Concurrent Test Generation

1

• Concurrent Test Generation

Vishwani D. Agrawal, vagrawal_at_eng.auburn.edu
Alok S. Doshi, dosias_at_auburn.edu
Auburn University, Department of Electrical and
Computer Engineering Auburn, AL 36849, USA For
more details, see http//www.eng.auburn.edu/vagra
wal
2
Problem Statement

• To find the smallest test set to detect all
  single stuck-at faults in a combinational
  circuit.
• An existing solution
• Group faults into fault sets using fault
  independence
• Generate concurrent tests for each group
• Contribution of this paper Devise a
  simulation-based implementation for this solution.

3
Outline

• Introduction
• Simulation-based Independence Fault Collapsing
• Simulation-based Concurrent Test Generation
• Results
• Conclusions

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Introduction

• Problem of finding a minimal test
• Static compaction cannot guarantee optimality.
• Dynamic compaction is complex.
• Solution Target both faults F1 and F2 at the
  same time to find a single test. We define this
  as concurrent test generation.

.
.
.
T(F2)
T(F1)
Test set for fault F2
Test set for fault F1
v2
v1
v3
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Fault Classification
T(F1)
T(F1) T(F2)
T(F2)
F1 and F2 are equivalent.
F1 dominates F2.
T(F1)
T(F2)
T(F1)
T(F2)
F1 and F2 are independent.
F1 and F2 are concurrently testable.
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Definitions

• Independent Faults4
• Two faults are independent if and only if they
  cannot be detected by the same test vector.
• Concurrently-Testable Faults
• Two faults that neither have a dominance
  relationship nor are independent, are defined as
  concurrently-testable faults.

4 S. B. Akers, C. Joseph, and B. Krishnamurthy,
On the role of Independent Fault Sets in the
Generation of Minimal Test Sets, in Proc.
International Test Conf., 1987, pp. 1100-1107.
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Structural Independences
sa1
sa1
sa1
sa0
sa1
sa0
sa1
sa1
sa1
sa0
sa0
sa0
sa1
sa1
sa0
sa0
sa0
sa0
sa0
sa1
Functional Independences Found by ATPG-like
methods.
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Example Circuit
2
4
a
x
1
5
b
3
7
11
c
y
d
6
10
9
All faults are Stuck-at-1 type
e
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C17 - ISCAS85 Benchmark Circuit
1 R. K. K. R. Sandireddy and V. D. Agrawal,
Diagnostic and Detection Fault Collapsing for
Multiple Output Circuits, Proc. Design,
Automation and Test in Europe (DATE) Conf., Mar.
2005, pp. 1014 - 1019.
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Independence Matrix and Graph
Clique
C17 - ISCAS85 Benchmark Circuit
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Independence Fault Collapsing
A similarity based algorithm 2 collapses the
independence graph
Highly Similar Highly Dissimilar
Similarity of a fault-pair
5,11,7
1,8
3,9,2
4,6,10
C17 - ISCAS85 Benchmark Circuit
Equiv. Indep.
2 A. S. Doshi and V. D. Agrawal, Independence
Fault Collapsing, Proc. 9th VLSI Design and Test
Symp., Aug. 2005, pp. 357 - 364.
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Simulation-based Independence Fault Collapsing

• The independence graph generation procedure 2
  requires ATPG.
• Here we present a new method for graph generation
  using simulation
• Start with a fully-connected independence graph
  for an equivalence collapsed fault set.
• Simulation of random vectors without fault
  dropping removes edges between faults detected by
  the same vector.

2 A. S. Doshi and V. D. Agrawal, Independence
Fault Collapsing, Proc. 9th VLSI Design and Test
Symp., Aug. 2005, pp. 357 - 364.
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Simulation-based Independence Fault Collapsing
301
74181 4-bit ALU
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Simulation-based Concurrent Test Generation

• For each group, generate all test vectors for the
  first fault in the group.
• If the number of test vectors for a fault is
  large, use a subset (e.g., 250 maximum) of
  vectors.
• Simulate all faults in the group to select one
  vector that detects most faults in that group.
• If more vectors than one detect the same number
  of faults within the group, then select the
  vector that detects most faults outside the group
  as well.

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74181 4-bit ALU Result
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Results
Sun Ultra 5 Pentium Pro PC
Hamzaoglu and Patel, IEEE-TCAD, 2000
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Number of Vectors for Increasing Circuit Sizes
(100 Stuck-at Coverage)
Single-fault ATPG (no compaction)
Concurrent ATPG
Minimum achieved! (dynamic compaction)
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CPU Seconds for Increasing Circuit Sizes (100
Stuck-at Fault Coverage)
Concurrent ATPG
Minimum achieved! (dynamic compaction)
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Conclusion

• Concurrent test generation produces compact tests
  when combined with independence fault collapsing.
• ATPG and set covering problems have exponential
  time complexities. Hence, we cannot expect
  absolute optimality for large circuits.
• The concurrent ATPG procedure of this paper gives
  significantly smaller, and sometimes the optimum,
  test sets.
• There is scope for improving the simulation-based
  algorithms for independence fault collapsing and
  concurrent test generation.

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• Thank You!