A nonparametric exponentially weighted moving average control chart for online monitoring of independence based on sequential rank statistics

In multivariate statistical process control, existing control charts focus on shifts in the mean vector or covariance matrix, while online monitoring of dependence structures among variables remains underexplored. Existing tests are designed for cumulative independence testing and are not readily applicable to tracking gradual drifts from independence to dependence in continuous monitoring. We propose a nonparametric sequential rank-based exponentially weighted moving average control chart for online monitoring of dynamic dependence changes between two variables. The proposed method constructs a distribution-free dependence statistic based on sequential ranks, derives its exact sequential variance for stable standardized monitoring, and incorporates multiscale aggregation to enhance detection sensitivity across diverse dependence patterns. Simulation studies show that the chart achieves shorter out-of-control average run lengths than competing charts, particularly under nonnormal distributions, nonlinear dependence, and weak-signal scenarios. An application to IMS bearing data illustrates its utility in a continuously monitored industrial system.