A statistical model for estimating probability of crack detection

In the inspection of aircraft structures, the probability of detection has typically been determined based on the size of damage alone. However, the inspection process involves randomness due to variability in inspection conditions (including inspectorpsilas competence), as well as difficulties associated with the location and type of damages. To demonstrate the effects of these other factors, we present a simple model from the assumption that for each combination of crack location and inspector there is a threshold crack size such that all cracks above this size will be detected and all below that size will be missed. The proposed model adjusts the threshold crack size according to the difficulty associated with the crack location and the competence of inspectors. The model is then used to fit 2,603 detection events reported for 43 panels inspected by 62 technicians in an Air Force study. The threshold increments by location and inspector are obtained by maximizing the matching percentage in detection events between the model and the experiment. We first use 62 inspector thresholds only and find the best matching percentage of 78%. It is further increased to 81% when both inspector and location thresholds are considered. For comparison, the matching percentage using crack size alone is only 55%. We then add randomness to the process in order to include inconsistency on the part of inspectors. Replicating the observed inconsistency reduces the matching to about 72%. We conclude that most of the randomness in manual inspections is due to the circumstances of the inspections. We speculate that much of this randomness will be eliminated by automated structural health monitoring (SHM), which will be an important benefit of SHM.