Non-Restarting CUSUM charts and Control of the False Discovery Rate

Abstract: Cumulative sum (CUSUM) charts are typically used to detect changes in a stream of observations e.g. shifts in the mean. Usually, after signalling, the chart is restarted by setting it to some value below the signalling threshold. We propose a non-restarting CUSUM chart which is able to detect periods during which the stream is out of control. Further, we advocate an upper boundary to prevent the CUSUM chart rising too high, which helps detecting a change back into control. We present a novel algorithm to control the false discovery rate (FDR) pointwise in time when considering CUSUM charts based on multiple streams of data. We prove that the FDR is controlled under two definitions of a false discovery simultaneously. Simulations reveal the difference in FDR control when using these two definitions and other desirable definitions of a false discovery.