An CUSUM Test with Observation-Adjusted Control Limits in Change Detection

In this paper, we not only propose an new optimal sequential test of sum of logarithmic likelihood ratio (SLR) but also present the CUSUM sequential test (control chart, stopping time) with the observation-adjusted control limits (CUSUM-OAL) for monitoring quickly and adaptively the change in distri...

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Bibliographic Details
Published in:arXiv.org 2023-03
Main Authors: Tang, Fuquan, Han, Dong
Format: Article
Language:English
Subjects:
Change detection
Control charts
Control limits
Likelihood ratio
Online Access:Get full text
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Summary:In this paper, we not only propose an new optimal sequential test of sum of logarithmic likelihood ratio (SLR) but also present the CUSUM sequential test (control chart, stopping time) with the observation-adjusted control limits (CUSUM-OAL) for monitoring quickly and adaptively the change in distribution of a sequential observations. Two limiting relationships between the optimal test and a series of the CUSUM-OAL tests are established. Moreover, we give the estimation of the in-control and the out-of-control average run lengths (ARLs) of the CUSUM-OAL test. The theoretical results are illustrated by numerical simulations in detecting mean shifts of the observations sequence.
ISSN:2331-8422