Bayesian Update of the Number of Defects Present in the Pipeline

Analysis of reliability methods which are currently used in design and operation of pipelines as systems shows that the classical approach, imported from the structural reliability theory—considering the pipeline as a system of sequentially connected elements—does not work. The main reason for this is that not all defects present in the pipeline actually provide an input into the total probability of failure (POF) of the pipeline system, given the depth of failure prediction, and the actual deterioration model. The second reason is that the results of any in-line or DA inspection don’t give the actual number of true defects. The set of defects detected by the ILI tool always contains some sub-set of false (phantom) defects, and doesn’t contain a sub-set of missed out defects. Both these sub-sets may seriously influence the quantitative assessment of the POF. This paper is dedicated to creating a practical method of updating the true number of defects in a pipeline after conducting an ILI and consequent verification of ILI results. A straightforward method of doing this was initially proposed by one of the authors in an IPC paper [7]. A more accurate comprehensive method based on the Bayesian procedure is presented is this paper. It is assumed that the prior experimental data and the probability distribution function (PDF) for this data are known. The goal is to find the best fit parameter of this PDF, having results of the verification measurements. Algorithm for solving this problem is presented in the paper. This approach was used detected during an ILI, followed by verification measurements [7]. Having the numbers of discovered and true defects, a prediction is made of the most probable number of true defects in each of the intervals of defects’ parameter of interest. This result can be used when assessing the quality of the ILI tool, the results of a specific pig run, used as an input when solving corresponding problems of pipeline POF, and for planning the risk based inspections.