Transcript slides

Diagnostic and Detection Fault
Collapsing for Multiple Output Circuits
Raja K. K. R. Sandireddy and Vishwani D. Agrawal
Dept. Of Electrical and Computer Engineering,
Auburn University, Auburn, AL-36849 USA.
Outline
 Introduction
 Fault Equivalence and Fault Dominance
 Functional collapsing




Fault Equivalence and Dominance definitions
Results of functional collapsing
Hierarchical fault collapsing
Conclusions and Future work.
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Equivalence
R Structural equivalence1: Two faults f1 and f2 are
said to be R structurally equivalent if they produce
the same reduced circuit graph [netlist] when
faulty values are implied and constant edges
[signals] are removed.
Functional equivalence1: Two faults f1 and f2 are
said to be functionally equivalent if they modify
the Boolean function of the circuit in the same
way, i.e., they yield the same output functions.
E. J. McCluskey and F. W. Clegg, “Fault Equivalence in Combinational
Logic Networks,” IEEE Trans. Computers, vol. C-20, no. 11, Nov. 1971, pp.
1286-1293.
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Structural Dominance
A fault fi is said to dominate fault fj if the faults
are equivalent with respect to test set of fault fj.
a0 a1
c0 c1
b0 b1
Equivalence collapsed set = {a0, b0, c0, c1}
Dominance collapsed set = {a0, b0, c1}
Example: Full adder circuit.
Total faults: 60
Structural equivalence collapsed set2, 3 = 38 (0.63)
Structural dominance collapsed set3 = 30 (0.5)
2 Using Hitec, 3 Using Fastest
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Functional Dominance4
F1
F0
1
Z
0
1
F2
If the fault introduced in block F1 dominates the fault in
block F2, then Z is always 0.
For the full adder, functional dominance collapsed set = 12 (0.20)
{Structural equiv. = 38, Structural dom. = 30, Functional equiv.= 23}
V. D. Agrawal, A. V. S. S. Prasad, and M. V. Atre, “Fault Collapsing via
Functional Dominance,” Proc. International Test Conf., 2003, pp. 274-280.
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Equivalence Definitions
For multiple output circuits,
 Diagnostic Equivalence - Two faults of a Boolean circuit
are called diagnostically equivalent if and only if the functions
of the two faulty circuits are identical at each output.
 Detection Equivalence - Two faults are called detection
equivalent if and only if all tests that detect one fault also
detect the other fault, not necessarily at the same output.
A
B
s-a-0
Y
Z
c
s-a-0
The faults c0 and Y0 are
detection equivalent faults,
but not diagnostic equivalent.
For the full adder, diagnostic equivalence collapsed set = 26 (0.43),
detection equivalence collapsed set = 23 (0.38)
{Structural equiv. = 38, Structural dom. = 30, Functional equiv.= 26,
Functional dom.= 12}
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Dominance Definitions
Fault Dominance5
- A fault fi is said to
dominate fault fj if (a) the set of all vectors that
detects fault fj is a subset of all vectors that detects
fault fi and (b) each vector that detects fj implies
identical values at the corresponding outputs of
faulty versions of the circuit.
Conventionally dominance is defined as:
 A fault fi is said to dominate fault fj if the faults are
equivalent with respect to test set of fault fj.
 If all tests of fault fj detect another fault fi, then fi is
said to dominate fj.
F. Poage, “Derivation of Optimum Tests to Detect Faults in Combinational
Circuits", Proc. Symposium on Mathematical Theory of Automata, 1962, pp.
483-528.
5 J.
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Dominance Definitions contd.
For multiple output circuits, the two possible interpretations of
dominance:
 Diagnostic dominance - If all tests of a fault f1 detect
another fault f2 on the exact same outputs where f1
was detected, then f2 is said to diagnostically
dominate f1.
 Detection dominance - If all tests of a fault f1 detect
another fault f2, irrespective of the output where f1
was detected, then f2 is said to detection dominate
f1 .
Diagnostic dominance implies detection dominance.
For the full adder, diagnostic dominance collapsed set = 12 (0.2)
detection dominance collapsed set = 6 (0.1)
{Structural equiv. = 38, Structural dom. = 30, Diagnostic equiv.= 26,
Detection equiv.= 23}
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Results: Functional Collapsing
Number of Collapsed Faults (Collapse Ratio)
Functional Collapsing – New Results
Circuit
Name
All
Faults
Structural
Functional4
Diagnostic
Criterion
Detection
Criterion
Equiv.2
Dom.3
Equiv.
Dom.
Equiv.
Dom.
Equiv.
Dom.
XOR
24
16
(0.67)
13
(0.54)
10
(0.42)
4
(0.17)
10
(0.42)
4
(0.17)
10
(0.42)
4
(0.17)
Full
Adder
60
38
(0.63)
30
(0.50)
26
(0.43)
14
(0.23)
26
(0.43)
12
(0.20)
23
(0.38)
6
(0.10)
8-bit
Adder
466
290
(0.62)
226
(0.49)
194
(0.42)
112
(0.24)
194
(0.42)
96
(0.21)
191
(0.41)
48
(0.10)
ALU
(74181)
502
301
(0.60)
248
(0.49)
--
--
253
(0.50)
155
(0.31)
234
(0.47)
92
(0.18)
2 Using
Hitec (obtained from Univ. of Illinois at Urbana-Champaign)
3 Using Fastest (obtained from Univ. of Wisconsin at Madison)
4 Agrawal et al. ITC’03
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Results: Test Vectors
Test vectors obtained using Gentest ATPG6.
No. of test vectors (no. of target faults)
Circuit
Structural
Equivalence Dominance
Functional – New Results
Diagnostic
Dominance
Detection
Dominance
Full Adder
6 (38)
6 (30)
7 (12)
6 (6)
8-bit Adder
33 (290)
28 (226)
32 (96)
28 (48)
ALU
44 (293)
44 (240)
39 (147)
38 (84)
T. Cheng and T. J. Chakraborty, “Gentest: An Automatic Test Generation
System for Sequential Circuits,” Computer, vol. 22, no. 4, pp. 43–49, April
1989.
6 W.
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Hierarchical Fault Collapsing
Comparison of hierarchical fault collapse ratios
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Flattened Equiv.
(structural)
Hierarchical Equiv.
(functional)
Flattened Dom.
(structural)
Hierarchical Dom.
(functional)
Full
Adder
64-bit 1024-bit
Adder Adder
c432
c499
Total Faults:
Full Adder: 60, 64-bit Adder: 3714, 1024-bit Adder: 59394,
c432:1116, c499:2646
Detection collapsing can be used only for those subcircuits whose outputs are POs at the top-level.
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CPU time (sec) for hierarchical collapsing
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Conclusions
 Diagnostic and detection collapsing should be used
only with smaller circuits.
 Collapse ratios using detection dominance
collapsing is about 10-20%.
 Hierarchical fault collapsing:
 Better (lower) collapse ratios due to functional collapsed
library
 Order of magnitude reduction in collapse time.
 Smaller fault sets:
 Fewer test vectors
 Reduced fault simulation effort
 Easier fault diagnosis.
 Use caution when using dominance collapsing!!
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Future Work
 Generate fault collapsing library of standard
cells (Mentor Graphics, etc.).
 Efficient redundancy detection program.
 Customized ATPG to obtain minimal test
vector set.
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