Estimation of weld defects size distributions, rates and probability of detections in fabrication yards using a Bayesian theorem approach

Estimation of probability detection curves for non-destructive evaluation (NDE) typically involves the manufacturing of a high number of defect specimens followed by trial NDE and statistical analysis of the data based on the hit/miss approach. This is a time-consuming and costly procedure. Besides, probability of detection (POD) depends on a number of variables, such as human factors (operator), and the testing environment, resulting in a significant mismatch between those POD curves generated in the lab and those in practice. One application of POD curves is in the quality control of welded joints [1]. Weld quality is often characterised by the number of defects found and their size which is, inevitably, dependent on the POD of the employed NDE. Therefore, a predefined generic POD curve has certain limitations. In this paper, a method of estimating POD curves based on the Bayesian theorem of conditional probability is presented and its applicability is validated by studying an existing database under both Bayesian and the hit/miss methods. Overall, the POD predicted by the Bayesian theorem is found to be consistent with the commonly used hit/miss model. Finally, the Bayesian model is used to estimate the POD, and the true weld defect size and frequency in two ship manufacturing yards. The estimated weld defect size and frequency models provide valuable information to estimate the fatigue and fracture reliability of ship and offshore structures. It is shown that one of the yards has both better weld quality production and superior NDE detection. This will have a valuable benefit for weld quality control (QC) programmes through saving the testing resources.