Estimating Dependence Among Lumber Strength Properties With Copula Models

Abstract

A copula-based approach is used to estimate the dependence among three lumber strength properties: modulus of elasticity (MOE), modulus of rupture (MOR), and ultimate tensile strength (UTS). MOR and UTS are destructive measurements so they cannot be obtained simultaneously for lumber specimens. The dependence modeling is possible under an appropriate experimental design with i) a shoulder group for rupture, ii) a shoulder group for tension, and iii) other groups proof loaded in either the rupture or tension mode with survivors tested to failure in the mode that was not initially tested. With a fitted copula model based on an assumption of no damage due to the proof loading procedure, we conclude that there is a strong dependence between MOR and UTS conditioning on MOE. To assess the “no damage assumption,” a graphical method with simulated data from the fitted copula model is used. It suggests that there may be some damage to the lumber specimens due to proof loading, especially for weaker lumber specimens. Information from the dependence model can potentially help reduce monitoring costs in the lumber industry.