A dependent fatigue lifetime model

An ARMA(p,q) Box-Jenkins fatigue model which allows to take into account the dependence between the strengths of neighbouring pieces of material for constant stress range is presented and the asymptotic convergence, for large lengths of materials, to a Gumbel distribution is shown. When the stress range varies, a regression model, compatible with Gumbel result, is derived. This model is based on a functional equation which is solved and a three parameter family is obtained as the only solution. Finally, an example of application with real fatigue data is included. Monte Carlo simulations give the distribution functions of the fatigue strength of wires of different lengths and allow their design. In this way, the influence of dependence is analyzed.