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The paper provides an engineering analysis approach for estimating non-destructive evaluation (NDE) flaw size using smaller number of hit-miss data-points. Probability of detection (POD) analysis of inspection test data provides a flaw size, denoted as a90/95. The flaw size has 90% POD and minimum 95% confidence. In this approach, we do not estimate a90/95 flaw size. Here, goal is to estimate the flaw detectability size that is larger than the unknown a90 for the NDE technique. The approach is devised using a large set of simulated signal response data and estimating population a90/95p using an â versus a POD model. The signal response data is converted to hit-miss data using a decision threshold. A hit-miss or â versus a POD model is assumed here. Then a sampling scheme is set-up for generating limited number of data-points and flaw size estimation equations are established by substituting POD model quantities by their approximate estimates based on demonstrated flaw sizes. The data sampling scheme used here is like a Monte Carlo simulation allowing evaluation of engineering estimation approach. The distribution of multiple engineering flaw size estimates provides a confidence on the engineering estimate being larger than a90/95p used in the simulation. NDE practitioner normally uses some rule of thumb to estimate flaw size based on limited flaw detection data. A typical rule of thumb may be to multiply the smallest detected flaw size by a factor such as two. The rule of thumb is subjective. Compared to the rule of thumb, paper provides more complex equations and demonstrates these equations on simulated randomized data. NDE flaw detection size is used in fracture mechanics analysis of aerospace structures. Fracture mechanics uses flaw growth analysis using NDE flaw size to determine service life of the part. The part design is optimized for performance, weight, service life and cost. In order to tolerate larger NDE flaw size, parts are designed to be stronger and heavier to reduce stress. Therefore, a90/95 flaw size is desirable. But many times, POD demonstration, requiring a large number of real known size flaws, is cost prohibitive. Thus, if we can estimate risk or confidence associated with the engineering estimate of flaw detectability size, program managers may accept the engineering approach. Here, we need to assess confidence that engineering estimate of flaw size is greater than or equal to estimated a90/95p of the simulated data. Also, we need to assess smallest possible value of the flaw size estimate and compare it with the estimated a90/95p. Lastly, the probability of false positive (POF) also needs to be assessed. A technique is considered reliable, if it provides flaw detectability size with 90/95 POD/confidence and also provides a POF less than or equal to a chosen value i.e. 1%. Linear correlation is used between the signal response data and flaw size. POD software mh1823 uses generalized linear model (GLM) in POD analysis after transforming the flaw size and signal response, if needed, using logarithm. Therefore, this simulation approach is in agreement with the linear signal correlation used in mh1823. The approach is conservative and is designed to provide a larger flaw detectability size compared to POD approach with high confidence and takes into account number of data-points used. Such NDE flaw detectability size estimation approach, although, not as rigorous as POD, can be cost effective if the larger estimated flaw size can be tolerated.
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