While all of the NDI systems are capable of finding “small” cracks, damage tolerance analyses are based on the largest crack that might be in the structure after an inspection.  Thus, the focus of NDI capability evaluation for damage tolerance is the largest crack that might be missed at an inspection.  NDI techniques do not always produce a correct indication when applied by inspectors to cracks of the same size.  The ability and attitude of the operator, the geometry and material of the structure, the environment in which the inspection takes place, and the location, orientation, geometry and size of the crack all influence the chances of detection.  When considering the efficacy of an NDI system as a function of only crack size, uncertainty is introduced as a result of ignoring the other factors.  This uncertainty is quantified in terms of the probability of detection (POD) of cracks of a fixed size. POD(a) is defined as the proportion of all cracks of size a that will be detected by the NDI system when applied by representative inspectors to the population of structural elements in a defined environment.  At present, demonstrating the capability of an NDI system for a specific application requires a carefully controlled experiment with a valid statistical analysis of the resulting data.  Figure 3.1.3 presents an example POD(a) function with a 95 percent confidence bound for a liquid penetrant inspection of turbine engine blades.  Each data point represents the proportion of times cracks of the indicated size were detected.

Figure 3.1.3.  Example POD(a) Curve with Confidence Bound for Liquid Penetrant Inspections

The statistically-based characterization of NDI capability has two significant ramifications.  First, for a given NDI application, the true probability of detection as a function of crack size (or for a single crack size) will never be known exactly.  The capability of an NDI system can only be demonstrated by inspecting representative structures with known crack sizes.  The true POD(a) function is estimated from the responses to the inspection stimuli or by the observed percentages of correct positive indications.  The estimated POD(a) is subject to the statistical variation that can result from all of the uncontrolled factors that lead to variability in positive indications for all cracks of a particular size.  However, statistical methods (which depend on the experimental procedure) are available which yield confidence limits on the true probability of detection.  Protection against making a wrong decision on the basis of a set of non-typical results is provided by the confidence limits.

Second, in the real-world structural integrity problem, no inspection procedure will provide 100 percent assurance that all cracks greater than some useful size will be detected.  Current NDI capabilities at the short crack lengths of interest in aircraft applications dictate that a reliably detectable crack size, can only be specified in terms of a size for which a high percentage of cracks will be detected.  To reflect the statistical uncertainty, a confidence bound is often placed on this estimate of crack size.  Such single crack size characterizations of NDI capability are expressed in terms of the crack sizes for which there is at least a given POD at a defined level of confidence (the POD/CL crack size).  Such characterizations provide a stand-alone measure of the NDI system that is valid for applications represented by the demonstration test conditions.  For example, JSSG-2006 states that smaller initial crack sizes can be used for slow crack growth structures if it can be shown that there is 95 percent confidence that at least 90 percent of all cracks of the smaller size will be detected by the manufacturers’ NDI system.

There are three major limitations associated with the POD/CL type characterization:

1)      The choice of particular POD and confidence limits has been made on a rather arbitrary basis.  For example, 90/95 values were selected for JSSG-2006 recommended crack sizes even though there is no real interest in a crack length that is detected only 90 percent of the time.  Rather, 90/95 limits were selected because higher POD or confidence limit values would have required much larger sample sizes in the demonstration programs for the analysis methods being used.  The 95 percent confidence limit is assumed to provide the required degree of conservatism.

2)      A POD/CL limit is not a single, uniquely defined number but, rather, is a statistical or random quantity. Any particular POD/CL estimate is only one realization from a conceptually-large number of repeats of the demonstration program. Berens & Hovey [1981] showed there can be a large degree of scatter in these POD/CL estimates and the scatter depends on the POD function, analysis method, POD value, confidence level and number of cracks in the demonstration program.

3)      The POD/CL characterization is not related to the size of cracks that may be present in the structure after an inspection. To calculate the probability of missing a large crack requires knowledge of both POD(a) for all cracks sizes and the distribution of the sizes of the cracks in the population of structural details being inspected.

MIL-HDBK-1823 and Berens [1988] present in considerable detail an acceptable approach to demonstrating NDI capability in terms of a POD/CL characterization.  Other approaches are also in use.  After a brief description of the design of NDI capability experiments, the following paragraphs present a description of the analyses that are in current use for calculating POD/CL limits.