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Transition faults: Driving capture cell to known values for fault detectability

vijay82

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The circuit diagram attached shows node values for initial and final vectors required to detect a possible slow-to-rise transition fault at the 1st AND gate output. As shown, Xs are assigned to PIs in the initialization vector phase as a result of which the capture cell input also goes to X. Waveforms, as attached, however show that only when capture cell's input X=1 will the faulty and ideal capture cell output differ and the fault be detectable. In the X=0 case, the output is same making detection impossible. Shouldn't the capture cell input then be necessarily driven to a known value, specifically the opposite of the ideal post capture value, using PIs so that detection is deterministic?

Yet, in all texts I've seen so far, initialization vectors are only supposed to set the node in focus to an initial value (without caring about PIs) and the final vector to be a SA vector (SA0 for slow-to-rise) with PIs appropriately justified to propagate the transition to the capture cell.
 

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