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Test Generation 165 f Primary output cone for PO #4 Excitation cone Inputs outside of PO cone are not needed for detection of fault f PIs POs Propagation of fault effect ± FIGURE 4.4 Detection of a fault. If the detection probability, d f , for the hardest fault is known, N can be readily computed by solving the following inequality: 1 ± 1 d f ² N p where p is the probability that N vectors should detect fault f . If the detection probability is not known, it can be computed directly from the circuit. The detection probability of a fault is directly related to: (1) the control- lability of the line that the fault is on, and (2) the observability of the fault-effect to a primary output. The controllability and observability computations have been introduced previously in the chapter on design for testability. It is worth noting that the minimum detection probability of a detectable fault f can be determined by the output cone in which f resides. In fact, if f
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Unformatted text preview: is detectable, it must be excited and propagated to at least one primary output, as illustrated in Figure 4.4. It is clear that all the primary inputs necessary to excite f and propagate the fault-effect must reside in the cone of the output to which f is detected. Thus, the detection probability for f is at least ± ³ 5 ² m , where m is the number of primary inputs in the cone of the corresponding primary output. Taking this concept a step further, the detection probability of the most difficult fault can be obtained with the following lemma [David 1976] [Shedletsky 1977]. Lemma 1 In a combinational circuit with multiple outputs, let n max be the number of primary inputs that can lead to a primary output. Then, the detection probability for the most difficult detectable fault, d min , is: d min ≥ ± ³ 5 ² n max Proof The proof follows from the preceding discussion....
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