Nondestructive evaluation (NDE) techniques are widely used to detect flaws in critical components of systems like aircraft engines, nuclear power plants and oil pipelines in order to prevent catastrophic events. Many modern NDE systems generate image data. In some applications an experienced inspector performs the tedious task of visually examining every image to provide accurate conclusions about the existence of flaws. This approach is labor-intensive and can cause misses due to operator ennui. Automated evaluation methods seek to eliminate human-factors variability and improve throughput. Simple methods based on peak amplitude in an image are sometimes employed and a trained-operator-controlled refinement that uses a dynamic threshold based on signal-to-noise ratio (SNR) has also been implemented. We develop an automated and optimized detection procedure that mimics these operations. The primary goal of our methodology is to reduce the number of images requiring expert visual evaluation by filtering out images that are overwhelmingly definitive on the existence or absence of a flaw. We use an appropriate model for the observed values of the SNR-detection criterion to estimate the probability of detection. Our methodology outperforms current methods in terms of its ability to detect flaws.