Extreme value analysis (EVA) of inspection data and its uncertainties

Extreme value analysis (EVA) is a statistical tool to estimate the likelihood of the occurrence of extreme values based on a few basic assumptions and observed/measured data. While output of this type of analysis cannot ever rival a full inspection, it can be a useful tool for partial coverage inspection (PCI), where access, cost or other limitations result in an incomplete dataset. In PCI, EVA can be used to estimate the largest defect that can be expected. Commonly the return level method is used to do this. However, the uncertainties associated with the return level are less commonly reported on. This paper presents an overview of how the return level and its 95% confidence intervals can be determined and how they vary based on different analysis parameters, such as the block size and extrapolation ratio. The analysis is then tested on simulated wall thickness data that has Gaussian and Exponential distributions. A curve that presents the confidence interval width as a percentage of the actual return level and as a function of the extrapolation ratio is presented. This is valid for the particular scale parameter (σ) that was associated with the simulated data. And for this data it was concluded that, in general, extrapolations to an area the size of 500-1000 times the inspected area result in acceptable return level uncertainties (<20% at 95% confidence). When extrapolating to areas that are larger than 1000 times the inspected area the width of the confidence intervals can become larger than 30-50% of the actual return level. This was deemed unacceptable: for the example of wall thickness mapping that is used throughout this paper, these uncertainties can represent critical defects of nearly through wall extent. The curve that links the confidence interval width to the return value as a function of extrapolation ratio is valid only for a particular scale parameter value of the EVA model. However, it is imagineable that a few of such relations for different scale parameters σ could be simulated. By picking the relation with the closest σ value (based on observation or estimation) for the inspection dataset, the presented approach can then be used to quickly estimate the uncertainty associated with an EVA extrapolation.