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N-detection test sets are useful in improving the coverage of unmodeled faults. We introduce a measure of quality that allows us to compare two test sets in terms of their ability to detect unmodeled faults based on the concept of n-detections. Using this measure, we describe a procedure for ordering an n-detection test set for stuck-at faults such that the quality of a test set comprised of the first K tests of the test set is as high as possible. This is useful when only K tests of the test set can be accommodated in the tester memory or to help ensure that unmodeled faults are detected as early as possible during the test application process. We present experimental results demonstrating that the proposed ordering yields test sets with increased coverage of unmodeled faults.