Probability of Detection Analysis for Eddy Current Inspection Systems Fall 2011 Mini-Paper
Abstract: Eddy Current (EC) inspection is a Nondestructive Testing (NDT) method commonly used for flight quality assurance of commercial, military, and rocket engine hardware. One application of EC inspection is to detect surface or near-surface anomalies before they grow to a critical length which could impact the structural integrity of the hardware. EC inspection uses the principal of electromagnetism or the production of a magnetic field by current flowing in a conductor. Anything placed in the magnetic field that has electric and/or magnetic properties will change the field and produce an EC signal. Understanding the relationship between crack size and system response is the basis for determining the detection capability of an EC system. For a given EC system, the relationship between the EC response and crack size can be evaluated by scanning a set of standard specimens with a known number and distribution of crack sizes. The results are analyzed using the "a-hat versus a" analysis method to quantify the relationship between the EC response (i.e., a-hat) and actual crack size (i.e., a) and develop a Probability of Detection (POD) curve, which defines the crack size that can be detected with a specified level of reliability. The "a-hat versus a" analysis method is based on established statistical methods, namely regression with censored data and probability theory. Having a basic understanding of the underlying statistical methods is essential to assessing the capability of an EC system.
Keywords: Nondestructive Testing (NDT) - Nondestructive Evaluation (NDE) - Probability of Detection (POD) - Regression - Maximum likelihood estimation - Censoring - Eddy Current Inspection - Residuals