RESIDUAL LIFE, LINEAR FATIGUE DAMAGE ACCUMULATION AND OPTIMAL STOPPING

An optimal stopping procedure is proposed for the operation of a component subjected to constant-amplitude cyclic loading. Prediction of a residual life distribution is based on the successive re-estimation of the density function of a component life only by raising the density curve. As in the case of Miner's rule, damage accumulation is assumed to be linear, with a simple treatment using a random variable that gives the explicit interpretation of a probability space in terms of fatigue failures of components under cyclic loading. The cost of stopping is given as a sequence of the random variables which are the costs of losses per unit time in consequence of possible stopping at every inspection period or failure. It is shown that the optimal stopping problem may be solved in the class of monotonic cases. The inferred decision rule has a very simple structure, and its other possible usages are discussed. Throughout the paper the idea of close interconnection between damage accumulation and decision rules is traced for the problem of optimal operation of a component in which a degradation process is developing.