A Two Phase Approach for Minimal Diagnostic Test Set Generation Mohammed Ashfaq Shukoor Vishwani D. Agrawal 14th IEEE European Test Symposium Seville, Spain, May 25-28, 2009 Auburn University, Department of Electrical and Computer Engineering Auburn, AL 36849, USA
19
Embed
A Two Phase Approach for Minimal Diagnostic Test Set Generation
Mohammed Ashfaq Shukoor Vishwani D. Agrawal. A Two Phase Approach for Minimal Diagnostic Test Set Generation. Auburn University, Department of Electrical and Computer Engineering Auburn, AL 36849, USA. 14th IEEE European Test Symposium Seville, Spain, May 25-28, 2009. Outline. Introduction - PowerPoint PPT Presentation
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
A Two Phase Approach for Minimal Diagnostic Test Set
GenerationMohammed Ashfaq Shukoor
Vishwani D. Agrawal
14th IEEE European Test SymposiumSeville, Spain, May 25-28, 2009
Auburn University, Department of Electrical and Computer Engineering Auburn, AL 36849, USA
• Fault dictionary is a database of simulated test responses for all modeled faults.
• Used by some diagnosis algorithms:– It is fast– No simulation at the time of diagnosis.
• Dictionary can be very large, however!• Two most popular forms of dictionaries are:
– Pass-Fail Dictionary– Full-Response Dictionary
May 27, 2009 ETS 2009 4
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
f1f2f3f4f5f6f7f8
10011111
01110010
11110001
01011000
01100001
Example:
Fault Syndrome (Signature)
‘1’ → detected (fail)
‘0’ → not detected (pass)
May 27, 2009 ETS 2009 5
Full-Response Dictionary
FaultsOutput Responses
t1 t2 t3 t4 t5
f1f2f3f4f5f6f7f8
1 01 11 10 10 00 00 00 0
1 01 11 10 11 01 00 01 0
1 01 01 00 00 10 10 11 0
1 01 11 00 10 01 01 01 0
0 01 01 10 00 00 00 01 0
‘1’ → detected
‘0’ → not detected
Fault Syndrome
• For each vector, store the 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:
2 outputs
May 27, 2009 ETS 2009 6
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.
Data in a full-response dictionary can be optimized by minimizing the number of vectors in the diagnostic test set.
May 27, 2009 ETS 2009 7
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
May 27, 2009 ETS 2009 8
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 ≥ 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
May 27, 2009 ETS 2009 9
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.
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 faults and produces an identical output response.
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
May 27, 2009 ETS 2009 12
Phase-1: Use existing ILP minimization technique 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.
[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.
May 27, 2009 ETS 2009 18
Conclusion• Minimization of a diagnostic test set is carried out without loss of
diagnostic resolution of a full-response dictionary.• We have formulated the diagnostic ILP which is an exact method to
minimize a diagnostic test set.• The newly defined generalized independence relation between pairs
of faults reduces the number of fault-pairs that needs to be distinguished.
• The two-phase approach has polynomial time complexity and is effective in producing compact diagnostic test sets.
• New problems to be solved:– Define a diagnostic coverage metric similar to the stuck-at detection coverage.– Develop ATPG algorithms to find a distinguishing test for a pair of faults.