Fault Modeling for Simulation and ATPG - Models in Hardware Testing - page 107

the integral in the denominator evaluates to 1. For a complete fault list f 1 ;:::; f N ,
P-FC is obtained by averaging:

X

N

1
N

P FC D P FC .f i /:

i D1

Hence, to calculate P-FC , the fault simulation algorithm must calculate C.f / for
each fault f . The disadvantage of P-FC is the uniform handling of uncovered bridge
resistances: the integral in the denominator contains all possible R sh values, includ-
ing ones corresponding to redundant defects. Hence, P-FC is typically significantly
below 100%, even for exhaustive test sets which detect all detectable defects. This
is the reason why P-FC is called pessimistic. P-FC is conceptually similar to fault
coverage for simple fault models because the effect of redundant faults and defects
is ignored by both definitions. However, redundant faults with respect to simple fault
models are rare in practical circuits. On the other hand, every resistive bridging fault
does have a range of very high resistances for which it is undetectable. Hence, the
error introduced by the inaccurate handling of redundancy tends to be prohibitive
when modeling resistive faults.
This is remediated by calculating the range G.f / of all bridge resistances for
which fault f is irredundant, i.e., is detected by at least one test pattern. G.f /
is called global analogue detectability interval (G-ADI). For circuits with a very
small number of inputs, G.f / can be obtained directly by simulating the exhaustive
test set, i.e., determining C.f / of that test set. G.f / can also be calculated by the
ATPG method described in Section 4.4 . The global fault coverage G-FC is defined
as follows:

R C.f / .r/ dr
R G.f / .r/ dr :
G-FC is the accurate fault coverage metric for resistive faults: G-FC of 100% in-
dicates that every detectable defect has been covered by the test set. In this sense,
G-FC is similar to fault efficacy for simple fault models. On the other hand, the cal-
culation of G- FC requires G-ADI. It could be proven that a polynomial algorithm to
calculate G-ADI would imply P D NP . Hence, the determination of G-ADI is as
unlikely to be done efficiently as the redundancy proof for simple fault models. As a
consequence, it has been suggested to approximate G-ADI if it cannot be calculated
in practical time by available methods 0 . The approximation is based on calculating
an upper bound R max for any resistance contained in G-ADI. The interval [0, R max ]
is used instead of its accurate subset G-ADI, resulting in a new fault coverage metric
E-FC :

G FC .f / D 100%

R C.f / .r/ dr
R R max
0

E FC .f / D 100%

.r/ dr :

Similar to P-FC , E-FC is an under-approximation of the accurate metric G-FC ,but
the inaccuracy is much smaller for E-FC compared with P-FC . The final metric is
called optimistic fault coverage or O-FC .Forafaultf which is detected for at least