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Fault equivalent & collapsing

Combinational circuits• faults f and g are equivalent iff Zf(x) = Zg(x)• equivalent faults are not distinguishable

For gate with controlling value c and inversion i :

all input sac faults and output sa(c ⊕ i) faults are equivalent

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sa0 sa1

sa0 sa1

sa0 sa1sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0sa1

sa0sa1

sa0sa0sa1sa1

sa0

sa1

sa0sa0sa1

sa1

AND

sa0 sa1

sa0 sa1

sa0 sa1NAND

OR

NOR

WIRE/BUFFER

NOT

FANOUT

INVERTER

Equivalence Rules Equivalence ExampleEquivalence Example

sa0 sa1sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

sa0 sa1

Faults in redremoved byequivalencecollapsing

20Collapse ratio = = 0.625

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Fault DominanceFault Dominance

• If all tests of some fault F1 detect another fault F2, then F2 is said to dominate F1.

• Dominance fault collapsing: If fault F2 dominates F1, then F2 is removed from the fault list.

• When dominance fault collapsing is used, it is sufficient to consider only the input faultsof Boolean gates.

• In a tree circuit (without fanouts) PI faults form a dominance collapsed fault set.

Fault dominaceCombinational circuits if f dominates g => any test that detects g will also detect f . Therefore , only dominating faults must be detected

xy

z

Example :[x, y] is the only test to deletedf1 = y sa1, since it detects f2 = z sa0 => f2 dominates

Fault dominance & collapsing

For gate with controlling value c & inversion i, the output sa(c’⊕i)dominates any input sac’sequential circuits dominance fault collapsing is not useful

Dominance ExampleDominance Example

s-a-1F1

s-a-1F2

001110 010

000101

100011

All tests of F2

Only test of F1s-a-1

s-a-1

s-a-1s-a-0

A dominance collapsed fault set(after equivalence collapsing)

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Equivalent to sa0 at the input

Equivalent to sa1 at the input

in dominance fault collapsingit is sufficient to consider only the input faults

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Checkpoint TheoremCheckpoint Theorem• Primary inputs and fanout branches of a combinational circuit

are called checkpoints.• Checkpoint theorem: A test set that detects all single

(multiple) stuck-at faults on all checkpoints of a combinational circuit, also detects all single (multiple) stuck-at faults in that circuit.

Total fault sites = 16

Checkpoints ( ) = 10

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