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:在本文中,我们不仅提议对对数概率比总和进行新的最佳顺序测试,而且还将CUSUM连续测试(控制图、停止时间)与观察调整控制限度(CUSUM-OAL)一起快速和适应地监测测序观测分布的变化。在最佳测试与CUSUM-OAL的一系列测试之间建立了两种限制关系。此外,我们提供了CUSUM-OAL测试的控制内和控制外平均运行长度的估计。在检测观测序列的中位变化中进行的数字模拟证明了理论结果。</s>