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Abstract

It has been a topic of great interest in wood engineering to understand the relationships between the different strength properties of lumber and the relationships between the strength properties and covariates such as visual grading characteristics. In our mechanical wood strength tests, each piece fails (breaks) after surviving a continuously increasing load to a level. The response of the test is the wood strength property -- load-to-failure, which is in a very different context from the standard time-to-failure data in Biostatistics. This topic is also called reliability analysis in engineering. In order to describe the relationships among strength properties, we develop joint and conditional survival functions by both a parametric method and a nonparametric approach. However, each piece of lumber can only be tested to destruction with one method, which makes modeling these joint strengths distributions challenging. In the past, this kind of problem has been solved by subjectively matching pieces of lumber, but the quality of this approach is then an issue. We apply the methodologies in survival analysis to the wood strength data collected in the FPInnovations (FPI) laboratory. The objective of the analysis is to build a predictive model that relates the strength properties to the recorded characteristics (i.e. a survival model in reliability). Our conclusion is that a type of wood defect (knot), a lumber grade status (off-grade: Yes/No) and a lumber's module of elasticity (moe) have statistically significant effects on wood strength. These significant covariates can be used to match pieces of lumber. This paper also supports use of the accelerated failure time (AFT) model as an alternative to the Cox proportional hazard (Cox PH) model in the analysis of survival data. Moreover, we conclude that the Weibull AFT model provides a much better fit than the Cox PH model in our data set with a satisfying predictive accuracy.