The document describes a novel technique called COMEDI that selects diagnostic test vectors from a pool of ATPG detection vectors to identify faults in chips during manufacturing testing. COMEDI constructs a combinatorial cover of the detection vector pool to determine a test set with high diagnostic coverage without using diagnostic test generation, circuit modification, or miter-based approaches. Experimental results on benchmark circuits show the method effectively reduces the size of the diagnostic test set while achieving high diagnostic coverage and requiring less CPU time compared to existing techniques. The proposed architecture is analyzed using Xilinx 14.2 in terms of logic size, area, and power consumption.