Control charts for the mean based on robust two-sample tests

We propose and investigate robust control charts for the detection of sudden shifts in sequences of very noisy observations with a naturally slowly varying mean. They sequentially apply local two-sample tests for the location problem. Thus, no previous knowledge about the in-control behaviour is necessary. We identify critical values for the tests to achieve a desired in-control average run length (ARL(0)) with extensive simulations. Control charts based on non-parametric tests or a randomization principle provide a satisfactory run length behaviour for different error distributions. They possess a nearly distribution-free ARL(0) and are fast in detecting present signal jumps in a time series. In our simulations and exemplary real-world applications from biosignal analysis, a test based on the two-sample Hodges-Lehmann estimator leads to very promising results regarding distribution independence, robustness and detection speed.