Reliability Implications in Wood Systems of a Bivariate Gaussian–Weibull Distribution and the Associated Univariate Pseudo-truncated Weibull

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.