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Impact of Autocorrelation on Principal Components and Their Use in Statistical Process Control
Luleå University of Technology, Department of Business Administration, Technology and Social Sciences, Business Administration and Industrial Engineering.ORCID iD: 0000-0003-1473-3670
Luleå University of Technology, Department of Business Administration, Technology and Social Sciences, Business Administration and Industrial Engineering.ORCID iD: 0000-0003-4222-9631
2016 (English)In: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 32, no 4, p. 1483-1500Article in journal (Refereed) Published
Abstract [en]

A basic assumption when using principal component analysis (PCA) for inferential purposes, such as in statistical process control (SPC) is that the data are independent in time. In many industrial processes frequent sampling and process dynamics make this assumption unrealistic rendering sampled data autocorrelated (serially dependent). PCA can be used to reduce data dimensionality and to simplify multivariate SPC. Although there have been some attempts in the literature to deal with autocorrelated data in PCA, we argue that the impact of autocorrelation on PCA and PCA-based SPC is neither well understood nor properly documented.This article illustrates through simulations the impact of autocorrelation on the descriptive ability of PCA and on the monitoring performance using PCA-based SPC when autocorrelation is ignored. In the simulations cross- and autocorrelated data are generated using a stationary first order vector autoregressive model.The results show that the descriptive ability of PCA may be seriously affected by autocorrelation causing a need to incorporate additional principal components to maintain the model’s explanatory ability. When all variables have the same autocorrelation coefficients the descriptive ability is intact while a significant impact occurs when the variables have different degrees of autocorrelation. We also illustrate that autocorrelation may impact PCA-based SPC and cause lower false alarm rates and delayed shift detection, especially for negative autocorrelation. However, for larger shifts the impact of autocorrelation seems rather small.

Place, publisher, year, edition, pages
2016. Vol. 32, no 4, p. 1483-1500
National Category
Reliability and Maintenance
Research subject
Quality Technology and Management
Identifiers
URN: urn:nbn:se:ltu:diva-8508DOI: 10.1002/qre.1858ISI: 000374681200016Scopus ID: 2-s2.0-84940099793Local ID: 705771ca-5615-41b6-ae3e-b4f8830b2252OAI: oai:DiVA.org:ltu-8508DiVA, id: diva2:981446
Projects
Statistiska metoder för förbättring av kontinuerliga tillverkningsprocesser
Note
Validerad; 2016; Nivå 2; 20150722 (erivan)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Vanhatalo, ErikKulahci, Murat

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