A Two Phase Approach for Minimal Diagnostic Test

A Two Phase Approach for Minimal Diagnostic Test Set Generation Mohammed Ashfaq Shukoor Vishwani D. Agrawal Auburn University, Department of Electrical and Computer Engineering Auburn, AL 36849, USA 14 th IEEE European Test Symposium Seville, Spain, May 25 -28, 2009

Outline Ø Introduction Ø Motivation Ø Fault Diagnostic Table Ø Diagnostic ILP Ø Diagnostic Fault Independence Ø 2 -phase Approach Ø Results Ø Conclusion & Future Work May 27, 2009 ETS 2009 2

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 May 27, 2009 ETS 2009 3

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: Test Vectors May 27, 2009 Faults t 1 t 2 t 3 t 4 t 5 f 1 f 2 f 3 f 4 f 5 f 6 f 7 f 8 1 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 ETS 2009 Fault Syndrome (Signature) ‘ 1’ → detected (fail) ‘ 0’ → not detected (pass) 4

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 Faults f 1 f 2 f 3 f 4 f 5 f 6 f 7 f 8 May 27, 2009 Output Responses t 1 t 2 t 3 t 4 t 5 10 11 11 01 00 00 10 11 11 01 10 10 00 01 01 01 10 10 11 10 01 00 10 10 10 00 10 11 00 00 10 ETS 2009 Fault Syndrome ‘ 1’ → detected ‘ 0’ → not detected 5

Motivation for Diagnostic Test Set Minimization q The amount of data in a full-response dictionary is (F T O). q Previous work on dictionary compaction has been concentrated on managing the dictionary organization and encoding. q 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 6

Fault Diagnostic Table Ø 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 Faults Output Responses T 1 T 2 T 3 T 4 T 5 F 1 1 1 0 00 F 2 2 2 1 2 0 00 00 F 3 3 2 1 0 0 00 01 00 F 4 3 3 0 00 01 00 11 F 5 0 0 2 0 1 00 00 01 00 00 F 6 0 0 2 0 0 F 7 10 00 01 F 7 1 0 2 F 8 00 10 10 10 00 F 8 0 1 1 1 0 T 1 T 2 T 3 T 4 T 5 F 1 10 10 00 F 2 11 11 10 11 F 3 01 11 10 F 4 01 01 F 5 00 F 6 Fault Diagnostic Table Full-response Dictionary May 27, 2009 ETS 2009 7

Diagnostic ILP Objective: If vj = 1, then vector j is included in the minimized vector set (1) • If vj a=ij 0, ≥ then vector is noti is coefficient 1 only if thej fault included in thej, minimized detected by vector else it is 0 vector set minimize Subject to constraints: (2) i = 1, 2, . . . , K Fault number ( k) vj 1 Vector number ( j ) 2 3 4. . . 2 1 0 1 1 . . . 2 3 1 2 0 0 . . . 0 0 2 . . (4). 3 . 1 (3) . . K 0 5 0 9 . . . 2 K is the number of faults in a combinational circuit J is the number of vectors in the unoptimized vector set May 27, 2009 J 1 j = 1, 4 2, . . . , 2 J 1 . . k = 1, 2, 1. . . , K-10 integer [0, 1], 0. . , . K. p 1= k+1, . ETS 2009 8

Fault Independence 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 T(f 1) T(f 2) f 1 and f 2 are not 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. May 27, 2009 ETS 2009 9

Example (Two-Output Circuit) (a) Fault independence Guaranteed diagnosis Fault detection Table (b) Generalized fault independence Guaranteed diagnosis Fault diagnostic Table May 27, 2009 ETS 2009 10

Effect of Generalized Independence Relation on the Constraint Set Sizes May 27, 2009 ETS 2009 11

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 detection test set of Phase-1 May 27, 2009 Minimal set of diagnostic vectors from Phase-2 ETS 2009 Complete diagnostic test set 12

Comparison Between 1 -Step Diagnostic ILP Run and 2 -Phase Method Complete Diagnostic Test Set c 17 February 4, 2009 4 -b ALU c 432 c 880 Shukoor: MS Thesis Defense 13

Results • • SUN Fire 280 R, 900 MHz Dual Core machine ATPG – ATALANTA Fault Simulator – HOPE AMPL Package with CPLEX solver formulating and solving Linear Programs February 4, 2009 Shukoor: MS Thesis Defense 14

2 -Phase Method Phase-1 Phase-2 Complete diagnostic test set Circuit No. of faults Original unoptim. vectors Minimal detection tests No. of undiag. faults No. of unoptim. vectors No. of constraints Minimized additional vectors 4 b ALU 227 270 12 43 258 30 6 18 c 17 22 32 4 6 28 3 2 6 c 432 520 2036 30 153 2006 101 21 51 c 499 750 705 52 28 653 10 2 54 c 880 942 1384 24 172 1358 41 7 33 c 1355 1566 903 84 1172 1131 12 2 86 c 1908 1870 1479 107 543 1372 186 21 128 c 2670 2630 4200 70 833 4130 383 51 121 c 3540 3291 3969 95 761 3874 146 27 122 c 5315 5291 1295 63 1185 1232 405 42 105 c 6288 7710 361 16 2416 345 534 12 28 c 7552 7419 4924 122 1966 4802 196 31 153 May 27, 2009 ETS 2009 15

Diagnostic Characteristics of Minimized Complete Diagnostic Test Set 1 Circuit 2 Total Vectors 3 No. of Faults 4 Uniquely Diagnosed Faults 5 No. of CEFS 6 Undiag. Faults (3 – 4) 7 No. of Syndromes (4 + 5) 8 Maximum Faults per Syndrome 9 Diagnostic Resolution 4 b ALU 18 227 0 0 227 1 1. 000 c 17 6 22 22 0 0 22 1 1. 000 c 432 51 520 488 16 32 504 2 1. 032 c 499 54 750 726 12 24 738 2 1. 016 c 880 33 942 832 55 110 887 2 1. 132 c 1355 86 1566 397 532 1169 929 3 1. 686 c 1908 127 1870 1380 238 490 1618 8 1. 156 c 2670 121 2630 2027 263 603 2290 11 1. 149 c 3540 122 3291 2720 234 571 3033 8 1. 085 c 5315 105 5291 4496 381 795 4877 4 1. 085 c 6288 28 7710 5690 1009 2020 6699 3 1. 151 c 7552 153 7419 5598 848 1821 6446 7 1. 151 February 4, 2009 Shukoor: MS Thesis Defense 16

2 -Phase vs. Previous Work 2 -Phase Approach [This work] Pass-fail dictionary compaction [1] Circuit Fault coverage % Minimized vectors Undisting. fault Pairs CPU s Fault coverage % Minimized vectors Undisting. Fault Pairs CPU s c 432 97. 52 68 93 0. 1 98. 66 54 15 0. 94 c 499 - - 98. 95 54 12 0. 39 c 880 97. 52 63 104 0. 2 97. 56 42 64 2. 56 c 1355 98. 57 88 878 0. 8 98. 60 80 766 0. 34 c 1908 94. 12 139 1208 2. 1 95. 69 101 399 0. 49 c 2670 84. 40 79 1838 2. 8 84. 24 69 449 8. 45 c 3540 94. 49 205 1585 10. 6 94. 52 135 590 17. 26 c 5315 98. 83 188 1579 15. 4 98. 62 123 472 25. 03 c 6288 99. 56 37 4491 1659 99. 56 17 1013 337. 89 c 7552 91. 97 198 4438 33. 8 92. 32 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, May ETS 2009 17 2006, 27, pp. 2009 75 -80.

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. May 27, 2009 ETS 2009 18

Thank you … May 27, 2009 ETS 2009 19