Fuzzy Measures of Uncertainty for Evaluating Non-Destructive Crack Inspection

Abstract A method is presented, based on fuzzy measures, to assess and compare the results of ultrasonic inspection in the weldings of a pressure vessel. Crack detection, identification of crack geometry and determination of location are all parts of the inspection process that find suitable representation in terms of fuzzy algebra. Necessity and possibility distributions offer a flexible formal tool to express imprecision and uncertainty. Therefore, the relative performance of different teams of operators engaged in the same case of non-destructive testing is evaluated with regard to three situations. In the first situation it is assumed that one team outperforms the others and can be taken as a reference. Then, the situation is considered where all teams are supposed to have an equivalent ability. Finally, a ranking in terms of risk is proposed for the regions of the welding which appear to contain defects. In all circumstances necessity and possibility measures allow to deal with the available information without introducing arbitrary models which could bias the evaluation. It must be remarked, however, that the information obtained may sometimes be complex and require proper reduction before any decision can be made.