Multivariate Statistical Process Control for Fault Detection using Principal Component Analysis. APACT Conference ’04 Bath Personnel Richard Southern, MSc. Trinity College Dublin, Ireland. Craig Meskell, PhD. Trinity College Dublin, Ireland. Peter Twigg, PhD. Manchester Metropolitan University, Uk. Ernst-Michael Bohne, PhD. IBM Microelectronics Division, Ireland. Outline Process Monitoring and Fault Detection and Isolation. Implement Statistical Quality Control prog. Maximise Yield through Statistical Data Analysis Application of RWM Development of NOC model Inference and Conclusions Real World Methodologies Statistical Process / Quality Control (SP/QC) Fault Detection & Isolation (FDI) Principal Component Analysis (PCA) Statistical process monitoring (uni & multivariate) Latent structures modelling (PLS) Exponentially Weighted Moving Average (EWMA) and MEWMA Batchwise or Run2Run strategies (R2R) Statistical Control The objective of SPC is to minimise variation and aim to run in a ‘state of statistical control’. Distinction between common cause (stochastic) variations and assignable cause Where process is operating efficiently When product is yielding sufficiently MSPC more realistic representation but more complex Performance enhancement Monitoring Improvement FDI Distinguish between product and test Consistently high quality product/process is a challenge FDI scheme: a specific application of SPC, where a distinction needs to be made between normal process operation and faulty operation. i.e. bullet pt. 1 Key points Process knowledge Fault classification Plant Overview IBM Microelectronics Division Testing vendor supplied μchips Many combinations (product & process) (wafer/lot/batch/tester/handler) Large data sets (inherent redundancy) This leads to the following pertinent question: Chip fault or evolving test unit malfunction?? Batch Process Finite duration ‘Open loop’ wrt to product quality non-linear behaviour & system dependent no feedback is applied to the process to reduce error through batch run 3-way data structure (batch x var x time) Parametric and non-std data formats Differing test times Yield is calculated as a % of starts/goods Yield is a logical AND of test metrics Test Matrix PROCESS Pass PRODUCT GOOD GOOD BAD Genuine Fails BAD False Fail Data Structure Unusual data set, complex in nature Different data structures (HP, Teradyne) Large data matrix (avg. batch ≈ 7-10K cycles) ≈ 180 metrics/μchip/cycle (MS/RF) Correlation/redundancy Analogue and Digital test vectors PCA Theory Rank reduction or data compression method Singular Value Decomposition (SVD) variance-covariance matrix Variance - eigenvalues (λ) Loadings - eigenvectors (PC’s) Linear transform equation yields scores 1st PC has largest λ, sub. smaller How many components? Subjective process Disregard λ < 1 Scree plots 70 – 90 % var [too many = over parameterise, noise] [too few = poor model, incomplete] PCA flowchart DB link pre-processing data set X (n x m) normalisation cov matrix SVD model eig% score & loading vector T2 & Q stat MEWMA Fault Detection NOC Model Pre-process the data normalise N~(0,1) apply limit files (separate components) partition data and work with subset of known goods SVD on subset eigenvalue contribution to model (≈70%) Post-multiply PC’s with normal batch data batch data normalised with model statistics (µ,σ) model results can be used to identify shift from normal NOC PC Score plot 10 NOC scores Principal Component 2 5 0 -5 -10 HP Data 0905 Yield=91.65% -15 -15 -10 -5 Pass Data Only 0 5 Principal Component 1 10 15 Monitoring PC Score plot 400 300 NOC Batch 0905 4984 1421 Principal Component 2 200 100 0 HP Data 0905 Yield=91.65% -100 230 3181 -200 5106 -300 -500 0 500 1000 1500 2000 Principal Component 1 2500 3000 3500 Monitoring PC Score plot 20 NOC Batch 0905 15 Zoom of scores cluster Principal Component 2 10 5 4363 0 4874 -5 -10 -15 -20 -100 -50 0 50 Principal Component 1 100 NOC PC Score plot NOC Principal Component 3 10 5 HP 1836 data NOC Model scores cluster 0 -5 5 10 0 5 -5 Principal Component 2 0 -10 -5 Principal Component 1 Monitoring PC Score plot NOC Batch 1836 Principal Component 3 600 400 200 HP 1836 data NOC & Batch 1836 scores cluster 0 -200 -400 1500 1000 1000 0 500 -1000 0 Principal Component 2 -2000 -500 -3000 Principal Component 1 HP 1836 data NOC & Batch 1836 scores cluster (Close Up) t2036 statistics Eigenvalue Pareto 90 99% 80 75% eigenvalue 70 contribution (14 PC’s) 60 no. faults = 117 50 Batch size = 2135 40 NOC model shows fault 30 clusters 20 88% 10 11% 0 77% 66% 55% 44% 33% 22% 1 2 3 4 5 6 7 8 9 10 0% NOC Scores 250 200 150 PC Score 2 100 50 0 -50 -100 -150 -150 -100 -50 0 50 PC Score 1 100 150 200 PC Monitoring Score Chart PC Score 3 0 -100 -200 -300 200 150 100 50 0 PC Score 2 -100 -50 -100 0 PC Score 1 100 NOC Scores 250 This fault cluster represent the same fault (8) 200 150 PC Score 2 100 50 0 -50 -100 -150 -150 -100 -50 0 50 PC Score 1 100 150 200 MEWMA Rational The PCA is used for a preconditioning, data reduction tool The scores (subjective level) are used as input to a MEWMA scheme Create single multivariate chart Weighted average nature is sensitive to subtle faults Robust to auto correlated data, Non-normal data Schematic SPC PCA MEWMA Supervisory Scheme DUT Batch loop DIB Test prog Product Handler Tester Loop times n Yield calc Production Data DB Summary Stats Conclusions Process at ‘cell level’ Reduction of large data sets Generation of NOC model Tester specific NOC model Product specific NOC model Tested with production batch data MEWMA method under development Single fault statistic to max. DUT FPY Acknowledgements IBM Microelectronics Division, Ireland Trinity College Dublin, Ireland APACT 04, Bath.
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