Optimality of Non-Restarting CUSUM charts

TL;DR

This paper demonstrates the optimality of non-restarting CUSUM charts with an upper boundary for detecting multiple distribution changes, highlighting their advantages over traditional restarting methods.

Contribution

It introduces and analyzes the use of non-restarting CUSUM charts with an upper boundary, showing their optimality in multiple change detection scenarios.

Findings

Non-restarting CUSUM charts are optimal for multiple change detection.

Imposing an upper boundary improves detection performance.

Simulation results illustrate the impact of boundary choices.

Abstract

We show optimality, in a well-defined sense, using cumulative sum (CUSUM) charts for detecting changes in distributions. We consider a setting with multiple changes between two known distributions. This result advocates the use of non-restarting CUSUM charts with an upper boundary. Typically, after signalling, a CUSUM chart is restarted by setting it to some value below the threshold. A non-restarting CUSUM chart is not reset after signalling; thus is able to signal continuously. Imposing an upper boundary prevents the CUSUM chart rising too high, which facilitates detection in our setting. We discuss, via simulations, how the choice of the upper boundary changes the signals made by the non-restarting CUSUM charts.