In the problem of quickest change detection (QCD), a change occurs at some unknown time in the distribution of a sequence of independent observations. This work studies a QCD problem where the change is either a bad change, which we aim to detect, or a confusing change, which is not of our interest. Our objective is to detect a bad change as quickly as possible while avoiding raising a false alarm for pre-change or a confusing change. We identify a specific set of pre-change, bad change, and confusing change distributions that pose challenges beyond the capabilities of standard Cumulative Sum (CuSum) procedures. Proposing novel CuSum-based detection procedures, S-CuSum and J-CuSum, leveraging two CuSum statistics, we offer solutions applicable across all kinds of pre-change, bad change, and confusing change distributions. For both S-CuSum and J-CuSum, we provide analytical performance guarantees and validate them by numerical results. Furthermore, both procedures are computationally efficient as they only require simple recursive updates.

翻译：在快速变化检测问题中，分布中的变化发生于某一未知时刻，观测序列相互独立。本文研究一种快速变化检测问题，其中变化分为两类：一类是目标检测的“不良变化”，另一类是无关的“混淆变化”。我们的目标是在避免因变化前状态或混淆变化引发虚警的前提下，尽可能快速地检测到不良变化。我们识别出一类特定的变化前分布、不良变化分布和混淆变化分布组合，其挑战性超出了标准累积和程序的应对能力。通过引入两种基于累积和统计量的新型检测程序S-CuSum和J-CuSum，我们提供了适用于所有类型变化前分布、不良变化分布和混淆变化分布的解决方案。针对S-CuSum和J-CuSum，我们给出了分析性能保证，并通过数值结果验证了其有效性。此外，两种程序仅需简单的递归更新，计算效率高。