Sequential calibration and detection-delay theory for rolling monitoring

Derive sequential calibration for the rolling transmission and spectral monitoring procedure, including threshold and consecutive-exceedance choices that control false alarms and characterize detection delays and missed detections.

Background

The rolling monitor tests many edges over overlapping windows and declares an alarm only after consecutive exceedances. Simulations show a substantial trade-off among false-alarm probability, detection delay, and missed detections as the threshold and run length vary.

The paper reports these operating characteristics empirically but does not provide a general sequential theory for selecting the threshold and run length to attain a target average run length or other error criterion. It also leaves unresolved the formal detection-delay behavior of the rolling procedure.

References

Theorem~\ref{thm:bootstrap} gives formal validity of a design-preserving variant under thresholded selection; uniformity over local-to-zero couplings and the detection-delay theory of Algorithm~\ref{alg:monitor} (measured empirically in Section~\ref{sec:sims}) remain open.

— Output-Only Identification and Spectral Monitoring of Coupled Feedback Networks with Known Time-Varying Actuation  (2608.25844 - Woo, 26 Aug 2026) in Section 5, immediately after Theorem 5 (Bootstrap validity under consistent selection)