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.

翻译：本文不仅提出了一种新的对数似然比之和（SLR）最优序列检验，还引入了具有观测调整控制限的CUSUM序列检验（控制图、停止时间），用于快速且自适应地监测序列观测分布的变化。建立了最优检验与一系列CUSUM-OAL检验之间的两种极限关系。此外，我们给出了CUSUM-OAL检验在受控状态和失控状态下的平均运行长度（ARLs）估计。通过检测观测序列均值漂移的数值模拟验证了理论结果。