JOINT ESTIMATION OF THE FLAW SIZE DISTRIBUTION AND POD FUNCTION

Life prediction and inspection interval decisions in aerospace applications require knowledge of the size distribution of unknown existing cracks and the probability of detecting a crack (POD), as a function of crack characteristics (e.g., crack size). The POD for a particular inspection method is usually estimated on the basis of experiments to a given specimen set. These experiments, however, cannot duplicate the conditions of in service inspections. Quantifying the size distribution of unknown existing cracks is more difficult. If reasonably precise crack size information is available for specimens with "crack find" decisions through inspection procedures, it is possible to estimate the joint distribution of crack size and signal response. This joint distribution can then be used to estimate both the in service POD and the crack size distribution. In this paper, we present a statistical model and methodology to do this estimation. We also illustrate the method on one set of simulated data.