Online change point detection is the process of identifying distributional changes in time-ordered data in real time. In applications such as mobile health (mHealth), repeated testing is often performed as new data arrive, creating a multiple testing problem. Traditional approaches for controlling the family-wise error rate (FWER) are not well suited to this setting because the tests are highly dependent and the number of tests is not fixed in advance. In this work, we introduce a sequential family-wise error rate (sFWER), defined as the probability of at least one false positive within a moving monitoring window. We propose a simulation-based calibration procedure to estimate monitoring thresholds that control the sFWER at a desired level. Through simulation studies, we demonstrate that the proposed procedure achieves the desired error control, while commonly used alternatives are either overly conservative or fail to adequately control false alarms. Finally, we illustrate the proposed approach using passively collected smartphone data from a cohort of adolescents and young adults with affective instability.

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