Abstract

Rapid advance of sensor technology is facilitating the collection of high-dimensional data streams (HDS). Apart from real-time detection of potential out-of-control (OC) patterns, post-signal fault diagnosis of HDS is becoming increasingly important in the filed of statistical process control to isolate abnormal data streams. The major limitations of the existing methods on that topic include (i) they cannot achieve reliable diagnostic results in the sense that their performance is highly variable, and (ii) the informative correlation among different streams is often neglected by them. This article elaborates the problem of reliable fault diagnosis for monitoring correlated HDS using the large-scale multiple testing. Under the framework of hidden Markov model dependence, new diagnostic procedures are proposed, which can control the missed discovery exceedance (MDX) at a desired level. Extensive numerical studies along with some theoretical results show that the proposed procedures can control MDX properly, leading to diagnostics with high reliability and efficiency. Also, their diagnostic performance can be improved significantly by exploiting the dependence among different data streams, which is especially appealing in practice for identifying clustered OC streams.

摘要

传感器技术的快速发展正在促进高维数据流 (HDS) 的收集。除了实时检测潜在的失控 (OC) 模式外，HDS 的信号后故障诊断在统计过程控制领域变得越来越重要，以隔离异常数据流。关于该主题的现有方法的主要局限性包括（i）它们无法获得可靠的诊断结果，因为它们的性能变化很大，以及（ii）不同流之间的信息相关性经常被它们忽略。本文阐述了使用大规模多次测试监测相关HDS的可靠故障诊断问题。在隐马尔可夫模型依赖的框架下，提出了新的诊断程序，它可以将错过的发现超出 (MDX) 控制在所需的水平。广泛的数值研究和一些理论结果表明，所提出的程序可以正确控制 MDX，从而实现高可靠性和高效率的诊断。此外，通过利用不同数据流之间的依赖关系，可以显着提高它们的诊断性能，这在实践中对于识别集群 OC 流特别有吸引力。