Statistics and Its Interface
Volume 10 (2017)
EWMA control charts for multivariate autocorrelated processes
Pages: 575 – 584
In this paper, a semiparametric control scheme for multivariate Markov processes of order one is introduced. We utilize copula-based semiparametric stationary Markov models to transform original multivariate autocorrelated processes to the ones in which the marginal information of the monitored characteristics are separate out from their dependence structures. Meanwhile, the autocorrelations within them are also characterized by copulas. As such, one could focus on monitoring changes in the location of characteristics marginally under a more generalized assumption that observations could be stochastically dependent. The proposed chart can reduce to the traditional multivariate EWMA charts if the underlying process is multivariate Gaussian with stochastically independent observations. In addition, the margin of each time series is fitted by a newly developed semiparametric approach using the transformed Bernstein polynomial prior. Specifically, it allows an initial parametric guess (such as normal) on a monitored characteristic; then by adding more details via data, any departure from this initial guess will be captured and used for adjusting the initial to obtain robust estimation. Gaussian copulas are then used for modeling both autocorrelations within each time series and correlations among them.
autocorrelated processes, Gaussian copulas, multivariate EWMA charts, semiparametric models, transformed Bernstein polynomial priors