Bivariate copula monitoring
Please always quote using this URN: urn:nbn:de:bvb:20-opus-276501
- The assumption of multivariate normality underlying the Hotelling T\(^{2}\) chart is often violated for process data. The multivariate dependency structure can be separated from marginals with the help of copula theory, which permits to model association structures beyond the covariance matrix. Copula‐based estimation and testing routines have reached maturity regarding a variety of practical applications. We have constructed a rich design matrix for the comparison of the Hotelling T\(^{2}\) chart with the copula test by Verdier and the copulaThe assumption of multivariate normality underlying the Hotelling T\(^{2}\) chart is often violated for process data. The multivariate dependency structure can be separated from marginals with the help of copula theory, which permits to model association structures beyond the covariance matrix. Copula‐based estimation and testing routines have reached maturity regarding a variety of practical applications. We have constructed a rich design matrix for the comparison of the Hotelling T\(^{2}\) chart with the copula test by Verdier and the copula test by Vuong, which allows for weighting the observations adaptively. Based on the design matrix, we have conducted a large and computationally intensive simulation study. The results show that the copula test by Verdier performs better than Hotelling T\(^{2}\) in a large variety of out‐of‐control cases, whereas the weighted Vuong scheme often fails to provide an improvement.…
Author: | Andrew Easton, Okki van Dalen, Rainer Goeb, Alessandro Di Bucchianico |
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URN: | urn:nbn:de:bvb:20-opus-276501 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Language: | English |
Parent Title (English): | Quality and Reliability Engineering International |
Year of Completion: | 2022 |
Volume: | 38 |
Issue: | 3 |
First Page: | 1272 |
Last Page: | 1288 |
Source: | Quality and Reliability Engineering International 2022, 38(3):1272-1288. DOI: 10.1002/qre.3034 |
DOI: | https://doi.org/10.1002/qre.3034 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Tag: | copula; multivariate Gaussian distribution; multivariate statistical process control (SPC); phase I; phase II |
Release Date: | 2023/06/28 |
Licence (German): | CC BY-NC-ND: Creative-Commons-Lizenz: Namensnennung, Nicht kommerziell, Keine Bearbeitungen 4.0 International |