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The Effect of Autocorrelation on the Hotelling T2 Control Chart
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. Technical University of Denmark, Department of Applied Mathematics and Computer Science.ORCID iD: 0000-0003-4222-9631
2015 (English)In: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 31, no 8, p. 1779-1796Article in journal (Refereed) Published
Abstract [en]

One of the basic assumptions for traditional univariate and multivariate control charts is that the data are independent in time. For the latter in many cases the data is serially dependent (autocorrelated) and cross-correlated due to, for example, frequent sampling and process dynamics. It is well-known that the autocorrelation affects the false alarm rate and the shift detection ability of the traditional univariate control charts. However, how the false alarm rate and the shift detection ability of the Hotelling 2T control chart are affected by various auto- and cross-correlation structures for different magnitudes of shifts in the process mean is not fully explored in the literature. In this article, the performance of the Hotelling T2 control chart for different shift sizes and various auto- and cross-correlation structures are compared based on the average run length (ARL) using simulated data. Three different approaches in constructing the Hotelling T2 chart are studied for two different estimates of the covariance matrix: [1] ignoring the autocorrelation and using the raw data with theoretical upper control limits; [2] ignoring the autocorrelation and using the raw data with adjusted control limits calculated through Monte Carlo simulations; and [3] constructing the control chart for the residuals from a multivariate time series model fitted to the raw data. To limit the complexity we use a first-order vector autoregressive process, VAR(1), and focus mainly on bivariate data.

Place, publisher, year, edition, pages
2015. Vol. 31, no 8, p. 1779-1796
National Category
Reliability and Maintenance
Research subject
Quality Technology and Management
Identifiers
URN: urn:nbn:se:ltu:diva-14668DOI: 10.1002/qre.1717ISI: 000368362900036Scopus ID: 2-s2.0-84955237459Local ID: e14c7d56-0954-4f78-900c-e6d900d3327dOAI: oai:DiVA.org:ltu-14668DiVA, id: diva2:987641
Projects
Statistiska metoder för förbättring av kontinuerliga tillverkningsprocesser
Note
Validerad; 2016; Nivå 2; 20140811 (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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