Fault Modeling and Fault Simulation
Luis Alejandro Cortés, Daniel Karlsson
Embedded Systems Laboratory
Department of Computer and Information Science
Linköping University
Outline
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■
Fault Modeling
❏
Logical Fault Models
❏
Fault Detection
❏
Single Stuck-Fault Model
❏
Multiple Stuck-Fault Model
Fault Simulation
❏
Serial Fault Simulation
❏
Parallel, Deductive, and Concurrent Fault Simulation
❏
Critical Path Tracing
Fault Modeling and Fault Simulation
Luis Alejandro Cortés, Daniel Karlsson
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Nov. 20, 2000
Basic Definitions
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Error : An instance of an incorrect operation of the CUT
Physical
Faults
Design Errors
■
Fabrication Errors
Fabrication Defects
Physical Failures
}
Error
Testing: “Are there faults
introduced during
manufacturing or operation?”
A fault is detected by observing an error caused by it
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Logical Fault Models
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■
Fault models are needed to analyze the result of the test
Logical Fault : Representation of the effect of the physical
faults on the operation of the system
❏
■
■
Only the logic function is usually considered (not timing)
Logical faults allow a mathematical treatment of testing
and diagnosis
Assumptions are considered to make the analysis feasible
❏
E.g. single-fault assumption
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Logical Fault Models (cont’d)
0
1
Stuck-at-1
Stuck-at-0
a.b
b
a+b
AND
a.b
a
AND-bridging
OR
a+b
OR-bridging
0
Stuck-at-0
Fault Modeling and Fault Simulation
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Fault Detection (Combinational Circuits)
x
Z(x)
C
faulty
Cf
x
Zf(x)
■
A test vector t detects a fault f iff Zf(t)=Z(t)
■
A fault f is detectable if there exists a test t that detects f
Fault Modeling and Fault Simulation
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Detectable Faults
x
z
y
0
f is undetectable
f
x
OR
g
y
z
t=00 is the only test
that detects g
z
t=00 does NOT detect g
in the presence of f
x
OR
y
g
0
f
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Nov. 20, 2000
Fault Detection (Sequential Circuits)
X
R(q,X)
S
faulty
Sf
X
■
Rf(qf,X)
A test sequence T detects a fault f iff, for every pair of initial
states q and qf, the output sequences R(q,T) and Rf(qf,T)
are different for some ti in T
Fault Modeling and Fault Simulation
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Nov. 20, 2000
Single Stuck-Fault (SSF) Model
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May represent different physical faults
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Technology independent
■
■
Test sets used to detect SSFs can detect other faults not
explicitly considered
The number of SSFs in a circuit is small, compared to other
fault models
☞ Successful model
Fault Modeling and Fault Simulation
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Nov. 20, 2000
SSF Model (cont’d)
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2n possible SSFs (n = no. lines in which a SSF may occur)
m=4
n=6
m
n =
∑ ( 1 + f i – qi )
i=1
s1
m = signal sources
s3
s2
s4
n = (G + I )(1 + f – q)
Fault Modeling and Fault Simulation
Luis Alejandro Cortés, Daniel Karlsson
f i = fanout count of signal s i
 1 if f i = 1
qi = 
 0 if f i > 1
f = average fanout count
q = fraction of signals with single fanout
G = no. gates
I = no. primary inputs
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Fault Equivalence
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The number of SSFs can be reduced based on equivalence
fault relations
A
B
D
C
B s-a-1, C s-a-0, and D s-a-1, are functionally equivalent
■
Determining whether two arbitrary faults are functionally
equivalent is an NP-complete problem (compute and show
the two faulty functions are identical)
❏
Relation analysis based on structural equivalence
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Nov. 20, 2000
Multiple Stuck-Fault (MSF) Model
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n = no. possible SSF sites
❏
2n SSFs
n
❏
∑
i=1
■
 n 2 i = 3 n – 1
 i
MSFs
If we consider k faults occurring simultaneously
k
❏
∑
i=1
❏
 n 2 i
 i
MSFs
Example: n=5000, k=2
50.000.000 MSFs (double faults)
10.000 SSFs
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