Span-Dependent Distributions of the Bending Strength of Spruce Timber

Tests data of bending strengths of a large number of timber beams of different spans obtained at the Swedish Institute for Wood Technology Research reveal a statistical structure that can be represented in a simple probabilistic model of series system type. A particular feature of the data from one of the large test series is that unintentionally the data became randomly censored upwards. This censoring of the data rules out both the moment estimation method and the maximum likelihood method. Instead valid parameter estimates can be obtained by maximizing the posterior density defined as the likelihood function multiplied by a suitably chosen noninformative prior density (MP method). Subsequently using bias factors assessed by simulation ensures that the corrected MP estimates are unbiased. A closed form analytical expression for the distribution function of the bending strength of a beam with any given number of defect clusters follows from the obtained distribution model for the bending strength of the random single defect cluster. The empirical distribution function of bending test results for a sample of beams with two defect clusters is well predicted, and for long beams with several defect clusters the same is the case in the lower tail up to at least about the 50% probability level.