# Quickest Change Detection in the Presence of a Nuisance Change

## TL;DR

This paper introduces a recursive, asymptotically optimal quickest change detection method that effectively distinguishes critical changes from nuisance changes, outperforming existing procedures in simulations and real-world bearing failure data.

## Contribution

A novel window-limited sequential detection procedure based on the generalized likelihood ratio test that handles nuisance changes and is proven to be asymptotically optimal.

## Key findings

- Proposed method outperforms FMA and 2-stage procedures in simulations.
- The recursive update scheme is computationally efficient.
- Real data experiments confirm the method's effectiveness.

## Abstract

In the quickest change detection problem in which both nuisance and critical changes may occur, the objective is to detect the critical change as quickly as possible without raising an alarm when either there is no change or a nuisance change has occurred. A window-limited sequential change detection procedure based on the generalized likelihood ratio test statistic is proposed. A recursive update scheme for the proposed test statistic is developed and is shown to be asymptotically optimal under mild technical conditions. In the scenario where the post-change distribution belongs to a parametrized family, a generalized stopping time and a lower bound on its average run length are derived. The proposed stopping rule is compared with the FMA stopping time and the naive 2-stage procedure that detects the nuisance or critical change using separate CuSum stopping procedures for the nuisance and critical changes. Simulations demonstrate that the proposed rule outperforms the FMA stopping time and the 2-stage procedure, and experiments on a real dataset on bearing failure verify the performance of the proposed stopping time.