A stochastic model of crack growth under periodic inspections

A stochastic model is described and fitted to a set of data on maximum crack depths in welds on a large system. The initial model is a two-stage empirical one, in that it models crack initiation and crack growth with time, and concentrates on explaining the data rather than on the physical processes which give rise to cracks. The model is fitted to the data by the method of maximum likelihood, and the goodness-of-fit is considered. Possible extensions of the basic model are also discussed, including a three stage model, in which the delay before which a defect becomes ‘visible’ is also considered. The main purpose of the modelling is to consider the prediction of crack growth in time and the consequences of carrying out periodical inspections, with the aim of minimizing the long term total cost per unit time of maintaining structural integrity.