In hydraulic engineering, a distinction can often be made between a structure's resistance (e.g. the crest-level of a dyke) and its design stress (e.g. the maximal water level to be withstood). A failure may then be defined as the event in which - due to stochastic deterioration - the resistance drops below the design stress. Even though it is common to model a deterioration process mathematically as a Brownian motion with drift, this model is inadequate in describing the deterioration of hydraulic structures. To illustrate, a dyke whose height is subject to a Brownian deterioration can, according to the model, spontaneously rise up, which cannot occur in practice. In order that stochastic deterioration processes have non-negative increments, they have been considered as generalised gamma processes. Examples are the deterioration processes of ongoing coastal erosion (dunes), crest-level decline (dykes), longshore rock transport (berm breakwaters), scour hole development (the block mats of the Eastern-Scheldt barrier), and current-induced rock displacement (the rock dumping of the Eastern-Scheldt barrier).
On the basis of generalised gamma processes, tailor-made models have been built and implemented to determine the following cost-optimal maintenance decisions: optimal sand nourishment sizes and optimal dyke heightenings which balance the initial cost of investment against the future cost of maintenance; optimal inspection intervals for berm breakwaters, and for the block mats and the rock dumping of the Eastern-Scheldt barrier, whose expected costs of maintenance and failure are minimal; and optimal decisions that reduce flood damage along the Meuse river. These decision models can be applied to many engineering systems for the purpose of maintenance optimisation and life cycle costing.