title: Confidence limits for contribution plots in multivariate statistical process control using bootstrap estimates.
abstract: In Multivariate Statistical Process Control, when a fault is expected or detected in the process, contribution plots are essential for operators and optimization engineers in identifying those process variables that were affected by or might be the cause of the fault. The traditional way of interpreting a contribution plot is to examine the largest contributing process variables as the most probable faulty ones. This might result in false readings purely due to the differences in natural variation, measurement uncertainties, etc. It is more reasonable to compare variable contributions for new process runs with historical results achieved under Normal Operating Conditions, where confidence limits for contribution plots estimated from training data are used to judge new production runs. Asymptotic methods cannot provide confidence limits for contribution plots, leaving re-sampling methods as the only option. We suggest bootstrap re-sampling to build confidence limits for all contribution plots in online PCA-based MSPC. The new strategy to estimate CLs is compared to the previously reported CLs for contribution plots. An industrial batch process dataset was used to illustrate the concepts.
authors.affiliation: University of Copenhagen, Faculty of Science, Department of Food Science, Spectroscopy & Chemometrics Section, Rolighedsvej 30, DK-1958 Frederiksberg, Denmark. Electronic address: hamba@food.ku.dk.
authors.forename: Hamid
authors.initials: H
authors.lastname: Babamoradi
authors.affiliation: University of Copenhagen, Faculty of Science, Department of Food Science, Spectroscopy & Chemometrics Section, Rolighedsvej 30, DK-1958 Frederiksberg, Denmark.
authors.forename: Frans
authors.initials: F
authors.lastname: van den Berg
authors.affiliation: University of Copenhagen, Faculty of Science, Department of Food Science, Spectroscopy & Chemometrics Section, Rolighedsvej 30, DK-1958 Frederiksberg, Denmark.
authors.forename: Åsmund
authors.initials: Å
authors.lastname: Rinnan
keywords: Bootstrap; Confidence limit; Fault diagnosis; Multivariate statistical process control; Process monitoring; Variable contributions