**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 • 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

**Pass Data Only **

**Zoom of scores cluster**

**HP 1836 data NOC Model scores cluster**

**HP 1836 data NOC & Batch 1836 scores cluster**

**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

**This fault cluster represent the same fault (8)**

**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.