Abstract
Analog circuit test point selection aims to find the least number of test points that can isolate all the fault modes (including the fault-free case). The fault dictionary, which uses the integer-valued codes to represent the diagnosability of a specific test point, is very popular and saves computation efforts. However, the classical fault dictionary has a limited ability to handle the component tolerances and continuous-valued monitoring variables. To solve the problem, the approach of clustering-based discretization (CBD) is used to abstract the information of data samples distribution. We also develop a new fault dictionary construction technique called extended fault dictionary (EFD). An element of EFD is a set containing either a single integer code or multiple integer codes. The fault isolation rules are redefined, and a novel entropy measure is created in line with CBD of the continuous values. The practical test point selection procedures are presented, which avoids the likelihood to include a redundant test point. Finally, two application studies of circuit test point election are presented, showing that the proposed method provides an effective implementation option for the engineering practice of circuit diagnosis.
Abbreviations
- EFD:
-
Extended fault dictionary
- CUT:
-
Circuit under test
- CBD:
-
Clustering-based discretization
- DBC:
-
Density-based clustering
- FMF:
-
Fuzzy membership function
- ASFE:
-
Fuzzy entropy by ambiguity sets
- F :
-
Set of candidate fault modes (including the fault-free case)
- L :
-
Total number of fault modes
- f l :
-
The kth fault mode with l = 1 , 2 , ⋯ , L
- T :
-
Set of candidate test points
- M :
-
Total number of test points
- t i :
-
The ith test point (dimension) with i = 1 , 2 , ⋯ , M
- X i :
-
One-dimensional data set corresponding to t i
- N :
-
Total number of data pieces
- x iu :
-
The uth data sample in X i with u = 1 , 2 , ⋯ , N
- τ u :
-
The uth label in the label vector corresponding to the uth data sample with u = 1 , 2 , ⋯ , N
- Λ i :
-
Set of clusters for the ith dimension with i = 1 , 2 , ⋯ , M
- J i :
-
Total number of clusters for the ith dimension
- Q ij :
-
The jth cluster in Λ i with j = 1 , 2 , ⋯ , J i
- \( {\tilde{Q}}_{ij} \) :
-
FMF corresponding to Q ij
- Ξ ij :
-
Set of data samples belonging to Q ij
- m ij :
-
Center of the data samples belonging to Q ij
- D ij :
-
Width of the data samples belonging to Q ij
- μ Q (x):
-
Membership degree under fuzzy set Q
- \( SD\left(\left.{Q}_{ij}\right|{f}_l\right) \) :
-
Conditional sub-degree with \( {Q}_{ij} \) based on f l
- \( {\varTheta}_{f_l}\left({X}_i\right) \) :
-
Set of elements in X i whose fault mode label is f l
- E = [e li ] L × M :
-
EFD for the circuit under test
- ε :
-
Confident threshold
- T opt :
-
Present set of optimal test points
- T comb :
-
Present set of a specific test points combination
- P :
-
Total number of ambiguity sets in accordance with T comb
- A p :
-
The pth ambiguity set in accordance with T comb where p = 1 , 2 , ⋯ , P
- \( SD\left({Q}_{ij}|{A}_p\right) \) :
-
Conditional sub-degree with \( {Q}_{ij} \) based on A p
- \( {\varOmega}_{A_p}\left({X}_i\right) \) :
-
Set of elements in X i whose fault mode (i.e. label) is contained in A p
- \( ASF{E}_i\left({Q}_{ij}|{A}_p\right) \) :
-
conditional ASFE associated with A p for test point t i
- ASFE i :
-
Total ASFE for test point t i
- t opt :
-
Optimal test point among the remaining candidate test points
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Acknowledgments
The authors express sincere appreciation to the editor and reviewers for their efforts to improve this paper. This work is sponsored by fund project Z132014B002.
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Cui, Y., Shi, J. & Wang, Z. Analog Circuit Test Point Selection Incorporating Discretization-Based Fuzzification and Extended Fault Dictionary to Handle Component Tolerances. J Electron Test 32, 661–679 (2016). https://doi.org/10.1007/s10836-016-5620-2
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DOI: https://doi.org/10.1007/s10836-016-5620-2