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Optimization of Distribution Parameters 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 inspector competence, difficulties associated with the location, and type of damage. To account for these other factors, we develop a simple inspection model from the assumption that for each combination of crack location and inspector there is a threshold crack size, such that larger cracks will be detected and smaller ones will be missed. The proposed model fits the threshold crack sizes to 2603 detection events reported for 43 panels inspected by 62 inspectors from a U.S. Air Force study. The threshold values are obtained by maximizing the matching detection events between the model and the inspection data. First, when 62 inspector thresholds are used, the model matches 78 % of detection events. It is further increased to 81 % when both inspector and location thresholds are employed. For comparison, the matching percentage using crack size alone is only 55%. Cross-validation of the fitting process indicates that part of the improvement represents fitting noise in the data, and that only about 72% matching is repeatable. The proposed model is further extended by including randomness to represent inconsistent behavior of inspectors. Replicating the observed inconsistency for the same inspector reduces the matching to about the same 72 %. Confidence intervals of the proposed model are presented. The proposed model may be used to assess the effect of better training for inspectors, and this is illustrated with a study that shows that, if the poorer half of inspectors is replaced by the top half, the crack size identified with 50% probability can be reduced by half.