Compaction of Diagnostic Test Set for a Full-Response

DictionaryMohammed Ashfaq Shukoor

Vishwani D. Agrawal

18th IEEE North Atlantic Test Workshop, 2009

Auburn University, Department of Electrical and Computer Engineering Auburn, AL 36849, USA

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Outline Introduction Motivation Fault Diagnostic Table Diagnostic ILP Diagnostic Fault Independence 2-Phase Approach Results Conclusion & Future Work

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Fault Dictionary Based Diagnosis

• Fault dictionary is a database of simulated test responses for all modeled faults in a fault list.

• Used by some diagnosis algorithms as it is fast; no simulation at time of diagnosis.

• Can be very large, however!• Two most popular forms of dictionaries are:

– Pass-Fail Dictionary

– Full-Response Dictionary

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Pass-Fail Dictionary• For each vector store the list of all detectable faults.• Total storage requirement: F T bits, where F is number of

faults and T is number of vectors.

Faults

Test Vectors

t1 t2 t3 t4 t5

f1

f2

f3

f4

f5

f6

f7

f8

1

0

0

1

1

1

1

1

0

1

1

1

0

0

1

0

1

1

1

1

0

0

0

1

0

1

0

1

1

0

0

0

0

1

1

0

0

0

0

1

Example:

Fault Syndrome (Signature)

‘1’ → fault detected (fail)

‘0’ → not detected (pass)

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Full-Response Dictionary

FaultsOutput Responses

t1 t2 t3 t4 t5

f1

f2

f3

f4

f5

f6

f7

f8

1 0

1 1

1 1

0 1

0 0

0 0

0 0

0 0

1 0

1 1

1 1

0 1

1 0

1 0

0 0

1 0

1 0

1 0

1 0

0 0

0 1

0 1

0 1

1 0

1 0

1 1

1 0

0 1

0 0

1 0

1 0

1 0

0 0

1 0

1 1

0 0

0 0

0 0

0 0

1 0

‘1’ → fault detected

‘0’ → not detected

Fault Syndrome

• For each vector, store fault detection data for all outputs.• Total storage requirement: F T O bits, where F is number

of faults, T is number of vectors and O is number of outputs.

Example:

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Motivation for Diagnostic Test Set Minimization

The amount of data in a full-response dictionary is F T O.

Previous work on dictionary compaction has been concentrated on managing the dictionary organization and encoding.

The data in the full-response dictionary can be optimized by minimizing the vectors in the diagnostic test set.

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FaultsOutput Responses

T1 T2 T3 T4 T5

F1 1 0 1 0 1 0 1 0 0 0

F2 1 1 1 1 1 0 1 1 0 0

F3 0 1 1 1 1 0 0 0 0 0

F4 0 1 0 1 0 0 0 1 0 0

F5 0 0 0 0 0 1 0 0 1 1

F6 0 0 0 0 0 1 0 0 0 0

F7 1 0 0 0 0 1 0 0 0 1

F8 0 0 1 0 1 0 1 0 0 0

FaultsOutput Responses

T1 T2 T3 T4 T5

1

2

2

3

0

0

0

1

1

1

1

0

2

2

2

1

F1

F2

F3

F4

F5

F6

F7

F8

0

0

0

0

1

0

2

0

1

2

0

3

0

0

0

1

Fault Diagnostic Table We compact the full-response dictionary into a diagnostic table, which contains information on detection and distinguishability of faults.

Example: Consider a circuit with 2 outputs, having 8 faults that are detected and diagnosed by 5 test vectors

Full-response Dictionary Fault Diagnostic Table

1

2

3

0

3

0

1

0

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Diagnostic ILP

Subject to constraints:

J

jjv

1Objective: minimize

integer [0, 1], j = 1, 2, . . . , J vj

i = 1, 2, . . . , K (2)

(4)

(1)

If vj = 1, then vector j is included in the minimized vector set• If vj = 0, then vector j is not included in the minimized vector set

K is the number of faults in a combinational circuit

J is the number of vectors in the unoptimized vector set

coefficient aij is >= 1 only if the fault i is detected by vector j, else it is 0

1.1

J

jpjkjj aav k = 1, 2, . . . , K-1 p = k+1, . . . , K (3)

11

J

jijjav

Faultnumber ( k)

Vector number ( j )1 2 3 4 . . . . . J

1 0 1 1 0 . . . . . 1

2 1 0 1 1 . . . . . 2

3 1 2 0 0 . . . . . 0

4 2 1 0 2 . . . . . 3

. . . . . . . . . . .

. . . . . . . . . . .

K 0 5 0 9 . . . . . 2

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Independent Faults [1]:Two faults are independent if and only if they cannot be detected

by the same test vector.

T(f1) T(f2)

f1 and f2 are independent f1 and f2 are not independent

T(f1) T(f2)

[1] S. B. Akers, C. Joseph, and B. Krishnamurthy, “On the Role of Independent Fault Sets in the Generation of Minimal Test Sets,” Proc. International Test Conf., 1987, pp. 1100–1107.

Generalized Fault Independence (Vector Specific, Multiple Outputs) – Present Work:

A pair of faults detectable by a vector set V is said to be independent with respect to vector set V, if there is no single vector that detects both the faults and produces an identical output response.

Fault Independence

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Fault detection Table

Fault diagnostic Table

(a) Independence Relation

(b) Generalized Independence Relation

Example

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0

200000

400000

600000

800000

1000000

1200000

1400000

ALU and Benchmark Circuits

Nu

mb

er o

f C

on

stra

ints

Initial Constraints 231 25,651 125,751 271,953 392,941 1,308,153

Final Constraints 61 3,074 14,162 133,698 48,761 106,448

c17 4 alu c432 c499 c880 c1908

Effect of Generalized Independence Relation on the Constraint Set Sizes

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Phase-1: Use existing ILP minimization techniques to obtain a minimal detection test set from the given unoptimized test set. Find the faults not diagnosed by the minimized detection test set.

Phase-2: Run the diagnostic ILP on the remaining unoptimized test set to obtain a minimal set of vectors to diagnose the undistinguished faults from phase-1.

Minimal detection test set of Phase-1

Minimal set of diagnostic vectors

from Phase-2

Complete diagnostic

test set

2-Phase Method

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Results• SUN Fire 280R, 900 MHz Dual Core machine• ATPG – ATALANTA• Fault Simulator – HOPE• AMPL Package with CPLEX solver for formulating and

solving Linear Programs

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CircuitNo. of Faults

Phase-1 Phase-2Complete diagnostic

test set

Original unoptim. vectors

Minimal detection

tests

No. of undiag. faults

No. ofunoptim.vectors

No. ofconstraints

Minimized additional

vectors

4b ALU 227 270 12 43 258 30 6 18

c17 22 32 4 6 28 3 2 6

c432 520 2036 30 153 2006 101 21 51

c499 750 705 52 28 653 10 2 54

c880 942 1384 24 172 1358 41 7 33

c1355 1566 903 84 1172 1131 12 2 86

c1908 1870 1479 107 543 819 186 21 127

c2670 2630 4200 70 833 4058 383 51 121

c3540 3291 3969 95 761 3874 146 27 122

c5315 5291 1295 63 1185 1232 405 42 105

c6288 7710 361 16 2416 345 534 12 28

c7552 7419 4924 122 1966 4802 196 31 153

2-Phase Method

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2-Phase vs. Previous Work

Circuit

Pass-Fail dictionary compaction [1] 2-Phase Approach [This work]

Fault Coverage

%

Minimized Vectors

Undisting. Fault Pairs

CPU

s

Fault Coverage

%

Minimized Vectors

Undisting. Fault Pairs

CPU

s

c432 97.52 68 93 0.1 98.66 54 15 0.94

c499 - - - - 98.95 54 12 0.39

c880 97.52 63 104 0.2 97.56 42 64 2.56

c1355 98.57 88 878 0.8 98.60 80 766 0.34

c1908 94.12 139 1208 2.1 95.69 101 399 0.49

c2670 84.40 79 1838 2.8 84.24 69 449 8.45

c3540 94.49 205 1585 10.6 94.52 135 590 17.26

c5315 98.83 188 1579 15.4 98.62 123 472 25.03

c6288 99.56 37 4491 1659 99.56 17 1013 337.89

c7552 91.97 198 4438 33.8 92.32 128 1289 18.57

[1] Y. Higami and K. K. Saluja and H. Takahashi and S. Kobayashi and Y. Takamatsu, “Compaction of Pass/Fail-based Diagnostic Test Vectors for Combinational and Sequential Circuits,” Proc. ASPDAC, 2006, pp. 75-80.

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Conclusion

• Compaction of a diagnostic test set is carried out without any loss in the diagnostic resolution of a full-response dictionary.

• We have formulated the diagnostic ILP that provides an exact minimization of a diagnostic test set.

• The newly defined generalized independence relation between pairs of faults reduces the number of fault-pairs that need to be distinguished; ILP constraints are significantly reduced.

• The 2-phase approach has polynomial time complexity and is effective in producing very compact diagnostic test sets.

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Thank you …