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1、Build Your Own POD David S. FORSYTH, TRI/Austin, Austin, TX USA John C. ALDRIN, Computational Tools, Gurnee, IL USA Abstract. In the context of the Reliability Model developed at the 1st European- American Workshop on Reliability of NDE, and the work of the Model-Assisted POD Working Group, we prese
2、nt concepts and results showing how POD can be practically estimated by assembling data from a variety of sources. These sources can include both empirical and modelled data. Some of the difficult issues of assessing so-called human factors can be partially or wholly addressed through this process.
3、1 Introduction This paper explores examples of how the combination of data from empirical and modelled sources can be used to estimate the probability of detection (POD) of a specific nondestructive testing (NDT) technique applied to a specific problem. The Model-Assisted Probability of Detection (M
4、APOD) Working Group was established in 2004 by the Air Force Research Laboratory (AFRL) in cooperation with the Federal Aviation Administration (FAA) and the National Astronautics and Space Agency (NASA), to explore those opportunities. The MAPOD Working Group has as its goal the promotion of the in
5、creased understanding, development and implementation of MAPOD methodologies. This is a voluntary activity in which working group members meet periodically in conjunction with an international meeting that many would be attending independent of this activity. The MAPOD Working Group has developed st
6、rategies for the estimation of POD using models and/or transfer function approaches, and this is described in more detail in another paper in this proceedings 1. There has been significant work in the community over the years to incorporate models as either a stand-alone estimator of POD or at least
7、 as a contributing source of information (see 1 for multiple references). In this paper, we provide a theoretical background and example of using empirical data to augment a POD estimate (although the same approach would apply to using models, for example see 2). 2 Probability of Detection As nondes
8、tructive testing is used in critical roles in process control, in manufacturing, and in inspection of safety-critical physical assets such as aircraft, pressure vessels, nuclear reactor components, etc.; the measurement of the performance of NDT has become 4th European-American Workshop on Reliabili
9、ty of NDE - Th.3.A It is no longer sufficient in many cases to simply assume that an inspection is a perfect process of unbounded capability, rather, it is imperative to know what is the probability of finding (or equivalently of missing) discontinuities of interest. This is usually referred to as t
10、he probability of detection (POD). The exact definition of POD, and the statistical methods used to estimate POD, have evolved over time. In the remainder of this paper, we will often describe POD in terms of cracks, but it is important to note that the POD approach is not limited to cracks, and has
11、 been applied to other discontinuities such as corrosion loss, impact damage, or delaminations. 2.1 Review of Probability of Detection Statistical Methods A very simple way to think of POD is as follows: The POD at a specific crack size “a”, denoted POD(a), can be estimated from a series of inspecti
12、ons of cracks of size a as: nnPOD(a)d= (1) where POD(a) is the probability of detection at the crack size a, and nd is the number of cracks of size a detected out of n the total number of cracks of size a in the trial. The first plots of POD as a function of crack size (often called POD curves) were
13、 constructed using moving averages or averaging the response of all cracks in an interval, and manually fitting a curve through these points (see for example 3,4,5). Eventually a number of methods were devised to plot POD curves over a range of crack sizes from multiple measurements at a single size
14、 (or small range of sizes) as defined in equation (1) above, and using binomial statistics to calculate confidence bounds 6. The event that spurred an updated statistical approach to POD was the analysis of a large United States Air Force (USAF) study of the capability of inspectors/inspections bein
15、g performed at USAF depots in the mid 1970s, widely known as the “Have Cracks, Will Travel” study 7. In this study many inspectors inspected each specimen, so it was possible to plot the mean POD for each crack, and fit a continuous POD curve through these points. It was noted in the analysis of thi
16、s data that cracks of the same size were detected equally: in addition to the variability in a repeated measurement on a single crac there was significant variability in the response of different cracks of the same size. not k, Based on their analysis of the above data, Berens and Hovey 8 proposed a probabilistic description of POD, where the POD is more than a function of jus
