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Abstract Test sets that target standard fault models may not always be sufficient for detecting all defects. To evaluate test sets for the detection of unmodeled defects,n-detect test sets (which detect all modeled faults at leastntimes) have previously been proposed. Unfortunately,n-detect test sets are often prohibitively long. In this paper, we investigate the ability of shadow flip-flops connected into a MISR (Multiple Input Signature Register) to detect stuck-at faults fortuitously multiple times during scan shift. We explore which flip-flops should be shadowed to increase the value ofnfor the least detected stuck-at faults for each circuit studied. We then identify which circuit characteristics are most important for determining the cost of the MISR needed to achieve high values ofn. For example, circuits that contain a few flip-flops with upstream fault cones that cover a large percentage of all faults in the circuit can often achieve highn-detect coverage fortuitously with a low-cost MISR. This allows a DFT engineer to predict the viability of this MISR-based approach early in the design cycle.