Reliable Post-Signal Fault Diagnosis for Correlated High-Dimensional Data Streams

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.