A Two Phase Approach for Minimal Diagnostic Test Set Generation

1. 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

2. Outline • Introduction • Motivation • Fault Diagnostic Table • Diagnostic ILP • Diagnostic Fault Independence • 2-phase Approach • Results • Conclusion & Future Work ETS 2009

3. Fault Dictionary Based Diagnosis • 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 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. Example: Fault Syndrome (Signature) ‘1’ → detected (fail) ‘0’ → not detected (pass) ETS 2009

5. Full-Response Dictionary • 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 Fault Syndrome ‘1’ → detected ‘0’ → not detected 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. ETS 2009

7. 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 1 2 2 3 0 0 0 1 F1 F2 F3 F4 F5 F6 F7 F8 1 1 1 1 0 2 2 2 1 1 2 0 3 0 0 0 1 0 0 0 0 1 0 2 0 2 3 3 0 0 1 0 Fault Diagnostic Table Full-response Dictionary ETS 2009

8. vj Diagnostic ILP • 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 Objective: minimize (1) coefficient aij≥ 1 only if the fault i is detected by vector j, else it is 0 Subject to constraints: (2) i = 1, 2, . . . , K (3) k = 1, 2, . . . , K-1 p = k+1, . . . , K (4) integer [0, 1], j = 1, 2, . . . , J K is the number of faults in a combinational circuit J is the number of vectors in the unoptimized vector set ETS 2009

9. Fault Independence Independent Faults [1]: Two faults are independent if and only if they cannot be detected by the same test vector. T(f2) T(f2) T(f1) T(f1) f1 and f2 are not independent f1 and f2 are independent Generalized Fault Independence (Vector-Specific, Multiple-Outputs): 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. [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. ETS 2009

10. Example (Two-Output Circuit) (a) Fault independence Guaranteed diagnosis Fault detection Table (b) Generalized fault independence Guaranteed diagnosis Fault diagnostic Table ETS 2009

11. Effect of Generalized Independence Relation on the Constraint Set Sizes ETS 2009

12. Two-Phase Method 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. Minimal set of diagnostic vectors from Phase-2 Complete diagnostic test set Minimal detection test set of Phase-1 ETS 2009

13. Comparison Between 1-Step Diagnostic ILP Run and 2-Phase Method Complete Diagnostic Test Set c432 4-b ALU c17 c880 Shukoor: MS Thesis Defense

14. 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 Shukoor: MS Thesis Defense

15. 2-Phase Method ETS 2009

16. Diagnostic Characteristics of Minimized Complete Diagnostic Test Set Shukoor: MS Thesis Defense

17. 2-Phase vs. Previous Work [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. 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. ETS 2009

19. Thank you … ETS 2009