge of the performance of traditional systems. This is not always an easy step to make. Ideally, the properties of a wood-based structure would not change over time and its structural reliability could be modeled with a known factor of safety. However, it is well known that wood properties change over time when the wood is exposed to a variety of conditions, such as high temperature or excessive moisture. This is especially so when the wood has been treated to enhance its service life under one set of conditions, but then is used in an environment under another set of conditions. Reliability-based design will help in the engineering of such structures, but once the structure has been built how do we determine if the structure still meets its design requirements? Can we accurately predict how long it continue to meet its design requirements? With RWU 4714, the Statistics Unit is actively investigating several different methods of non-destructive evaluation that give reasonable predictions of the current property states of the wood composing a structure. Future work with RWU 4714 will concentrate on combining this type of non-destructive data with kinetic models of treated wood degradation evaluated under the structure's environmental conditions. In addition, the Statistics Unit will assess the statistical procedures in reliability-based design to determine if they can affect the quality of estimates of structural reliability with treated wood. Four areas that need to be considered are the effectiveness of the Rackwitz-Fiessler transformation in handling non-normality, the effect of simplifying assumptions on the difference between beta and the probability of failure, the effect of censored data on reliability estimates, and the potential for development of nonparametric reliability methods.

    E. With RWU 4851, development of statistical model evaluation procedures for economic models based on the PELPS paradigm

    Several options exist for this evaluation. First, simple measures could be developed and tested on models with lengthy historical records. Second, sensitivity analysis in the recursive framework would offer the ability to help determine the most influential model input by cost ranging manufacturing coefficients and ranging capacity. Third, alternative futures (scenarios) are already commonly evaluated for the economic models. Stochastic linear programming or robust optimization procedures allow the attachment of probabilities to these futures and find a solution that would be robust under the probabilistic occurrence of any of the futures. Finally, as opposed to the post-optimal sensitivity analysis procedures, it may be possible to incorporate coefficient distributional information in the model and allow progressive ranging on the solution.

    Anticipated accomplishments for the next 5 years:

    1. Evaluation of the effectiveness of different methods of estimating the correlation between lumber strength properties when the properties must be estimated through a destructive test

    2. Evaluation of potential measures of sorting effectiveness, assuming both equal and unequal cost for any misclassification

    3. Evaluation of estimation methods and development of goodness-of-fit measures for complete and censored Weibull distributions

    4. Development of thermal degradation models for treated lumber

    5. Evaluation and development of a serviceability framework for treated wood structures

    6. Development of statistical model evaluation procedures that can be used to enhance economic models based on the PELPS paradigm


Scientist Years Within Project
Scientist Mission Problem Problem Area 2 Total
Evans 4.0 1.0 5.0
Totals 4.0 1.0 5.0

Professional Support Years Within Project
Scientist Mission Problem Problem Area 2 Total
Hatfield 3.5 0.5 4.0
Herian 4.5 0.5 5.0
Lebow 4.0 1.0 5.0
Verrill 4.0 1.0 5.0
Totals 16.0 3.0 19.0

[Forest Service] [Forest Products Lab] [FPL Statistics Unit]

We welcome your comments and suggestions.

This page was last modified on January 22, 1999.