Fault Diagnosis Using Fault Dictionaries and Probability

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Fault Diagnosis Using Fault Dictionaries and
Probability

• Adam Ray
• April 28, 2005

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Problem Statement

• Identify which fault occurred in a failing
  circuit
• Need a way to quantify inherent uncertainties
• Equivalent faults
• Truncated test sets
• Assumptions
• Single stuck-at faults
• Stuck-at fault is lowest replaceable unit (LRU)

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The Likelihood Function
Likelihood of fault i, time t Faults 0,,m
failed at time t-1 N(t)total of remaining
faults
  Test1 Test2 Test3 Test4 Test5 Test6
Fault1 0 1 0 0 0 0
Fault2 1 0 0 0 0 0
Fault3 1 0 0 0 0 0
Fault4 0 1 0 1 0 0
Fault5 0 0 0 1 0 0
Fault6 0 0 1 0 0 0
Fault7 0 0 0 0 0 1
Likelihood 0.14 0.2 0.33 0.5 1 1
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Diagnostic Algorithm
START LOOP END Assign beginning likelihoods to each fault Apply next test vector to faulty circuit If outputs are faulty (i.e. Test yields 1) Assign zero likelihood to faults that show 0 for current test vector Else Assign zero likelihood to faults that show 1 for current test vector Redistribute likelihoods using Likelihood Function Repeat LOOP Output final fault likelihoods
  Begin Test 1 Test2 Finish
Fault1 (0 1 0) 0.22 0.27 0.56 0.56
Fault2 (1 0 0) 0.11 0 0 0
Fault3 (1 0 0) 0.11 0 0 0
Fault4 (0 1 0) 0.11 0.16 0.45 0.45
Fault5 (0 0 0) 0.11 0.16 0 0
Fault6 (0 0 1) 0.22 0.27 0 0
Fault7 (0 0 0) 0.11 0.16 0 0
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Results on 4-Bit ALU
After Tests 1 2
After Tests 5 6
After All Tests
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More Results
Fault 22-1-1 found with several wrong faults
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Add beginning likelihoods
Faults (EQUIV) Beginning Likelihoods Ending Likelihoods
1 0 1 0.006 0.073
20 1 1 0.012 0.136
22 1 1 0.012 0.136
24 1 1 0.012 0.136
26 1 1 0.006 0.073
28 1 1 0.006 0.073
30 1 1 0.006 0.073
32 1 1 0.003 0.06
34 1 1 0.003 0.06
56 5 1 0.003 0.06
59 5 1 0.003 0.06
64 4 1 0.003 0.06
ALL OTHER FAULTS 0.003, 0.006, 0.012 0
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Conclusions

• Algorithm correctly identifies the fault
• Equivalent faults are incorrectly identified
• Likelihood makes results more conclusive
• Algorithm can be halted at any point
• New Algorithm for multiple faults