  Advanced computing and data acquisition technologies have made possible the
collection of high-dimensional data streams in many fields. Efficient online
monitoring tools which can correctly identify any abnormal data stream for such
data are highly sought after. However, most of the existing monitoring
procedures directly apply the false discover rate (FDR) controlling procedure
to the data at each time point, and the FDR at each time point (the point-wise
FDR) is either specified by users or determined by the in-control (IC) average
run length (ARL). If the point-wise FDR is specified by users, the resulting
procedure lacks control of the global FDR and keeps users in the dark in terms
of the IC-ARL. If the point-wise FDR is determined by the IC-ARL, the resulting
procedure does not give users the flexibility to choose the number of false
alarms (Type-I errors) they can tolerate when identifying abnormal data
streams, which often makes the procedure too conservative. To address those
limitations, we propose a two-stage monitoring procedure that can control both
the IC-ARL and Type-I errors at the levels specified by users. As a result, the
proposed procedure allows users to choose not only how often they expect any
false alarms when all data streams are IC, but also how many false alarms they
can tolerate when identifying abnormal data streams. With this extra
flexibility, our proposed two-stage monitoring procedure is shown in the
simulation study and real data analysis to outperform the exiting methods.
