1. Outlier Detection in Capacitive Open Test Data Using Principal Component Analysis
Xin He, Yashwant Malaiya, Anura P. Jayasumana Kenneth P. Parker and Stephen Hird

2. Outline Introduction Test Data Analysis & Results
---Capacitive Lead Frame Testing
---PCA Based Outlier Detection
Test Data
Analysis & Results
---Global Analysis
---Localized Analysis
Summary and Future Work

3. Capacitive Lead Frame Testing
good
open
Capacitance is formed between the tested pin and sense plate
Open defect existing on tested pin affects the normal signal level
Ref: Parker, Hird ITC 2007

4. Principal Component Analysis (PCA)
The 1st Principal Component
1st Principal Component is the axis containing largest variance from the data projection
2nd Principal Component is an axis orthogonal to the 1st one, containing as much of the remaining projected variance
The 2nd Principal Component
Measurement2
Measurement1
Is good at analyzing multi-dimensional interrelated data.

5. PCA for PCB Outlier Detection
Let M be (mxn) matrix of Capacitive Lead Frame Testing measurements
- m is the number of boards
- n is number of tested pins per board M Mc
Centering:

6. PCA for PCB Testing Mc = USVT where
Using Singular Value Decomposition,
Mc = USVT
where
Umxn gives scaled version of PC scores
Snxn diagonal matrix whose squared diagonal values are Eigen values arranged in ascending order.
VTnxn contains Eigen vectors (PCs). V is the transformation matrix.
Matrix Z = McV gives the z-score value of boards.
Z-score value of a board is a linear combination of all the corresponding measurement values for that board.

7. Test Statistic for Outlier Detection
zik : the value of the kth PC for the ith board
E : a subset of PCs --- most significant PCs are used here
Sort the boards with respect to the d1
Plot the cumulative distribution function (CDF) curve of d1
Outliers are clearly identifiable on the right side of the plot, and typically are separated from other devices by a clear margin

8. Test Data Data Name Board Runs Tested Pins Data_j27 15 147 Data_j24 83
145
Courtesy of Agilent Technologies

9. Global Analysis - (Data_j27)3 1
Total 15 board runs
First 5 PCs are used
Clear outliers: 2, 3 and 1

10. Global Analysis - (Data_j24)17
18,19,20,21,22
Total 83 board runs
First 5 PCs are used
Clear outliers: 17, 18, 19, 20, 21, 22 10

11. Pins in white color are VDD/grounded pins
Localized Analysis
Pin 1
Pin 120
Pin 121
Pin 240
Pins in white color are VDD/grounded pins

12. PCA Applied on Test Windows (Data_ j24)1 2 3 4 5 6 7 8 9 10 ……
Test Window 1
Test Window 10 12 12

13. Comparison of Global and Localized Methods
Pass
Fail
(ii)
(i)
(i) Sharp peak signal may exist, other measurements matches well
(ii) Slight variation exist in multiple pins measurement 13 13

14. Comparison of Global and Localized Methods (Example)6 4

15. PCA Flow Chart Measurement matrix M (m boards n tested pins)
Sort matrix according to pin location
Center matrix in each group
Derive Z scores for each group
Divide to w test windows
(w=1 for Global Analysis)
Evaluate d1 values in each group
Pass/Fail decision & outlier location
Compare maximum d1 value in different groups
Sort d1 Value

16. PCA vs. Standard Deviation (STDev)
Average + N*STDev
Average
Average - N*STDev 16

17. PCA vs. STDev N Abnormal PCB Detected Board runs No. 6 5.5 1 17 5 4.5
5.5 1 17 5
4.5 2
14, 17 4
3,11,14,17,83
3.5 11
3,4,5,6,8,11,14,15,17,59,83 3 18
3,4,5,6,8,9,11,14,15,16,17,18,19,20,21,51,59,83
2.5 35
3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,20,21,22 ,34,36,47,48,51,53,57,58,59,60,63,68,73,80,81,83 17

18. PCA vs. STDev PCA detected outliers: board run 17, 18, 19, 20, 21, 2214 3 83 11
PCA detected outliers: board run 17, 18, 19, 20, 21, 22 18

19. Summary PCA can effectively identify outlier boards
Localized analysis can increase test resolution and assist in the location of outliers
The global and localized analysis can be combined to filter the outliers
It can also be applied to other kinds of PCB test data beside Capacitive Lead frame test data

20. Future Work
On-line testing techniques to enhance the detection efficiency
Investigate data variation caused by measurement errors, mechanical and electrical tolerances
Technique to compensate for the effects of mechanical variations, parameter variations, etc.