Abstract
AbstractThe copula approach is a popular method for multivariate modeling applied in several fields; it defines non-parametric measures of dependence between random variables. In this paper, three families are proposed from elliptical and Archimedean copulas on the multivariate cumulative sum (MCUSUM) control chart when observations are draw from an exponential distribution. The performance of the control chart is based on the average run length (ARL)—via Monte Carlo simulations. A copula function for specifying the dependence between random variables is measured by Kendall’s tau. The numerical results indicate that the observations can be fitted and that the copula can be used on the MCUSUM for cases of small and large dependencies.
Highlights
Quality control charts are applicable for processes that have one variable or more, which are referred to as univariate or multivariate control charts, respectively
Multivariate detection procedures are based on a multi-normality assumption and independence; many processes exhibit non-normality and correlation. Most of these multivariate control charts are generalizations of their univariate counterparts (Mahmoud & Maravelakis, 2013), such as the Hotelling’s T2 control chart, the multivariate exponentially weighted moving average (MEWMA) control chart proposed by Lowry, Woodall, Champ, and Rigdon (1992), and the multivariate cumulative sum (MCUSUM) control chart (Bersimis, Panaretos, & Psarakis, 2005; Bersimis, Psarakis, & Panaretos, 2007)
This paper focuses on the normal copula and two families of Archimedean copulas, the Clayton and Frank copulas, because these copulas are well-known
Summary
Quality control charts are applicable for processes that have one variable or more, which are referred to as univariate or multivariate control charts, respectively. Multivariate control charts are widely used to simultaneously monitor several quality characteristics for detecting the mean changes in manufacturing industries. They are a powerful tool in statistical process control (SPC) for identifying an out-of-control process. Multivariate detection procedures are based on a multi-normality assumption and independence; many processes exhibit non-normality and correlation Most of these multivariate control charts are generalizations of their univariate counterparts (Mahmoud & Maravelakis, 2013), such as the Hotelling’s T2 control chart, the multivariate exponentially weighted moving average (MEWMA) control chart proposed by Lowry, Woodall, Champ, and Rigdon (1992), and the multivariate cumulative sum (MCUSUM) control chart (Bersimis, Panaretos, & Psarakis, 2005; Bersimis, Psarakis, & Panaretos, 2007). 2. Properties of the MCUSUM control chart In the univariate case, the cumulative sum (CUSUM) procedure is often designed for monitoring and detecting small changes. The theory that is the central foundation of the copula is described and shown in Table 1 (see Genest & McKay, 1986; Joe, 2015; Sklar, 1959; Trivedi & Zimmer, 2005)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
