Abstract Monitoring complex systems involving high-dimensional data streams (HDS) provides quick real-time detection of abnormal changes of system performance, but accurate and efficient diagnosis of the streams responsible has also become increasingly important in many data-rich statistical process control applications. Existing diagnostic procedures, designed for low/moderate dimensional multivariate process, may miss too much important information in the out-of-control streams with a high signal-to-noise ratio (SNR) or waste too many resources finding useless in-control streams with a low SNR. In addition, these procedures do not differentiate between streams according to their severity. In this article, we formulate the diagnosis problem of HDS as a multiple testing problem and provide a computationally fast diagnostic procedure to control the weighted missed discovery rate (wMDR) at some satisfactory level. The proposed procedure overcomes the limitations of conventional diagnostic procedures by controlling the wMDR and minimizing the expected number of false positives as well. We show theoretically that the proposed procedure is asymptotically valid and optimal in a certain sense. Simulation studies and a real data analysis from a semiconductor manufacturing process show that the proposed procedure works very well in practice.

中文翻译：

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基于漏检率控制的高维数据流诊断程序

摘要 监控涉及高维数据流 (HDS) 的复杂系统可以快速实时检测系统性能的异常变化，但准确有效的数据流诊断在许多数据丰富的统计过程控制应用中也变得越来越重要。为低/中维多变量过程设计的现有诊断程序可能会在具有高信噪比 (SNR) 的失控流中遗漏太多重要信息，或者浪费太多资源寻找无用的受控流具有低 SNR。此外，这些程序不会根据流的严重性来区分流。在本文中，我们将 HDS 的诊断问题表述为一个多重测试问题，并提供一个计算快速的诊断程序，以将加权遗漏发现率 (wMDR) 控制在某个令人满意的水平。所提出的程序通过控制 wMDR 并最大限度地减少误报的预期数量，克服了传统诊断程序的局限性。我们从理论上表明，所提出的程序在某种意义上是渐近有效和最优的。模拟研究和来自半导体制造过程的真实数据分析表明，所提出的程序在实践中非常有效。所提出的程序通过控制 wMDR 并最大限度地减少误报的预期数量，克服了传统诊断程序的局限性。我们从理论上表明，所提出的程序在某种意义上是渐近有效和最优的。模拟研究和来自半导体制造过程的真实数据分析表明，所提出的程序在实践中非常有效。所提出的程序通过控制 wMDR 并最大限度地减少误报的预期数量，克服了传统诊断程序的局限性。我们从理论上表明，所提出的程序在某种意义上是渐近有效和最优的。模拟研究和来自半导体制造过程的真实数据分析表明，所提出的程序在实践中非常有效。