  This paper proposes a gamma process for modelling the damage that accumulates
over time in the lumber used in structural engineering applications when stress
is applied. The model separates the stochastic processes representing features
internal to the piece of lumber on the one hand, from those representing
external forces due to applied dead and live loads. The model applies those
external forces through a time-varying population level function designed for
time-varying loads. The application of this type of model, which is standard in
reliability analysis, is novel in this context, which has been dominated by
accumulated damage models (ADMs) over more than half a century. The proposed
model is compared with one of the traditional ADMs. Our statistical results
based on a Bayesian analysis of experimental data highlight the limitations of
using accelerated testing data to assess long-term reliability, as seen in the
wide posterior intervals. This suggests the need for more comprehensive testing
in future applications, or to encode appropriate expert knowledge in the priors
used for Bayesian analysis.
