Optimal sample size for probability of detection curves

Abstract

The use of probability of detection curves to quantify the reliability of non-destructive examination (NDE) systems is common in the aeronautical industry, but relatively less so in the nuclear industry, at least in European countries. Due to the nature of the components being inspected, sample sizes tend to be much lower. This makes the manufacturing of test pieces with representative flaws, in sufficient numbers, so to draw statistical conclusions on the reliability of the NDT system under investigation, quite costly. The European Network for Inspection and Qualification (ENIQ) has developed an inspection qualification methodology, referred to as the ENIQ Methodology. It has become widely used in many European countries and provides assurance on the reliability of NDE systems, but only qualitatively. The need to quantify the output of inspection qualification has become more important as structural reliability modelling and quantitative risk-informed in-service inspection methodologies become more widely used. A measure of the NDE reliability is necessary to quantify risk reduction after inspection and probability of detection (POD) curves provide such a metric. The Joint Research Centre, Petten, The Netherlands supported ENIQ by investigating the question of the sample size required to determine a reliable POD curve. As mentioned earlier manufacturing of test pieces with defects that are typically found in nuclear power plants (NPPs) is usually quite expensive. Thus there is a tendency to reduce sample sizes, which in turn increases the uncertainty associated with the resulting POD curve. The main question in conjunction with POS curves is the appropriate sample size. Not much guidance on appropriate sample sizes can be found in the published literature. Often only qualitative advice is given.The aims of the work summarized in this paper were to develop numerical simulations to determine appropriate and effective inspection target sizes, their number, and distribution to produce valid POD vs. size curves, and to summarize these findings as guidelines for the NDE practitioner in designing an experiment to assess system inspection effectiveness.