Assessment of ROC curves for inspection of random fields

Inspection by non-destructive testing (NDT) techniques of existing structures is not perfect and it has become a common practice to model their reliability in terms of probability of detection (PoD), probability of false alarms (PFA) and receiver operating characteristic (ROC) curves. These results are generally the main inputs needed by owners of structures in order to achieve inspection, maintenance and repair plans (IMR). The assessment of PoD and PFA is even deduced from intercalibration of NDT tools or from the modelling of the noise and the signal. In this last case when the noise and the signal depend on the location on the structure PoD and PFA are spatially dependent. This paper presents how to define PoD and PFA when damage and detection are stochastic fields or spatially dependent. Corrosion of coastal structures in harbours is considered for illustration and ROC curves are deduced. Identification of probability density functions on polynomial chaos is shown to be more suitable than predefined probability distribution functions (pdf) in view of fitting noise and signal plus noise distributions.