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Some Bivariate Distributions For Modeling The Strength Properties Of Lumber
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Book Synopsis Some Bivariate Distributions for Modeling the Strength Properties of Lumber by : Richard Arnold Johnson
Download or read book Some Bivariate Distributions for Modeling the Strength Properties of Lumber written by Richard Arnold Johnson and published by . This book was released on 1999 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accurate modeling of the joint stochastic nature of the strength properties of dimension lumber is essential to the determination of reliability-based design safety factors. This report reviews the major techniques for obtaining bivariate distributions and then discusses bivariate distributions whose marginal distributions suggest they might be useful for modeling the joint distribution of two strength properties. Finally, we pick a bivariate Weibull distribution and show that we can write its likelihood function under a proof loading scheme, offering the possibility that it can be used to model the joint distribution of two properties that must each be measured using a destructive test.
Book Synopsis Some Bivariate Distributions for Modeling the Strength Properties of Lumber by : Richard A. Johnson
Download or read book Some Bivariate Distributions for Modeling the Strength Properties of Lumber written by Richard A. Johnson and published by . This book was released on 1999 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Models for the Distribution of Modulus of Elasticity and Modulus of Rupture in Lumber with Implications for Reliability Calculations by : S. P. Verrill
Download or read book Statistical Models for the Distribution of Modulus of Elasticity and Modulus of Rupture in Lumber with Implications for Reliability Calculations written by S. P. Verrill and published by . This book was released on 2017 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is common practice to assume that a two-parameter Weibull probability distribution is suitable for modeling lumber properties. Verrill and co-workers demonstrated theoretically and empirically that the modulus of rupture (MOR) distribution of visually graded or machine stress rated (MSR) lumber is not distributed as a Weibull. Instead, the tails of the MOR distribution are thinned via “pseudotruncation.” The theoretical portion of Verrill’s argument was based on the assumption of a bivariate normal–Weibull (Gaussian–Weibull) MOE–MOR distribution for the full population of lumber (as opposed to the bivariate distribution of visual or MSR grades of lumber). We felt that it was important to investigate this assumption. In the absence of data sets in the literature that were drawn from the full population at a mill, we determined to obtain such a sample for analysis. In this paper, we report the results from this analysis. From the current experiment on mill run lumber, we conclude that if reliability engineers are entertaining the idea of obtaining new efficiencies via careful probability modeling of strength properties, then additional experimental research must be done on the fundamental question of valid models for stiffness and strength distributions for full populations of lumber from a single mill on a single day. Further, we suspect that even if research determines that a simple model can characterize such a distribution, further research will determine that this simple model varies fromday to day, mill to mill, and region to region so that an ever-changing mixture model is the correct model. In this case, to ensure that reliability goals are efficiently met, reliability engineers might need to develop detailed computer models that yield real-time, in-line estimates of lumber strength based on measurements of stiffness, specific gravity, knot size and location, slope of grain, and other strength predictors.
Book Synopsis A Fit of a Mixture of Bivariate Normals to Lumber Stiffness by : S. P. Verrill
Download or read book A Fit of a Mixture of Bivariate Normals to Lumber Stiffness written by S. P. Verrill and published by . This book was released on 2018 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Research Paper FPL-RP written by and published by . This book was released on 1986 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dividends from Wood Research written by and published by . This book was released on 1999-07 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Fit of a Mixture of Bivariate Normals to Lumber Stiffness by : S. P. Verrill
Download or read book A Fit of a Mixture of Bivariate Normals to Lumber Stiffness written by S. P. Verrill and published by . This book was released on 2018 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been common practice to assume that a two-parameter Weibull probability distribution is suitable for modeling lumber strength properties. In a series of papers published from 2012 to 2018, Verrill et al. demonstrated theoretically and empirically that the modulus of rupture (MOR) distribution of a visual grade of lumber or of lumber that has been “binned” by modulus of elasticity (MOE) is not a two parameter Weibull. Instead, the tails of the MOR distribution are thinned via “pseudo-truncation.” The theoretical portion of Verrill et al.’s argument was based on the assumption of a bivariate normal–Weibull MOE–MOR distribution for the full (“mill run”) population of lumber. Verrill et al. felt that it was important to investigate this assumption. In a recent pair of papers, they reported results obtained from a sample of size 200 drawn from a mill run population. They found that normal, lognormal, three-parameter beta, and Weibull distributions did not fit the sample MOR distribution of these data. Instead, it appeared that the MOR data might be fit by a skew normal distribution or a mixture of two univariate normals. In this paper, we investigate whether the joint MOE–MOR data from Verrill et al.’s recent mill run study can be well modeled as a mixture of two bivariate normals.
Book Synopsis Continuous Bivariate Distributions by : N. Balakrishnan
Download or read book Continuous Bivariate Distributions written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2009-05-31 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with a review of general developments relating to bivariate distributions, this volume also covers copulas, a subject which has grown immensely in recent years. In addition, it examines conditionally specified distributions and skewed distributions.
Book Synopsis Maximum Likelihood Estimation of the Parameters of a Bivariate Gaussian-Weibull Distribution from Machine Stress-rated Data by : S. P. Verrill
Download or read book Maximum Likelihood Estimation of the Parameters of a Bivariate Gaussian-Weibull Distribution from Machine Stress-rated Data written by S. P. Verrill and published by . This book was released on 2016 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multiple Proof Load Designs for Estimating the Correlation Under Destructive Testing by : Wenqing Lu
Download or read book Multiple Proof Load Designs for Estimating the Correlation Under Destructive Testing written by Wenqing Lu and published by . This book was released on 2000 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Probabilities and Materials by : D. Breysse
Download or read book Probabilities and Materials written by D. Breysse and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most industrial and natural materials exhibit a macroscopic behaviour which results from the existence of microscale inhomogeneities. The influence of such inhomogeneities is commonly modelled using probabilistic methods. Most of the approaches to the evaluation of the safety of structures according to probabilistic criteria are somewhat scattered, however, and it is time to present such material in a coherent and up-to-date form. Probabilities and Materials undertakes this task, and also defines the great tasks that must be tackled in coming years. For engineers and researchers dealing with materials, geotechnics, solid mechanics, soil mechanics, statistics and stochastic processes. The expository nature of the book means that no prior knowledge of statistics or probability is required of the reader. The book can thus serve as an excellent introduction to the nature of applied statistics and stochastic modelling.
Book Synopsis Monthly Catalog of United States Government Publications by :
Download or read book Monthly Catalog of United States Government Publications written by and published by . This book was released on 1969 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Recent Advances in Reliability Theory by : N. Limnios
Download or read book Recent Advances in Reliability Theory written by N. Limnios and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents thirty-one extensive and carefully edited chapters providing an up-to-date survey of new models and methods for reliability analysis and applications in science, engineering, and technology. The chapters contain broad coverage of the latest developments and innovative techniques in a wide range of theoretical and numerical issues in the field of statistical and probabilistic methods in reliability.
Book Synopsis Reliability Implications in Wood Systems of a Bivariate Gaussian-Weibull Distribution and the Associated Univariate Pseudo-truncated Weibull by : Steve P. Verrill
Download or read book Reliability Implications in Wood Systems of a Bivariate Gaussian-Weibull Distribution and the Associated Univariate Pseudo-truncated Weibull written by Steve P. Verrill and published by . This book was released on 2014 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two important wood properties are the modulus of elasticity (MOE) and the modulus of rupture (MOR). In the past, the statistical distribution of the MOE has often been modeled as Gaussian, and that of the MOR as lognormal or as a two- or three-parameter Weibull distribution. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior of MOE and MOR for the purposes of wood system reliability calculations, we introduce a bivariate Gaussian-Weibull distribution and the associated univariate pseudo-truncated Weibull (PTW). We note that theoretical arguments suggest that the strength distributions of grades of lumber are likely to be PTW rather than Weibull. We describe a Web-based program that fits bivariate Gaussian-Weibull data sets (and thus fits PTW distributions to MOR data). We present data that demonstrate that strength distributions of visual grades of lumber are not Weibull and do display at least some of the characteristics of PTW data. Finally, we demonstrate via simulation that if we fit a Weibull distribution to PTW data (as is often done), we can obtain very poor estimates of probabilities of failure.
Book Synopsis Modeling Statistical Distributions and Evaluating Properties of Mill-run Lumber by : Guangmei Cao Anderson
Download or read book Modeling Statistical Distributions and Evaluating Properties of Mill-run Lumber written by Guangmei Cao Anderson and published by . This book was released on 2021 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although it is common to model modulus of elasticity (MOE) and modulus of rupture (MOR) of graded lumber as normal, lognormal, or Weibull distributions, recent theories and empirical practices have cast doubt on these models. Mathematical proofs have been used to shown how the MOR distributions of graded lumber can be derived from the MOR distributions of mill-run populations. The MOR distribution of a graded lumber subpopulation is "pseudo- truncated" and does not exhibit the same theoretical form as the mill-run population from which it was drawn. Therefore, it is essential to explore the properties of mill-run lumber populations and properly characterize their MOE and MOR distributions. To investigate this topic, this dissertation has three objectives: 1) to determine if the within-mill means and standard deviations of MOE and MOR in mill-run southern pine (Pinus spp.) lumber differ over time, 2) to determine the correlations among hand-held grain angle meter readings, MOE, and MOR in mill- run southern pine lumber, and 3) to model statistical distributions of MOE and MOR in mill-run red pine (Pinus resinosa) and spruce (Picea spp.) lumber. This research features four main sections: 1) an introduction summarizing the conclusions of each chapter, 2) a chapter investigating if there are statistically significant differences between the means and variances of MOE and MOR in mill-run southern pine lumber populations at the same mill over time, 3) a chapter evaluating the bivariate correlations among handheld grain angle meter readings, MOR, and three measures of MOE in mill-run southern pine lumber, and 4) a chapter modeling the distributions of MOE and MOR in mill-run red pine and spruce lumber populations and comparing those to previous work on mill-run southern pine lumber populations.
Book Synopsis Estimated Probability of Breakage of Lumber of a Fixed "grade" Can Vary Greatly from Mill to Mill and Time to Time by :
Download or read book Estimated Probability of Breakage of Lumber of a Fixed "grade" Can Vary Greatly from Mill to Mill and Time to Time written by and published by . This book was released on 2020 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: To evaluate the reliability of lumber structures, we need (among many other things) good models for the strength and stiffness distributions of visual and machine-stress rated (MSR) grades of lumber. Verrill et al. established theoretically and empirically that the strength properties of visual and MSR grades of lumber are not distributed as two parameter Weibulls. Instead, strength properties of grades of lumber must have (at least to a first approximation) “pseudo-truncated” distributions. To properly implement Verrill et al.’s pseudo-truncation theory, we must know the true mill run modulus of elasticity (MOE) and modulus of rupture (MOR) distributions. Owens et al. investigated the mill run distributions of MOE and MOR at two times for 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, two-parameter Weibull, or three-parameter Weibull distributions. Verrill et al. investigated a mixture of two bivariate normals model for the mill run bivariate MOE–MOR population at a single time at a single mill. (Some possible sources of two-component mixture relationships include a mixture of trees from a fast-grown plantation stand and a suppressed stand, trees of two separate species, small-diameter trees and large-diameter trees, and lumber from the pith region versus lumber from the bark region.) They found that a mixture of two bivariate normals model performed well. In this paper, we apply this model to all eight of the Owens et al. lumber samples. We find that the model continues to yield good fits. However, we also find that the fits differ from mill to mill and time to time. Some variability is, of course, to be expected. However, we find that the fitted models differ to such an extent that the calculated probability that a piece of lumber randomly drawn from a fixed “grade” breaks at a fixed load can vary by a factor as large as 35 when we permit both season and mill to vary, and as large as 15 when we permit only mill to vary. Similar factors were found when we replaced fixed loads with loads randomly drawn from fixed load distributions.
Book Synopsis A Method for Approximating Distributions of Mechanical Properties for Structural Lumber by : Virgilio Asuncion Fernandez
Download or read book A Method for Approximating Distributions of Mechanical Properties for Structural Lumber written by Virgilio Asuncion Fernandez and published by . This book was released on 1975 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present method of design for walls does not accurately predict the strength and stiffness of walls because load sharing and composite action are not taken into consideration. This results in the use of higher strength materials and walls which are overdesigned. A new method of design for walls using finite element analysis is being developed (16). This method accounts for load-sharing and composite action in wall systems. To apply this new method the strength and stiffness distributions of the population of studs from which a wall system is formed must be estimated. In this study, regression models were developed to predict distributions of certain mechanical properties of stud grade Douglas fir studs using stress at proportional limit and conventional modulus of elasticity as independent variables. These regression models were used to predict similar mechanical properties of utility grade Engelmann spruce studs with known properties to test the reliability of the model.
