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Multivariate Statistical Process Control for Fault Detection using Principal Component Analysis. APACT Conference ’04 Bath. Personnel. Outline. Process Monitoring and Fault Detection and Isolation. Implement Statistical Quality Control prog. Maximise Yield through Statistical Data Analysis
Multivariate Statistical Process Control for Fault Detection using Principal Component Analysis. APACT Conference ’04 Bath
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) • Statistical process monitoring (uni & multivariate) • Fault Detection & Isolation (FDI) • Principal Component Analysis (PCA) • 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 • non-linear behaviour & system dependent • ‘Open loop’ wrt to product quality • 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
PROCESS GOOD BAD GOOD PRODUCT BAD Test Matrix False Fail Pass Genuine Fails
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 largestλ, sub. smaller • How many components? Subjective process • Disregard λ < 1 • Scree plots [too many = over parameterise, noise] • 70 – 90 % var [too few = poor model, incomplete]
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 PCA flowchart
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
HP 1836 data NOC & Batch 1836 scores cluster (Close Up)
t2036 statistics • 75% eigenvalue contribution (14 PC’s) • no. faults = 117 • Batch size = 2135 • NOC model shows fault clusters
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
SPC PCA MEWMA Supervisory Scheme Batch loop Yield calc DUT DIB Testprog Production Data Summary Stats Product Handler Tester DB Loop n times Schematic
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.