This article develops a method to construct the optimal sequential test for monitoring the changes in the distribution of finite observation sequences with a general dependence structure. This method allows us to prove that different optimal sequential tests can be constructed for different performance measures of detection delay times. We also provide a formula to calculate the value of the generalized out-of-control average run length for every optimal sequential test. Moreover, we show that there is an equivalent optimal control limit which does not depend on the test statistic directly when the post-change conditional densities (probabilities) of the observation sequences do not depend on the change time.

中文翻译：

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监测有限观测序列分布变化的最佳序列检验

本文开发了一种构建最优序列检验的方法，用于监测具有一般依赖结构的有限观测序列分布的变化。该方法使我们能够证明可以针对检测延迟时间的不同性能度量构建不同的最佳顺序测试。我们还提供了一个公式来计算每个最佳顺序测试的广义失控平均运行长度的值。此外，我们表明，当观测序列的变化后条件密度（概率）不依赖于变化时间时，存在不直接依赖于检验统计量的等效最优控制限。