Comparison of bootstrap and asymptotic confidence limits for control charts in batch MSPC strategies

Chemometrics and Intelligent Laboratory Systems

Volumn 127, Issue , 2013, Pages 102-111

  Babamoradi, Hamid ^a   Van den Berg, Frans ^a   Rinnan, Åsmund ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Bootstrap; Confidence limit; False alarms; Overall Type I II errors; Statistical process control

Indexed keywords

ARTICLE; ASYMPTOTIC CONFIDENCE LIMITS; BATCH PROCESS; BOOTSTRAPPING; INTERMETHOD COMPARISON; MULTIVARIATE STATISTICAL PROCESS CONTROL; PREDICTION; PRINCIPAL COMPONENT ANALYSIS; PRIORITY JOURNAL; PROCESS CONTROL; SIMULATION; STATISTICAL ANALYSIS;

EID: 84880393702     PISSN: 01697439     EISSN: 18733239     Source Type: Journal    
DOI: 10.1016/j.chemolab.2013.06.005     Document Type: Article

References (29)

1. Nomikos P., MacGregor J. Multivariate Spc charts for monitoring batch processes. Technometrics 1995, 37:41-59.
2. Martin E., Morris A. Non-parametric confidence bounds for process performance monitoring charts. Journal of Process Control 1996, 6:349-358.
3. Kim S.B., Sukchotrat T., Park S. A nonparametric fault isolation approach through one-class classification algorithms. IIE Transactions 2011, 43:505-517.
4. Phaladiganon P., Kim S.B., Chen V.C.P., Baek J., Park S. Bootstrap-based T2 multivariate control charts. Communications in Statistics - Simulation and Computing 2011, 40:645-662.
5. Chou Y., Mason R., Young J. The control chart for individual observations from a multivariate non-normal distribution. Communications in Statistics - Theory and Methods 2001, 30:1937-1949.
6. Efron B., Tibshirani R. An Introduction to the Bootstrap 1993, Chapman & Hall, New York.
7. Davison A.C., Hinkley D.V. Bootstrap Methods and Their Applications 1997, Cambridge Univ. Press, Cambridge.
8. Martin E., Morris A., Papazoglou M., Kiparissides C. Batch process monitoring for consistent production. Computers and Chemical Engineering 1996, 20:S599-S604.
9. Polansky A. A general framework for constructing control charts. Quality and Reliability Engineering International 2005, 21:633-653.
10. Wang F., Eldon Y. Confidence intervals in repeatability and reproducibility using the bootstrap method. Total Quality Management and Business Excellence 2003, 14:341-354.
11. Camacho J., Pico J., Ferrer A. The best approaches in the on-line monitoring of batch processes based on PCA: does the modelling structure matter?. Analytica Chimica Acta 2009, 642:59-68.
12. Camacho J., Pico J. Online monitoring of batch process using multi-phase principal component analysis. Journal of Process Control 2006, 16:1021-1035.
13. Ramaker H., van Sprang E., Westerhuis J., Smilde A. Fault detection properties of global, local and time evolving models for batch process monitoring. Journal of Process Control 2005, 15:799-805.
14. Box G. Some theorems on quadratic forms applied in the study of analysis of variance problems. 1. Effect of inequality of variance in the one-way classification. Annals of Mathematical Statistics 1954, 25:290-302.
15. Jackson J., Mudholkar G. Control procedures for residuals associated with principal component analysis. Technometrics 1979, 21:341-349.
16. Tracy N., Young J., Mason R. Multivariate control charts for individual observations. Journal of Quality Technology 1992, 24:88-95.
17. Babamoradi H., van den Berg F., Rinnan Å. Bootstrap based confidence limits in principal component analysis - a case study. Chemometrics and Intelligent Laboratory Systems 2013, 120:97-105.
18. Peres-Neto P., Jackson D., Somers K. Giving meaningful interpretation to ordination axes: assessing loading significance in principal component analysis. Ecology 2003, 84:2347-2363.
19. Milan L., Whittaker J. Application of the parametric bootstrap to models that incorporate a singular-value decomposition. Journal of the Royal Statistical Society: Applied Statistics 1995, 44:31-49.
20. Efron B. Better bootstrap confidence-intervals. Journal of the American Statistical Association 1987, 82:171-185.
21. Babamoradi H. Bootstrap-Based Confidence Estimation in PCA and Multivariate Statistical Process Control 2012, PhD Thesis, University of Copenhagen, Frederiksberg, Denmark, (http://www.models.life.ku.dk/theses).
22. Ramaker H., van Sprang E., Westerhuis J., Smilde A. The effect of the size of the training set and number of principal components on the false alarm rate in statistical process monitoring. Chemometrics and Intelligent Laboratory Systems 2004, 73:181-187.
23. Efron B., Tibshirani R. Improvements on cross-validation: the .632+ bootstrap method. Journal of the American Statistical Association 1997, 92:548-560.
24. Lei F., Rotboll M., Jorgensen S. A biochemically structured model for Saccharomyces cerevisiae. Journal of Biotechnology 2001, 88:205-221.
25. Bro R., Kjeldahl K., Smilde A.K., Kiers H.A.L. Cross-validation of component models: a critical look at current methods. Analytical and Bioanalytical Chemistry 2008, 390:1241-1251.
26. Wehrens R., Putter H., Buydens L. The bootstrap: a tutorial. Chemometrics and Intelligent Laboratory Systems 2000, 54:35-52.
27. J. Camacho Páez, J.M. González Martínez, A.J. Ferrer Riquelme, Multivariate Statistical Engineering Group (MSERG), Valencia, Spain (). http://mseg.webs.upv.es/Software_e.html.
28. Ramaker H., van Sprang E.N.M., Ramaker H., van Sprang E.N.M., Westerhuis J.A., Gurden S.P., Smilde A.K., van der Meulen F.H. Performance assessment and improvement of control charts for statistical batch process monitoring. Statistica Neerlandica 2006, 60:339-360.
29. Conlin A., Martin E., Morris A. Confidence limits for contribution plots. Journal of Chemometrics 2000, 14:725-736.