Principal Component Analysis-Based Compensation for Measurement Errors Due to Mechanical Misalignments in PCB Testing

Transcription

1 Principal Component Analysis-Base Compensation for Measurement Errors Due to Mechanical Misalignments in PCB Testing Xin He 1, Yashwant Malaiya 2, Anura P. Jayasumana 1 Kenneth P. Parker 3 an Stephen Hir 3 1 Department of Electrical an Computer Engineering, 2 Department of Computer Science, Colorao State University, Fort Collins, CO Agilent Technologies, Lovelan, CO 8537 {philiphe@engr.colostate.eu, malaiya@cs.colostate.eu, Anura.Jayasumana@Colostate.eu, kenneth_parker@agilent.com, steven_hir@agilent.com} Abstract Capacitive Leaframe Testing is capable of etecting open soler efects in Printe Circuit Boars (PCB). Principal Component Analysis (PCA)-base approach has been shown to be effective in ientifying outlier evices using Capacitive Leaframe Testing measurements. In practice, when a sense plate orientation is shifte or tilte, the resulting measurement variation makes etecting outliers harer. Approaches are introuce to compensate for the abnormal measurements ue to sense-plate variations. A PCA base technique is evelope to estimate the relative amount of tilt an shift in sense plates. Such estimates can be use to compensate for mechanical misalignments. It can also isolate the misalignment relate information from the efect relate information in the ata. The effectiveness of this technique in the presence of the two common forms of mechanical variations is illustrate using experimental measurements from a laboratory setting. The approach is not sensitive to the orer of pins, an as such, shows promise for etection of complex but systematic errors introuce by sense plate misalignments. Keywors: Boar testing, Capacitive open testing 1 Introuction Testing for efects in printe circuit boars has to aress challenges such as parameter variations an increase circuit ensities. Capacitive Leaframe Testing (also calle TestJet in inustry) is very effective in etecting open soler efects in PCB testing [1]-[3]. Outlier etection technique base on Principal Component Analysis (PCA) was emonstrate in a recent stuy to be capable of further enhancing fault etection [4]. The PCA-base approach treats multi-variable measurements from connectors in a holistic manner to overcome the measurement an component parameter variations inherent in test ata. Sensitivity of the approach can be enhance by selecting winows of physically ajacent pins. When goo boars are teste uner ifferent fixtures which are subject to mechanical alignment variations of the sense plate, the measure values may vary epening on the egree of misalignment. This paper consiers approaches to compensate for the measurement ifferences of ifferent fixtures to enhance accuracy of etection of outliers. We analyze the impact ue to variation of the tilt an the vertical shift of sense plate using measurements conucte in a laboratory setting. A PCA base technique is presente for ata sets containing ifferent moes of misalignment illustrating its ability to ientify the egree of misalignment. A technique for compensating for tilt an shift base misalignments of the sense plate in testing PCBs is presente an evaluate. The propose technique shows significant promise of being able to hanle complex but systematic error patterns such as those introuce by fixture-to-fixture variations. Section 2 escribes Capacitive Leaframe testing an illustrates the problem of mechanical variations of fixtures. Section 3 outlines the PCA base outlier etection algorithm. Section 4 investigates the impact of sensor plate tilt an shift variations on measurement ata. Section 5 contains the major contributions of this paper: PC base approaches for extracting tilt an shift information from measurements, an compensating for such variations in testing PCBs. The approaches are evaluate using atasets that inclue the impact of two potential types of mechanical misalignment uring the Capacitive Leaframe Testing. The major observations an future research are ientifie in the final section. 2 Capacitive LeaFrame Testing Ball Connections (internal conuctors) Test access pa Buffer Vacant Connector In-Circuit access Signal (to Tester) Tester AC Source stimulates one pin, all others are groune Sense plate PC Boar Figure 1 The Capacitive Leaframe test mechanical structure Capacitive Leaframe testing measures the capacitance between the test pins an a sense plate, as shown in Figure 1, to ientify open soler efects. When an AC signal Paper 1.1 INTERNATIONAL TEST CONFERENCE /1/$2. (c) 21 IEEE

2 stimulates the teste pin, the sense plate suspene over the connector will transfer a capacitively couple signal into a buffer an then to the tester, where the signal is converte to a measure of capacitance. The measure capacitance may be fairly small, often uner 1 femtofaras (ff). If there is an open soler efect existing between the boar an the connector pin, the capacitance etecte by the tester often ecreases significantly, to perhaps 1 ff or even less. Variations in these measurements must be accounte for to avoi false pass/fail inications. Mechanical variations in the connector or the sense plate cause changes in the measurement values although the connector itself an its connections are not efective. Such situations may occur when there is variation in connector height with respect to pin height within the connector, or coplanarity of the connector ball connections is lopsie causing the sense plate to be tilte or vertically shifte. Buffer Vacant Connector Sense plate Spacers place between plate an connector at one en. Again, the spacers have a ifferent ielectric constant from air. Figure 2 Simulation of mechanical 'tilt' on the sense plate Figure 2 shows one normal connector uner test with mechanical variation on a sense plate, where the sense plate has a variation in its planarity relative to the connector that is, it is tilte with the left sie slightly higher than the right. (This can be cause by the connector itself having a planarity problem relative to the boar itself, ue to irregular solering.) We refer to this as a right-tilte sense plate. This in turn opens a gap between the left sie of the sense plate an the connector. In Figure 2 the angle of the tilte sense plate angle is exaggerate for illustration. The practical angles in our experiments are smaller than.2 egree, simulating very small mechanical variations that are har to control. In our tilt experiments we simulate small increments of tilt by inserting spacers on one sie an later, on the other sie. Figure 3 shows a connector teste with a vertically shifte sense plate. The sense plate is raise a bit higher with respect to the internal connector pins being sense. A simple variation in the height of the plastic connector housing can cause this. Inee, typical specifications on connector housing height are given in max form with no tolerance. The actual tolerance is probably in the +/-.4 inch (.1 millimeter) range, but is unspecifie. Another source of variation comes from using connectors from more than one connector venor. Again, the height specification may vary significantly between venors. In our shift experiments, we simulate shift variations by inserting equal-height spacers on both sies of the connector. Buffer Vacant Connector Sense plate Spacers place between plate an connector. Most connector pin tips see an air gap to the sense plate, but at the ens, the gap has a ifferent ielectric constant. Figure 3 Simulation of mechanical shift on the sense plate In a laboratory setting, we injecte specific mechanical variations of both shift an tilt types, an then collecte ata for a variety of connectors on a small set of boars. Figure 2 an Figure 3 show the experimental setups for the experiments. The amounts of shift or tilt injecte were relatively small offsets from a zero reference. They were 8, 1 an 24 thousanths of an inch (mils) or,.2,.41 an.1 millimeters. The respective setups (see Table 1) will be name as Tilt_1, Tilt_2, Tilt_3 an Shift_1, Shift_2, an Shift_3 in the following text. The shift an tilt experiments were inepenent; we i not combine their effects. Tilt_ an Shift_ both refer to the reference case, which oes not contain any variation. Since a single boar may be teste more than once, a ata recor is terme as boarrun for each test of the evices. Setup Left or right En Tilt Height (mils) Setup Vertical Shift Height (mils) Tilt_ Shift_ Tilt_1 8 Shift _1 8 Tilt_2 1 Shift_2 1 Tilt_3 24 Shift_3 24 Table 1. Experimental ata sets 3 PCA Base Outlier Detection In this section, we provie a general escription of the PCA base outlier etection metho. Let M mxn be the matrix of capacitance measurements, where m is the number of boars an n is the number of pins teste on each boar [4]. Let M c be the centere matrix where mean value of its column is subtracte from each element. Singular Value Decomposition (SVD) ecomposes the matrix into the form Mc =USV. The Principle Component score or Z-score matrix Z mxn is given by, Z=MV [5]-[11]. Each principle component (PC) is statistically inepenent, an they are arrange such that an earlier PC is more significant than a later one. Paper 1.1 INTERNATIONAL TEST CONFERENCE 2

3 With Z, each boar is now characterize by the Z-scores, given by the corresponing row of Z. The metho propose in [4] selects a subset of the Z-scores for each boar, an compresses it into one value 1i [11], which characterizes the boar i for outlier etection, where E is = 2 1i z ik k E (1) a subset of PCs, which are more significant than the remaining subset of the PCs. The carinality of the subset for our experiment was set to be 5. The evices with higher 1i values are the potential outliers. For illustration, let us consier the outlier etection scheme with a set of measurements, referre to as Data_j31, corresponing to a J31 stanar connector on a set of 22 boarruns. Visual inspection of Figure 4 which shows the row measurement values in Data_j31, ientifies the boarruns 1, 3, 4 an 22 as clear outliers Connector j31 1,3,4,22 Figure 4 Raw measurement plot for Data_j31 Figure 5 CDF plot of 1 for Data_j31 Next we use the first 5 Principal Components (PCs) to calculate the 1 value. Figure 5 shows the cumulative istributive function (CDF) plot for 1 for all of the boarruns in Data_j31. Boarruns, 4, 22, 1 an 3 all clearly stan out at the high en of CDF curve where they inicate much larger 1 values than the other boarruns. Remaining 17 boarruns are clustere together on the left sie of the plot. The five boarruns show a clear break from others which means that they are far ifferent from others base on the holistic PCA analysis. This technique can effectively filter the abnormal boarruns. 4 Fixture Misalignments In a real test environment, DUTs teste uner abnormal sense plate positions, such as tilte or vertically shifte sense plates, may result in measurements significantly ifferent from those teste with normal sense plates. Consequently, even a non-efective boar teste with a ifferent fixture containing mechanical variations will have measurement values ifferent from those from the reference fixture. We may raw incorrect conclusions when comparing the test results from the two fixtures. Here is an example taken from the experimental ata. For pin 2 of connector J1, we see Shift_ measurement average of 8.2 ff. The Shift_1 average was 75.3, the Shift_2 value was 8.3 an the Shift_3 average was 2.7 ff. This gives a sprea of almost 18 ff across the test cases. However, the stanar eviations of these measurements were, in all specific setups, less than.5 ff. Thus, if we set test limits base on, for example, 12 stanar eviations, that woul be +/- ff. But, since we typically have only a small sample of known-goo boars available to erive the basis of the test value an test limits, we can buil a test that will later fail falsely because a mechanical variation has now appeare. In setting test limits base only on a given pin s measurements, we can encounter false fails if the limits are set too tightly, or, we coul get false passes if the limits are set too loosely. Here we are intereste in juging pass/fails base on ata across a collection of pins in any given test an applying corrections base on perceive variations that are mechanically inuce rather than the effects of efects. 1 In this section, we present analytical expressions representing such variations an iscuss regression-base methos to compensate for the effects cause by DUT an fixture mechanical misalignments. Later in Section 5 we present a PCA base scheme which can avoi having to use regression separately to ientify the compensation equation coefficients for an iniviual evice, that can be use to estimate the tilt or shift, an thereby generate coefficients for the compensation equations. The goal of this section therefore is to ientify an compensate for the measurement variation cause by abnormal sense plate positions so that it alone oes not cause a DUT to be flagge as an outlier. 1 The apparent sensitivity of the measurement to mechanical variation shoul also give pause to venors who buil test fixtures with sense plates in them. It may not have been appreciate in the past that some relatively small mechanical variations can lea to larger measurement variability. Paper 1.1 INTERNATIONAL TEST CONFERENCE 3

4 4.1 Effects on Measurements ue to a Tilte Sense Plate The capacitance between sense plate an the connector pin is given by: A C = ε (1) where is the istance between connector an sense plate, an A is some effective area between pin an the sensor plate. Note that this relationship hols most accurately for a square area an A >> 2, conitions that are stretche a bit in this case. However this relationship is a goo first approximation for unerstaning what is happening ue to sense plate misalignments. When a sense plate is tilte, as shown in Figure, the value, which is the ifference from original istance, woul change from minimum to maximum value linearly epening on the pin position. Here we consier only the variation along the length, although the analysis may be extene when such variation exists both along the length an with. The ratio CR of the capacitance values with an without tilt is approximately linear along the length as given below: ε * A ε * A + CR = ( ) /( ) = = With istance along the normal sense plate, changes linearly with pin physical position on connector from left to right (see Figure ). Equation (2) results in Equation (3) below where x is the normalize position along the connector: Figure Fixture with (a) normal sense plate (b) left tilte sense plate CR ( x) = A + Bx (3) For measurements with left tilte sense plate, where the right sie of plate, near pins 12 an 24 corresponing to the two rows as shown in Figures 7 an 8) is lifte, the ratio, relative to the normally positione measurement, theoretically shoul be a straight line with intercept at A ( ~ 1) at y-axis. For the right tilte measurement, the ratios woul ecrease from left to right. The atasets use in this section inclues measurement for boars with connector name J3 an J1. Four boars of each type were involve, they were terme boars B1, B2, B3 an B5. (There was a boar B4 not inclue here as it is seee with efects.) Besies the normal Tilt_ test (ientifie as reference), each boar was also teste uner sense plate for 3 ifferent right tilt angles, three ifferent left tilt angles, an 3 ifferent vertical shift heights. Thus there is a total of 1 ifferent measurements for one (2) connector on a single boar. We iscuss below in etail the ata an the analysis for the left tilt setups, an also some of the shift setups. We analyze below in etail the left tilt cases, an present some shift cases Figure 7 Raw measurements for B2 with one normal an three left tilte sense plates Capacitance Ratio Capacitance Raito Tilt_ Tilt_1 J3 boar2 left Tilt_1,2,3 Tilt_1 ratio Tilt_2 ratio Tilt_3 ratio (a) J3 boar2 right Tilt1,2,3 Tilt_1 ratio Tilt_2 ratio Tilt_3 ratio (b) Tilt_3 Tilt_2 Figure 8 Capacitance ratio (CR) for J3 connector in B2 with (a) left tilte sense plates, an (b) right tilte sense plates Figure 7 shows one example of J3 measurements, corresponing to boar B2. The reference measurement is Tilt_, with Tilt_1, Tilt_2 an Tilt_3 with the tilte sense plates as specifie in Table 1. Capacitance Ratio CR Paper 1.1 INTERNATIONAL TEST CONFERENCE 4

5 obtaine by iviing the normal measurement by its respective tilte one, is shown in Figure 8, for both left an right tilt cases. All the plots in Figure 8 follow the linear Equation (3) fairly closely, although we observe a slight nonlinearity. The abnormal reaings ientifie by the re ovals are cause by the paper spacers use in the experiment, which has a ifferent ielectric constant from that of air. Therefore to make it more representative, our analysis exclues such pins, which are inicate by a re oval in subsequent figures as well. To fin a metho to compensate for tilt variation, measurements with highest ae tilt (an hence the highest CR), given by Tilt_3 in Figure 8(a), were selecte for analysis. The measurement ratios for the two rows of the connector are slightly ifferent, which may be cause by the specific physical layout in the two rows. Thus, we nee to plot the measurement ratios for two rows, row with pin 1 to pin 12 an row with pin 121 to pin 24, separately. above. The fit appears reasonable, not quite as well as expecte. In reality, the complex istribution of the electromagnetic fiel makes etermination of the actual capacitance value a bit more complicate than the simple plate capacitance moel assume. Note that the fit can be significantly improve if a thir orer polynomial is use for regression as shown in Figure 1. Data for the other boars also inicate similar results, i.e., the first orer moel is reasonably accurate, but thir orer moel may be use when higher accuracy is neee. Next we illustrate proceure for regression base compensation for the tilt an its effectiveness. We start with a ata set consisting of J3 connector on boars B2, B3 an B5, as well as Tilt_3 version of B2, as shown in Figure 11(a). The measurement at each pin of the abnormal measurement is multiplie by the inverse of the ratio obtaine using regression analysis Equations (4) an (5). The results for the three boars after compensation are shown in Figure 11(b). Capacitance Raito J3 boar2 left Tilt3 row by row y =.53x y =.45x row with pin 1 to 12 row with pin 121 to J3 3 normal an 1 Tilt_3 measurments B2 B3 B5 B2 Tilt_3 Pin Position Figure 9 Measurement ratio curves fitte with 1st orer tren lines for connector j3 in ataset B2. Capacitance Raito J3 boar2 left Tilt3 row by row y = 3E-7x 3-7E-5x x y = 3E-7x 3-5E-5x 2 +.7x row with pin 1 to 12 row with pin 121 to (a) J3 3 normal an 1 compensate measurments B2 B3 B5 Compensate Pin Position Figure 1 Capacitance ratio (CR) curves fitte with 3 r orer tren lines for connector J3 of boar B2, Tilt_3 Figure 9 an 1 give the CR plots for connector J3 in boar B2 where the x-axis now gives the pin position. Note that the horizontal axis in Figures 9 an 1 correspon to pin position. We have also eliminate pins affecte by the spacers. In Figure 9, the ata points are fitte using regression to the expression in Equation (3) (b) Figure 11 Regression base compensation illustrate using Data J3 B3 (a) Measure values for boars B2, B3, B5 an Tilt_3 B2; an (b) Plot with Tilt_3 B2 value correcte via regression curve. Pins affecte by the spacer are remove Figure 12 illustrates the results of PCA base outlier etection with an without regression-base compensation for tilt. Paper 1.1 INTERNATIONAL TEST CONFERENCE 5

6 After Compensation Before Compensation Figure 12 CDF plot for B2 (1), B3(2), B5(3) an Tilt_3 B2 (4) before an after compensation Comparing the two CDF plots in Figure 12 we can clearly see the compensation effect to the measurement. Labels 1, 2, 3 an 4 in Figure 12 correspon to B2, B3, B5 an Tilt_3 of B2 respectively. The 1 value of B2 Tilt_3 is ecrease from 17 to less than 3 implying that it is no longer an outlier. This inicates that the approach works. But we nee to be able to estimate the tilt in orer to be able to compensate for it without having to run regression analysis for each evice. Our measurements also inicate that the regression curves obtaine for B2 are accurate for other boars of the same type (B1-B5) for the corresponing amount of tilt. Thus the regression analysis nees to be carrie out only for one boar with a particular tilt to be able to obtain the CR. Thus if the tilt for a boar is known, we can apply the appropriate correction. For regression-base or theoretical moel base correction to be more practical, methos nee to be evelope to estimate tilts automatically, as well as to obtain regression coefficients for such ifferent tilts. A regression analysis base approach has another complication in that it is very epenent on the orering of the pins in the ata set. We want to remove the epenence on orering so that we o not nee to know the physical layout of pins in orer to perform compensation. Estimation of tilt from measurements is aresse further in Section Effects on Measurements ue to a Shifte Sense Plate the connector. In this case, CR can be shown to be a constant value inepenent of the pin position. Figure 14 shows the measurements for boar B5 for connector J3 with 4 ifferent sense plate heights,, 8, 1 an 24 mils respectively as escribe in Table Figure 14 Plot of measurements with normal an vertical shifte sense plate for boar B5 for connector J3 Figure 15 illustrates the CR plots of connector J3 in ataset for B5. Although the ifference of measurement ratios between the two rows is clear, the ratios still have an important role to play in the compensation. Furthermore, the figure illustrates that the CR eviates from a constant value inepenent of pin position to some egree. Capacitance Ratio Shift_ Shift_1 Shift_3 row with pin 1 to pin 12 row with pin 121 to pin 24 y = 2E-7x 3-3E-5x 2 -.9x y = 7E-7x 3 -.1x x Pin Position Shift_2 Figure 15 CR curves fitte with 3r orer tren lines for connector J3 of B5 Figure 13 Connector with (a) normal positione sense plate (b) vertical shifte sense plate Normal an vertically shifte sense plate iagrams are shown in Figure 13(a) an (b). The vertical mechanical variation of sense plate as shown in Figure 3 is cause by variability in the height of the plate above the pin tips in After Compensation Before Compensation Figure 1 CDF plots for B2(1), B3(2), B5(3), an Shift_3 of B2(4) before an after compensation Paper 1.1 INTERNATIONAL TEST CONFERENCE

7 Figure 1 gives the CDF plot before an after the compensation using regression base values. As is shown, the 1 value of original outlier B2 shift_3 (the number 4 in Figure 17) is ecrease significantly, which means it is not flagge as an outlier any longer. Here also, if there is a way of ientifying the shift by an inepenent means, then it is possible to generate parameters for the compensation curve an then apply it to compensate for the shifte plate. We aress this in the next section. 5 PCA Base Tilt an Shift Evaluation The objective of this section is to investigate how to ientify the amount of tilt in a sense plate so that parameters for the compensation curves can be erive. 5.1 Evaluation of Tilt an Shift of Sense Plates For this iscussion, consier four ifferent sense plates, each with a ifferent tilt. By measuring the same boar using these ifferent sense plates, we show that we can ientify the egree of tilt of ifferent plates. Figure 17 shows plots corresponing to B1 incluing reference case (Tilt_) an for three values of tilt. The corresponing PC plots in Figure 18 shows the values of ifferent PCs for the four cases. Only 4 of them are visible as the remaining PCs have values close to zero in this case. Note that the value of 1 st PC is almost linearly proportional to the tilt corresponing to the boar. The same phenomenon is observe on measurements with vertical shifte sense plate. Figure 19 is the plot of ata B2 with vertical shifte sense plates. Base on the PC plot of Figure 2, it is clear that the first PC is able to ientify the amount of shift in the sense plate as well. Note that the PC coefficients are ifferent in the case of tilt from those for shift, as the PC coefficients are ata epenent. Above results inicate that PC base analysis can extract the information associate with tilts an shifts. For example, if a boar is sent through multiple fixtures each of which is ifferent from others only in its tilt, the tilt can be ientifie, an possibly compensate for. In practice fixtures may iffer in both tilt an shift an may exhibit even more complex variations. However, the two basic cases are of interest in eveloping a theoretical basis for compensation. A very important factor to note is that PC calculation ignores the orer of the pins, yet is able to ientify the amount of shift or tilt. Human observations, on the other han, epen on the orer of the pins to recognize whether shift or tilt is present Tilt_ Tilt_1 Tilt_2 Tilt_ Shift_ Shift_1 Shift_3 Shift_2 Figure 17 Plot of raw measurement of ata B1 with three left tilte plate measurements Figure 19 Raw measurement of ata B2 with three vertical shifte plate measurements Principal Component Value n PC 3r PC 1st PC Boarrun Number Principal Component Value r PC 2n PC 1st PC Boarrun Number Figure 18 Plot to principal component values to ata B1 for tilte plates Figure 2 Plot of principal component values to ata B2 Paper 1.1 INTERNATIONAL TEST CONFERENCE 7

8 For example, if pin numbers are shuffle ranomly for ata shown in Figure 19, a human observer will be unable to etect the pattern corresponing to a shift or tilt. This shows the potential of PC base analysis to etect complex, yet systematic variations introuce alignment variations from fixture to fixture. 5.2 Overcoming Effects ue to Misalignment As first PC contains information about the tilt or shift of the sense plate, a number of options become available for tackling the problem of compensating for shift or tilt. First option is to use (constant) scale factors that convert the Y- axis of Figures 18 an 2 to corresponing tilt angle an shift respectively. Once such scale factors are erive, the CR value can be analytically evaluate, for example, using Equation (2) for the case involving tilts. Below, we look at a secon option, in which we remove shift an tilt relate information from measurement ata, an attempt to etect the faults base on remaining value. The relationship between the set of measurements M an the PCs (i.e., the Z scores) Z is given by Z = MV. The i th column of M correspons to the measure capacitance values of i th pin for the ifferent boars. Similarly, the i th column of Z correspon to the i th PC for the ifferent boar measurements. Thus if we replace the i th column of Z with zeros (say Z ), an obtain the corresponing M =Z V -1, M correspons to capacitance values with the i th PC remove. We call such values, ajuste capacitances. Figure 21 plots the ajuste capacitances in which all but the 1 st PC are set to. As expecte, it shows the ifferent trens corresponing to ifferent egrees of tilts. The plots show ivergences corresponing to tilt for each row as shown in Equation (2). The ifference is ue to the fact that the first PC also capture much of the common variation among the ifferent boars. Thus removing the first PC will not result in an exact correction to the measurement values to explicitly compensate for tilts, but it will also remove some of the variation that is common to all the boars in the measurement set. This also accounts for the negative values. In Figure 22, we show the ajuste capacitance values reconstructe by removing the first PC, but leaving the others intact, which compensates for systematic tilt variation among sense plate. To evaluate whether the ajuste capacitances, by removing component ue to the 1 st PC, can isolate the tilt relate information, we use two synthetic measurement traces in aition to ata use before. The new ata set, shown in Figure 23 contains two simulate efective boars, inicate by Def_1, Def_2, in which the Tilt_2 capacitance measurements of pins 124 an 15 have been change to 7fF corresponing to typical open faults. Ajuste Capacitance (ff) Ajuste Capacitance (ff) Figure 21 Ajuste capacitances by setting all but 1st PC equal to for ata B1 of Figure Figure 22 Ajuste capacitances by setting only 1st PCs equal to for ata B1 of Figure Tilt_ Tilt_3 Tilt_ Tilt_3 Tilt_1 Tilt_1 Def_1 Tilt_2 Tilt_2, Def_1,Def_2 Def_2 Figure 23 Data set incluing two synthetic traces, Def_1 an Def_2 simulating open faults on pins 121 an 15 Paper 1.1 INTERNATIONAL TEST CONFERENCE 8

9 Ajuste Capacitance (ff) Tilt_ Tilt_3 Tilt_1 Tilt_2, Def_2, Def_3 The above results make a convincing case that the PC base analysis can extract systematic changes to measurements that are introuce ue to shift an tilt base misalignments. However, given the fact that the PC base analysis is agnostic to the pin configuration, there is a high likelihoo that the approach will work for other misalignment patterns. -24 Shift_ Figure 24 Ajuste capacitance by setting all but 1 st PC to zero for ata in Figure 23 Shift_1 Shilft_2, Def_1, Def_2 Ajuste Capacitance (ff) Tilt_,Tilt_1,Tilt_2, Tilt_3, Def_1, Def_2 Def_1 Def_2 Shift_3 Def_1 Def_2 Figure 2 Data set incluing two synthetic traces, Def_1 an Def_2 simulating open faults on pins 75 an 15 Figure 25 Ajuste capacitances by setting only 1st PCs to for ata in Figure 24 Figure 24 shows the corresponing curves by retaining only the contribution ue to the first PC. Note that the Tilt_2, Def_1 an Def_2 curves are almost overlapping, which inicates that the PC1 successfully captures the tilt information even though the last two contains low capacitances corresponing to injecte faults. Ajuste Capacitance (ff) Shift_1 Shift_3 Shift_ Shift_2, Def_1, Def_2 Next we generate the ajuste capacitances by removing the tilt information by setting the first PC to zero, while retaining all the other PCs. Figure 25 shows the resulting traces, where the two efects stan out. This is a clear inication that the PC base metho can compensate for tilt relate information while retaining efect information. Next we repeat the proceure for shift base misalignments. In Figure 2, we introuce two traces in which efects are injecte in the Shift_2 ata at pins 75 (Def_1) an 15 (Def_2) respectively, by setting the corresponing capacitances to 7fF. Figure 27, which contains ajuste capacitances corresponing to 1 st PC again inicates that it is capable of extracting the shift. Note that the Shift_2 curve overlaps with Def_1 an Def_2, which correspon to Shift_2 injecte with faults. Figure 28 contains the ajuste capacitance traces by removing the first PC contribution to compensate for the shift. The injecte efects can be clearly seen in the ajuste capacitance curve. Figure 27 Ajuste capacitance by setting all but 1st PC to zero for ata in Figure 2. Ajuste Capacitance (ff) Tilt_,Tilt_1, Tilt_2, Tilt_3, Def_1, Def_2 Def_1 Def_2 Figure 28 New raw matrix base on setting only 1st PC to Paper 1.1 INTERNATIONAL TEST CONFERENCE 9

10 Summary The misalignment of the sense plate can iminish the accuracy of outlier ientification using PCA for TestJetbase boar testing. Approaches for compensating for the misalignment are examine in this stuy. Test ata was presente to inicate the impact of tilt an shift type misalignments. We simulate these in a laboratory setting not relying on prouction ata which is poorly controlle. A simple parallel plate capacitance moel was use to obtain the influence of tilts an shifts on measurements. Regression analysis was use to evaluate the moel. Given the amount of shift or tilt, or the corresponing parameters for regression curves, it is possible to compensate for misalignments. However, obtaining such information is not trivial. We have emonstrate a PCA base metho that coul be use to ientify the egree of tilt (or shift) present in a sense plate. It yiels values that are linearly proportional to the shift or the tilt. With proper calibration, this metho can be use to obtain the exact shift or tilt, which may then be use to correct the measurement errors cause by misalignments. Further research is neee to extract the absolute values of the tilt/shift from the PCA analysis an to use it in a moel for correction. In aition, we emonstrate a PC base technique to irectly remove misalignment relate component in the ata, while retaining efect relate information. The techniques evelope have been evaluate using a limite set of test ata, an only for sensor plate misalignments corresponing to shifts or tilts. Further evaluation is necessary to generalize the strategy for more complex misalignment errors. A PCA base approach oes not nee to ientify the physical positions of specific pins. Therefore, the approach presente in this paper shows promise for etection of complex but systematic errors introuce by sense plate misalignments, beyon visually ientifiable patterns corresponing to shifts an tilts. The matrices neee for the calculation can be evaluate base on ata obtaine by testing the same boar using sense plates with ifferent tilts. We plan to evelop this scheme further, an evaluate using aitional test ata. References [1] K. P. Parker an S. Hir, Fining Power/Groun Defects on Connectors A New Approach, Proc. IEEE International Test Conference, paper 28.2, Santa Clara CA, Oct. 27. [2] S. Hir an R. Weng, Fining Power/Groun Defects on Connectors Case Stuy, Proc. IEEE International Test Conference, paper 15.2, Santa Clara, Oct. 28. [3] D. Gizopoulos, Avances in Electronic Testing: Challenges an Methoologies, Springer-Verlag, 2, pp [4] X. He, Y. K. Malaiya, A. P. Jayasumana, K. P. Parker an S. Hir, "An Outlier Detection Base Approach for PCB Testing," Proc. IEEE International Test Conference, paper 1.3, Austin, Nov 29. [5] A. Sharma, A. P. Jayasumana, Y. K. Malaiya, X- IDDQ: A Novel Defect Detection Technique using IDDQ Data, Proc. IEEE VLSI Test Symposium, 2. [] P. M. O Neill, Prouction Multivariate Outlier Detection Using Principal Components, Proc. IEEE International Test Conference, paper 1.2, Santa Clara, 28. [7] A. S. Banthia, A.P.Jayasumana an Y.K. Malaiya, "Data Size Reuction for Clustering-Base Binning of ICs using Principal-Component Analysis, Proc. IEEE International Workshop on Defect Base Testing (DBT 25), CA, May, 25 [8] I. T. Jolliffe, Principal Component Analysis, Springer-Verlag, 22, pp [9] L. Elen, Matrix Methos in Data Mining an Pattern Recognition (Funamentals of Algorithms), Society for Inustrial an Applie Mathematics, 27. [1] A. Nahar, R. Daasch, Burn-in Reuction using Principal Component Analysis, Proc. IEEE International Test Conference, paper 7.2, 25. [11] P. Praus, SVD-base Principal Component Analysis of Geochemical Data, Central European Journal of Chemistry (25), pp Acknowlegements The Authors woul like to acknowlege the Agilent University Relations program for its generous support. Paper 1.1 INTERNATIONAL TEST CONFERENCE 1