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

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

May 27, 2009ETS 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, 2009ETS 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 f Example: Fault Syndrome (Signature) ‘1’ → detected (fail) ‘0’ → not detected (pass)

May 27, 2009ETS Full-Response Dictionary Faults Output Responses t1t2t3t4t5 f1 f2 f3 f4 f5 f6 f7 f ‘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, 2009ETS 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, 2009ETS Faults Output Responses T1T2T3T4T5 F F F F F F F F Faults Output Responses T1T2T3T4T F1 F2 F3 F4 F5 F6 F7 F 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

May 27, 2009ETS 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 ≥ 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 ) J K

May 27, 2009ETS 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): 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. Fault Independence

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

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

May 27, 2009ETS 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 Minimal set of diagnostic vectors from Phase-2 Complete diagnostic test set Two-Phase Method

February 4, 2009Shukoor: MS Thesis Defense13 Comparison Between 1-Step Diagnostic ILP Run and 2-Phase Method Complete Diagnostic Test Set 4-b ALU c17 c432 c880

February 4, 2009Shukoor: MS Thesis Defense14 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

May 27, 2009ETS 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 c c c c c c c c c c c Phase Method

February 4, 2009Shukoor: MS Thesis Defense16 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 4b ALU c c c c c c c c c c c

May 27, 2009ETS 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 c c c c c c c c c c [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

May 27, 2009ETS 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, 2009ETS Thank you …