Outlier Detection in Capacitive Open Test Data Using Principal Component Analysis

1

Xin He, Yashwant Malaiya, Anura P. JayasumanaKenneth P. Parker and Stephen Hird

Outline Introduction ---Capacitive Lead Frame Testing

---PCA Based Outlier Detection Test Data Analysis & Results ---Global Analysis

---Localized Analysis Summary and Future Work

2

Capacitive Lead Frame Testing

3

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

Principal Component Analysis (PCA)

4

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

PCA for PCB Outlier Detection

5

mnm

n

xx

xx

...

......

......

...

1

111

...

...

......

...

11

1

11

11

m

xx

m

xx

m

kk

n

m

kk

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

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.

6

Test Statistic for Outlier Detection

7

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

Test Data

8

Data Name Board Runs Tested Pins

Data_j27 15 147

Data_j24 83 145

Courtesy of Agilent Technologies

Global Analysis - (Data_j27)

9

Total 15 board runs First 5 PCs are used Clear outliers: 2, 3 and 1

2

3

1

Global Analysis - (Data_j24)

17

18,19,20,21,22

10

Total 83 board runs First 5 PCs are used Clear outliers: 17, 18, 19, 20,

21, 22

Localized Analysis

Pins in white color are VDD/grounded pins

Pin 120

Pin 240Pin 121

Pin 1

11

0

10

20

30

40

50

60

70

80

1 2 3 4 5 6 7 8 9 10

Window Number

Ma

xim

um

d1

Va

lue1 2 3 4

5 6

7 8

9 10

……Test Window 1 Test Window 10

12

PCA Applied on Test Windows (Data_ j24)

13

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

Comparison of Global and Localized Methods (Example)

14

4

6

PCA Flow Chart

15

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

Average + N*STDev

Average - N*STDev

Average

PCA vs. Standard Deviation (STDev)

16

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 3,4,5,6,8,11,14,15,17,59,83

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

PCA vs. STDev

17

3 1783

14

11

PCA detected outliers: board run 17, 18, 19, 20, 21, 22

18

PCA vs. STDev

19

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

20

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