Outlier Detection in Capacitive Open Test Data Using Principal Component Analysis
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Outlier Detection in Capacitive Open Test Data Using Principal Component Analysis
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Xin He, Yashwant Malaiya, Anura P. JayasumanaKenneth P. Parker and Stephen Hird
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Outline Introduction ---Capacitive Lead Frame Testing
---PCA Based Outlier Detection Test Data Analysis & Results ---Global Analysis
---Localized Analysis Summary and Future Work
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Capacitive Lead Frame Testing
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SenseplateBuffer
Signal(to Tester)
PC Board
Ball Connections
In-Circuit access
Tester AC Source stimulates one pin, all others are grounded
Test access pad
Vacant Connector
(Internal conductors)
Capacitance is formed between the tested pin and sense plate
Open defect existing on tested pin affects the normal signal level
good open
Ref: Parker, Hird ITC 2007
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Principal Component Analysis (PCA)
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The 2nd Principal Component
The 1st Principal Component
Is good at analyzing multi-dimensional interrelated data.
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
0Measurement1
Measurem
ent2
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PCA for PCB Outlier Detection
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mnm
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m
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m
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kk
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M Mc
Centering:
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
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PCA for PCB Testing
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. VT
nxn 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.
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Test Statistic for Outlier Detection
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Ek
iki zd 21
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
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Test Data
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Data Name Board Runs Tested Pins
Data_j27 15 147
Data_j24 83 145
Courtesy of Agilent Technologies
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Global Analysis - (Data_j27)
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Total 15 board runs First 5 PCs are used Clear outliers: 2, 3 and 1
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Global Analysis - (Data_j24)
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18,19,20,21,22
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Total 83 board runs First 5 PCs are used Clear outliers: 17, 18, 19, 20,
21, 22
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Localized Analysis
Pins in white color are VDD/grounded pins
Pin 120
Pin 240Pin 121
Pin 1
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1 2 3 4 5 6 7 8 9 10
Window Number
Max
imum
d1
Valu
e1 2 3 4
5 6
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9 10
……Test Window 1 Test Window 10
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PCA Applied on Test Windows (Data_ j24)
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Global
LocalizedPass Fail
Pass Pass (ii)
Fail (i) Fail
(i) Sharp peak signal may exist, other measurements matches well(ii) Slight variation exist in multiple pins measurement
Comparison of Global and Localized Methods
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Comparison of Global and Localized Methods (Example)
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PCA Flow Chart
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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)
Pass/Fail decision & outlier location
Compare maximum d1 value in different groups
Evaluate d1 values in each group
Sort d1 Value
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Average + N*STDev
Average - N*STDev
Average
PCA vs. Standard Deviation (STDev)
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NAbnormal
PCB Detected
Board runs No.
6 05.5 1 175 1 17
4.5 2 14, 174 5 3,11,14,17,83
3.5 11 3,4,5,6,8,11,14,15,17,59,833 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
PCA vs. STDev
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3 1783
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PCA detected outliers: board run 17, 18, 19, 20, 21, 22
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PCA vs. STDev
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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
Summary
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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.
Future Work