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This paper considers the bivariate copula-based first-order Markov models to describe nonlinear dependence in autocorrelated data. Then the cumulative sum (CUSUM) charts based on log-likelihood ratio are developed to monitor the mean shifts. The performance of the proposed CUSUM charts is studied in both linear and nonlinear time series under weak, moderate and strong dependence by numerical simulations. Comparisons with the AR(1) model-based CUSUM and EWMA charts are present under the same range of scenarios. Simulation results show that the Clayton copula-based CUSUM charts are more effective to almost all the mean shifts and further have an obvious advantage in strong dependence. An example from chemical production is given to illustrate the implementation of the proposed control scheme.

Bivariate copula-based CUSUM charts for monitoring conditional nonlinear processes with first-order autocorrelation