Quantifying Uncertainty in Lumber Grading and Strength Prediction: A Bayesian Approach

Abstract

This article presents a joint distribution for the strength of a randomly selected piece of structural lumber and its observable characteristics. In the process of lumber strength testing, these characteristics are ascertained under strict grading protocols, as they have the potential to be strength reducing. However, for practical reasons, only a few such selected characteristics among the many present, are recorded. We present a data-generating mechanism that reflects the uncertainties resulting from the grading protocol. A Bayesian approach is then adopted for model fitting and construction of a predictive distribution for strength that accounts for the unrecorded characteristics. The method is validated on simulated examples, and then applied on a sample of specimens tested for bending and tensile strength. Use of the predictive distribution is demonstrated, and insights gained into the grading process are described. Details of the lumber testing experiments can be found in the online supplementary materials.

• Bayesian predictive model
• Sawn structural lumber
• Structural lumber testing
• Visual stress grading
• Wood strength-reducing characteristics

ACKNOWLEDGMENTS

The work reported in this article was partially supported by FPInnovations and grants from the Natural Sciences and Engineering Research Council of Canada. We thank Roy Abbott for professionally grading the lumber test samples used in this study, and the staff at FPInnovations for assisting with the testing procedure. We thank Yilan Zhu, Yan Cheng, Yanling Cai, Jessica Chen, Yang Liu, Yongliang Zhai, and Chen Xu for their assistance in the FPInnovations laboratory to produce the datasets used in this study. Thanks to Lynne Zidek for entering the experimental data. Thanks to Yang Chen for some helpful discussions. Finally, an expression of appreciation to the anonymous reviewers, the associate editor, and the former editor, Hugh Chipman, for many suggestions that greatly enhanced the article’s clarity.