We present a novel real-time univariate monitoring scheme for detecting a sustained departure of a process mean from some given standard assuming a constant variance. Our proposed stopping rule is based on the total variation of a nonparametric taut string estimator of the process mean and is designed to provide a desired average run length for an in-control situation. Compared to the more prominent CUSUM fast initial response (FIR) methodology and allowing for a restart following a false alarm, the proposed two-sided taut string (TS) scheme produces a significant reduction in average run length for a wide range of changes in the mean that occur at or immediately after process monitoring begins. A decision rule for when to choose our proposed TS chart compared to the CUSUM FIR chart that takes into account both false alarm rate and average run length to detect a shift in the mean is proposed and implemented. Supplementary materials are available online.

我们提出了一种新颖的实时单变量监控方案，用于检测过程均值与某个给定标准的持续偏离，假设方差恒定。我们提出的停止规则基于过程均值的非参数紧弦估计量的总变化，旨在为受控情况提供所需的平均运行长度。与更突出的 CUSUM 快速初始响应 (FIR) 方法相比，并允许在出现错误警报后重新启动，所提出的两侧拉紧弦 (TS) 方案可显着减少平均游程长度，以适应各种变化。意味着在过程监控开始时或之后立即发生。与 CUSUM FIR 图相比，何时选择我们提出的 TS 图的决策规则提出并实施，该规则同时考虑了误报率和平均运行长度以检测均值的变化。补充材料可在线获取。