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Bivariate copula monitoring
Author(s) -
Easton Andrew,
van Dalen Okki,
Goeb Rainer,
Di Bucchianico Alessandro
Publication year - 2022
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.3034
Subject(s) - copula (linguistics) , bivariate analysis , multivariate statistics , mathematics , econometrics , weighting , covariance matrix , multivariate normal distribution , statistics , computer science , medicine , radiology
The assumption of multivariate normality underlying the HotellingT 2 $T^2$ 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 HotellingT 2 $T^2$ 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 HotellingT 2 $T^2$ in a large variety of out‐of‐control cases, whereas the weighted Vuong scheme often fails to provide an improvement.