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A Monte Carlo Approach for Testability Analysis

A Monte Carlo Approach for Testability Analysis. Speaker: Chuang-Chi Chiou Advisor: Chun-Yao Wang 2007.01.29. Outline. Introduction Previous Work Background Monte Carlo Approach for testability analysis Experiment Results Conclusion Future Work. Outline. Introduction Previous Work

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A Monte Carlo Approach for Testability Analysis

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  1. A Monte Carlo Approach for Testability Analysis Speaker: Chuang-Chi Chiou Advisor: Chun-Yao Wang 2007.01.29 1

  2. Outline • Introduction • Previous Work • Background • Monte Carlo Approach for testability analysis • Experiment Results • Conclusion • Future Work 2

  3. Outline • Introduction • Previous Work • Background • Monte Carlo Approach for testability analysis • Experiment Results • Conclusion • Future Work 3

  4. Single Stuck-At Fault Only one line is faulty Fault line permanently set to 1 or 0 Fault can be an input or output of a gate One of the gate input terminal was mistakenly connected to ground Fault: B stuck at 0 Signal B is always be 0 Fault Model G1 A B 4

  5. Testability Analysis • Controllability • The difficulty of setting a particular logic signal to 0 or 1 ( 0’s controllability or 1’ controllability ) • Observability • The difficulty of observing the state of a logic signal • Fault detection probability • Stuck-at-1 fault testability • Stuck-at-0 fault testability • The difficulty of observing the state of a logic signal to be 0 or 1 5

  6. Motivation • Give a warning to designer which nodes are hard-to-test • Redesign • Add test circuits such as test point insertion • Provide guidance for ATPG • Avoid hard-to-control point • Provide estimation of fault coverage and test vector set length 6

  7. Outline • Introduction • Previous Work • Background • Monte Carlo Approach for testability analysis • Experiment Results • Conclusion • Future Work 7

  8. Previous Work (1/2) • SCOAP • First elegant formulation • Use integer to represent difficulty for testing a wire • Results are not easy to use • Parker and McCluskey • Definition of probabilistic controllability • Symbolic expression • Expression grows exponentially • COP • Probability based • Correlation is not taken into account • Very fast but low accuracy 8

  9. Previous Work (2/2) • PREDICT • First exact probabilistic measures • Use supergate concept • High accuracy but exponential computation • TAIR • Use ATPG to revise the result of COP • Much accurate than COP • Still has 20%–30% inaccuracy in general circuits • Inaccuracy is augmented by the correlation 9

  10. Outline • Introduction • Previous Work • Background • Monte Carlo Approach for testability analysis • Experiment Results • Conclusion • Future Work 10

  11. Monte Carlo Approach • Random number generator • Sampling rule • Scoring • Accumulate into overall scores for the quantities • Error estimation • Estimation of the statistical error as a function of the number of trials 11

  12. Example for MC approach • Estimate π, “hit and miss” concept • Generate random number between 0 and 1 • Sampling rule • Sample interval 1000 points • Scoring • Accumulate sample data • Error estimation • Confidence interval • Define stop condition y 1 x 1 0 12

  13. Outline • Introduction • Previous Work • Background • Monte Carlo Approach for testability analysis • Experiment Results • Conclusion • Future Work 13

  14. Problem Description • Given a circuit only consists of AND, OR and INV gates • Calculate controllability, observability and s-a-0, s-a-1 fault detection probability for each node 14

  15. Random Pattern Architecture • RPG is a N-output circuit with parameterr • Generates N 2r-bit patterns 2rbits S R P G N M … … r 15

  16. Sampling Rule (1/5) • Controllability C0= 1/4 0110 C0= 2/4 a C1= 3/4 C0= 1/4 d C1= 2/4 0111 C1= 3/4 f C0= 2/4 0011 0011 0111 b C1= 2/4 0111 C0= 1/4 C1= 3/4 0011 e C0= 2/4 0101 c C1= 2/4 16

  17. Sampling Rule (2/5) • Observability O = 3/4 0110 a O = 1/4 d O = 4/4 0111 f 0011 0011 0111 b O = 2/4 O = 1/4 0111 O = 3/4 O = 1/4 0011 e 0101 c O = 1/4 17

  18. Sampling Rule (3/5) • Fault detection probability T1 = 0/4 T1 = 0/4 T0 = 3/4 0110 T1 = 1/4 a T0 = 1/4 d T0 = 3/4 0111 f 0011 0011 T1 = 0/4 0111 b T1 = 0/4 T1 = 0/4 T0 = 2/4 T0 = 3/4 0111 T0 = 1/4 T1 = 0/4 T0 = 1/4 0011 e T1 = 0/4 0101 c T0 = 1/4 18

  19. Sampling Rule (4/5) • Multiple path sensitization O = 3/4 0110 a O = 1/4 d O = 4/4 0111 f 1110 0011 0011 0111 b O = 2/4 1100 1100 1100 O = 3/4 0111 O = 3/4 O = 1/4 1101 O = 1/4 0011 0011 e 1100 0101 c O = 1/4 19

  20. Sampling Rule (5/5) • Multiple path sensitization O = 3/4 0110 a O = 1/4 d O = 4/4 0111 f 1110 0011 0011 0110 b O = 3/4 1100 1100 1010 O = 3/4 1110 O = 2/4 O = 1/4 1011 O = 2/4 0011 e 1100 1010 c O = 1/4 20

  21. Objective of Testability Analysis • Fast • Almost linear time complexity to circuit size • Provide high-accuracy approximate result • Neglect self-masking and multiple path sensitization 21

  22. Scoring (1/2) • Circuit: C6288 • Gates: 3540 • Frame : 1024 bits • Iteration: 100000 • Observe point : output • Normal Distribution 22

  23. Scoring (2/2) 23

  24. Error Estimation • Unknown mean unknown standard deviation • : sample mean, t*: value from t-distribution table at specified confidence level S : sample standard deviation n : number of iterations • We simulate the circuit until • ε: specified error 24

  25. Confidence Level • More confidence level more similar to Normal Distribution 25

  26. t-distribution Table • We choose 95% confidence level 5-degrees freedom 26

  27. Flow • Read circuit in BLIF format • Iteration • Random patterns for PIs • Evaluate • Back trace • Run several iterations to find check point • Highest standard deviation point • Check stopping criterion • Specified confidence level and error • Error estimation 27

  28. Start Specify r, c, ε,n i++ Generate 2r patterns Sample data no i > n ? yes Determine check point yes error <ε? no Average all sample data Generate 2r patterns Sample data Finish

  29. Outline • Introduction • Previous Work • Background • Monte Carlo Approach for testability analysis • Experiment Results • Conclusion • Future Work 29

  30. Experiment Results (1/5) • Frame: 8192 (213), Initial iterations: 10, C: 99.9%, ε: 0.005 30

  31. Experiment Results (2/5) • Frame: 8192 (213), Initial iterations: 10, C: 99.9%, ε: 0.005 31

  32. Experiment Results (3/5) • Frame: 8192 (213), Initial iterations: 10, C: 99.9%, ε: 0.005 32

  33. Experiment Results (4/5) • Frame: 8192 (213), Initial iterations: 10, C: 99.9%, ε: 0.005 33

  34. Experiment Results (5/5) 34

  35. Outline • Introduction • Previous Work • Background • Monte Carlo Approach for testability analysis • Experiment Results • Conclusion • Future Work 35

  36. Conclusion • Monte Carlo Approach is used for testability analysis • Parallel Pattern Simulation and Critical Path Tracing techniques is introduced as sampling rule • Our method is fast, high-accuracy and flexible 36

  37. Outline • Introduction • Previous Work • Background • Monte Carlo Approach for testability analysis • Experiment Results • Conclusion • Future Work 37

  38. Future Work • Finish ITC paper 38

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