Model for predicting ultrasonic pulse-echo probability of detection

Abstract

Abstract This paper describes a mathematical model for predicting the theoretical probability of detection (POD) of planar buried defects, for conventional ultrasonic pulse-echo inspection. A model for the scattering of ultrasound by well-oriented planar defects is combined with noise theory to produce a calculated capability of detection, based on the likelihood that the defect signal exceeds the specified threshold. The problem of false indications, the recording of a defect when none is present, is also addressed by the model, showing how any improvement in POD predictions must be considered in parallel with the associated change in the probability of false indication. We use examples to illustrate how the model may be used to check on proposed inspections, showing how factors such as reporting threshold, probe scan pattern and the criterion for the number of probe positions at which an indication must be seen before a defect is recorded, all affect the probability of detection and of false indication. The effects of defect roughness on detection probabilities are studied. We also use the model to quantify the uncertainties that result in POD predictions, when defect properties such as orientation, roughness, aspect ratio and depth within the specimen are themselves uncertain. The problems of equipment and human error are not addressed, although we discuss how, if these can be quantified, they may be incorporated into the model.