1. Compaction of Diagnostic Test Set for a Full-Response Dictionary Mohammed Ashfaq Shukoor Vishwani D. Agrawal 18th IEEE North Atlantic Test Workshop, 2009 Auburn University, Department of Electrical and Computer Engineering Auburn, AL 36849, USA

2. May 14, 2009NATW 20092 Outline  Introduction  Motivation  Fault Diagnostic Table  Diagnostic ILP  Diagnostic Fault Independence  2-Phase Approach  Results  Conclusion & Future Work

3. May 14, 2009NATW 20093 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

4. May 14, 2009NATW 20094 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 t1t2t3t4t5 f1 f2 f3 f4 f5 f6 f7 f8 1001111110011111 0111001001110010 1111000111110001 0101100001011000 0110000101100001 Example: Fault Syndrome (Signature) ‘1’ → fault detected (fail) ‘0’ → not detected (pass)

5. May 14, 2009NATW 20095 Full-Response Dictionary Faults Output Responses t1t2t3t4t5 f1 f2 f3 f4 f5 f6 f7 f8 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 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:

6. May 14, 2009NATW 20096 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.

7. May 14, 2009NATW 20097 Faults Output Responses T1T2T3T4T5 F11 0 0 F21 1 01 0 F30 11 1 00 F40 1 0 0 10 F50 0 10 1 F60 0 10 F71 00 0 10 0 1 F80 1 0 0 Faults Output Responses T1T2T3T4T5 1223000112230001 1110222111102221 F1 F2 F3 F4 F5 F6 F7 F8 0000102000001020 1203000112030001 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

8. May 14, 2009NATW 20098 Diagnostic ILP Subject to constraints: Objective: minimize integer [0, 1], j = 1, 2,..., Jvjvj i = 1, 2,..., K (2) (4) (1) If v j = 1, then vector j is included in the minimized vector set If v j = 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 a ij is >= 1 only if the fault i is detected by vector j, else it is 0 k = 1, 2,..., K-1 p = k+1,..., K (3) Fault number ( k) Vector number ( j ) 1 2 3 4..... J 10 110.....1 21011.....2 31200.....0 42102.....3...................... K0509.....2

9. May 14, 2009NATW 20099 Independent Faults [1] : Two faults are independent if and only if they cannot be detected by the same test vector. T(f 1 ) T(f 2 ) f 1 and f 2 are independent f 1 and f 2 are not independent T(f 1 ) T(f 2 ) [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

10. May 14, 2009NATW 200910 Fault detection Table Fault diagnostic Table (a) Independence Relation (b) Generalized Independence Relation Example

11. May 14, 2009NATW 200911 Effect of Generalized Independence Relation on the Constraint Set Sizes

12. May 14, 2009NATW 200912 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

13. May 14, 2009NATW 200913 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

14. May 14, 2009NATW 200914 Circuit No. of Faults Phase-1Phase-2 Complete diagnostic test set Original unoptim. vectors Minimal detection tests No. of undiag. faults No. of unoptim. vectors No. of constraints Minimized additional vectors 4b ALU 227270124325830618 c17 22324628326 c432 52020363015320061012151 c499 750705522865310254 c880 942138424172135841733 c1355 1566903841172113112286 c1908 1870147910754381918621127 c2670 2630420070833405838351121 c3540 3291396995761387414627122 c5315 52911295631185123240542105 c6288 77103611624163455341228 c7552741949241221966480219631153 2-Phase Method

15. May 14, 2009NATW 200915 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 c43297.5268930.198.6654150.94 c499----98.9554120.39 c88097.52631040.297.5642642.56 c135598.57888780.898.60807660.34 c190894.1213912082.195.691013990.49 c267084.407918382.884.24694498.45 c354094.49205158510.694.5213559017.26 c531598.83188157915.498.6212347225.03 c628899.56374491165999.56171013337.89 c755291.97198443833.892.32128128918.57 [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.

16. May 14, 2009NATW 200916 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.

17. May 14, 2009NATW 200917 Thank you …