Fault Equivalence

1
(No Transcript)
2
Fault Equivalence

• Number of fault sites in a Boolean gate circuit
  is PI gates (fanout
  branches)
• Fault equivalence Two faults f1 and f2 are
  equivalent if all tests that detect f1 also
  detect f2.
• If faults f1 and f2 are equivalent then the
  corresponding faulty functions are identical.
• Fault collapsing All single faults of a logic
  circuit can be divided into disjoint equivalence
  subsets, where all faults in a subset are
  mutually equivalent.
• A collapsed fault set contains one fault from
  each equivalence subset.

3
Fault equivalence 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

4
Equivalence Rules
WIRE/BUFFER
sa0
sa0
sa0 sa1
sa0 sa1
sa1
sa1
sa0 sa1
sa0 sa1
AND
OR
sa0 sa1
INVERTER
sa0 sa1
sa0
sa1
NOT
sa0
sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
NAND
sa0
NOR
sa1
sa0
sa0 sa1
sa0 sa1
sa1
sa0
FANOUT
sa1
5
Equivalence Example
6
Fault 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.
• Any set that detects F1 also detects F2 (that
  dominates F1)
• When dominance fault collapsing is used, it is
  sufficient to consider only the input faults of
  Boolean gates.
• In a tree circuit (without fanouts) PI faults
  form a dominance collapsed fault set.

7
Fault dominace

• Combinational circuits
  
• If f dominates g gt any test that detects g will
  also detect f .
• Therefore, only dominating faults must be detected

Example x, y1 0 is the only test to
detect f1 y sa1, Since it also detects f2 z
sa0 gt f2 dominates
8
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

9
Dominance Example
10
MINIMAL SETS OF NON-DOMINATING FAULTS FOR
TWO-INPUT GATES
Or equivalently
0
0
1
1
0
0
1
1
1
1
0
0
11
Dominance Example
sa0 sa1
Faults in red removed by equivalence collapsing
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
Faults in green removed by dominance collapsing
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
sa0 sa1
15 Collapse ratio --
0.47 32
12
(No Transcript)
13
CIRCUIT WITH FANOUT-FREE SUBCIRCUITS SHOWN
14
(No Transcript)
15
(No Transcript)
16
EXAMPLE OF AN FANOUT-FREE CIRCUIT WITH SET OF
DOMINANCE-REDUCED FAULTS
Equivalent to sa1 at the input
in dominance fault collapsing it is sufficient to
consider only the input faults
Equivalent to sa0 at the input
17
(No Transcript)
18
Checkpoint 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.

19
(No Transcript)
20
DOMINANCE-REDUCED FAULT LIST
21
(No Transcript)
22
EXAMPLE OF PRUNING AND STRIPPING
23
The multiple stuck-fault model
Definition Let Tg be the set of all tests that
detect a fault g, we say that a fault f
functionally masks the fault g iff the multiple
fault f, g is not detected by any test in Tg
If f masks g then f, g is not detected by t
?Tg but it may be detected by other tests
24
The multiple stuck-fault model
Example Consider the faults c sa0, a sa1 t
011 is the only test that detects fault c sa0
but t does not detect c sa0, a sa1 gt a sa1
masks c sa0
25
The multiple stuck-fault model
Example Test set T 1111, 0111, 1110, 1001,
1010, 0101 detects all SSF in following
circuit, but the only test which detects B sa1
and C sa1 is 1001
1 0/1 0/1 1
26
The multiple stuck-fault model
Example Using Rajskis method
B sa1 detectable if no A sa0 while C sa1 detected
with no conditions
11,00 00,11 01,00,11 00,11
27
The multiple stuck-fault model
Properties of MSF(Multiple Stuck Faults)

• in a irredundant two_level circuit , any complete
  test set for SSF detects all MSF
• in a fanout-free circuit , any complete test set
  for SSF detects all double and triple faults
  there is a complete test set for SSF that detects
  all MSF

28
The multiple stuck-fault model

• in an internal fanout-free circuit, any complete
  test for SSF detects at least 98 of MSF with K lt
  6 and detects all MSF unless C contains a
  subcircuit with interconnection