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Theorem 1. If there is only a single stuck-at fault present in a failing circuit
under diagnosis ( CUD ) , the diagnosis algorithm will always identify that fault
as a prime suspect, irrespective of the detection or diagnostic coverage of the test
pattern set.
Proof. Assume that CUD has a single stuck-at fault that causes N
k out of N
test patterns to fail. The remaining k are passing patterns. Because a fault free
circuit cannot have any failing test pattern, the presence of failing test patterns
indicates the presence of some failure s . In other words, a test pattern can only
fail because a fault that it detects is present. Hence all N
k patterns detect
the fault s and the remaining k patterns do not detect the fault s .Ifall N
k
patterns detect some fault present in the circuit, it has to be the same fault that
all the N
k patterns detect, because there is no more than one fault present in
the circuit according to our assumption in the beginning. Moving forward with
this revelation, Phase 3 will always come up with one or more prime suspects
including the actual fault, as the intersection of the faults detected by all failing
patterns.
Many possible cases of single stuck-at faults, multiple stuck-at faults without
masking, multiple stuck-at faults with masking, and multiple stuck-at faults with
interference have been analyzed in detail [6]. Figure 4 shows the comparison of
simulation effort between the proposed diagnosis procedure and the traditional
fault dictionary diagnosis method. It is plotted for a multiple (two) stuck-at
fault case of C432 ISCAS'85 benchmark circuit. This circuit has a total of 1078
single stuck-at faults in the fault list. The test vector set with 100% diagnostic
coverage of detectable faults contains 462 test vectors (with output selection
implemented). The dictionary method involves simulation of all faults for all
test vectors. Hence, the entire area under the straight black line denotes the
simulation effort of the fault dictionary method. The considered failure case
produced 31 failing vectors and 431 passing vectors. The proposed fault diagnosis
procedure performs fault simulation with the failing test vectors first, which is
denoted by the solid red line. This line drops down steeply because, as and
when the faults are detected, they are dropped. We process fewer faults as we
proceed with the simulation. Next, the fault simulation of passing patterns is
performed, which is denoted by the dotted blue line. Note that the faults that
were detected and dropped during failing pattern simulation are those to be
simulated with passing patterns. In this case too, faults are dropped as and
when they are detected by the passing patterns, which explains the drop in the
line. Once again the number of faults to be simulated keeps reducing throughout
simulation. Beyond a certain point, not many remaining faults are detected by
the passing patterns, which makes the curve almost flat. After simulating all
passing patterns, the remaining faults become the suspects and surrogates. The
area under these lines (solid red and dotted blue) denotes the simulation effort of
the proposed procedure that is far lower than the traditional dictionary method.
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