Selection of Tube Samples for Inservice Inspection of Steam Generator Tubes

In Pressurized Water Reactors, a program of periodic inservice inspection of steam generator tubes is set up to monitor the integrity of the tubes. The inservice inspection is performed using nondestructive examination techniques, e.g., eddy current testing. Usually not all the tubes are inspected but the inspection is limited to a sample of tubes. Therefore, the objective of the inservice inspection is to provide reasonable insurance of steam generator tubing integrity. Consequently, the concern is the level of confidence that can be placed in the estimated knowledge about the whole population of the steam generator tubes from the information obtained from the examination of a sample. In replacement steam generators, the number of defective tubes is expected to be very low. The usual sample may then simply be too small to include a defective tube. Hence, the problem is the estimation of the number of defective tubes in the total population given that no defective tubes have been detected in a sample. Using the classical Bayesian method in inverse problem, the analytical estimation of the probability distribution of the number of defective tubes knowing that a random sample of tubes contains no defective tubes is first performed. Then a numerical application is carried out considering a noninformative flat prior distribution and, more specifically, the analytical expression of the estimator of the mean number of defective tubes in the whole population of the steam generator tubes is given. Some approximated analytical Bayesian estimations for other prior distributions are also given. Additionally, the calculations allow also to provide an answer to the question: when performing the inservice inspection of the steam generator tubes, is it sufficient to inspect a random sample from any steam generator or the inspection samples should be taken separately from each steam generator?