Abstract
The assumption of multivariate normality underlying the Hotelling (Formula presented.) 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 (Formula presented.) 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 (Formula presented.) in a large variety of out-of-control cases, whereas the weighted Vuong scheme often fails to provide an improvement.
| Original language | English |
|---|---|
| Pages (from-to) | 1272-1288 |
| Number of pages | 17 |
| Journal | Quality and Reliability Engineering International |
| Volume | 38 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Apr 2022 |
Bibliographical note
Funding Information:We gratefully acknowledge the compute resources and support provided by the University of Würzburg IT Centre and the German Research Foundation (DFG) through Grant No. INST 93/878‐1 FUGG.
Funding
We gratefully acknowledge the compute resources and support provided by the University of Würzburg IT Centre and the German Research Foundation (DFG) through Grant No. INST 93/878‐1 FUGG. We gratefully acknowledge the compute resources and support provided by the University of W?rzburg IT Centre and the German Research Foundation (DFG) through Grant No.?INST?93/878-1?FUGG.
Keywords
- copula
- multivariate Gaussian distribution
- multivariate statistical process control (SPC)
- phase I
- phase II