Fault classification for high-dimensional data streams: A directional diagnostic framework based on multiple hypothesis testing

In various modern statistical process control applications that involve high-dimensional data streams (HDDS), accurate fault diagnosis of out-of-control (OC) streams is becoming crucial. The existing diagnostic approaches either focus on moderate-dimensional processes or are unable to determine the shift direction accurately, especially when the signal-to-noise ratio is low. In this paper, we conduct a bold trial and consider the fault classification problem of the mean vector of HDDS where determining the shift direction of the OC streams is important to perform customized repairs. To this end, under the basic assumptions that the in-control data streams are normal with mean 0 and variance 1, and that the high-dimensional observations after the alarm are solely OC, the problem is formulated into a three-classification multiple testing framework, and an efficient data-driven diagnostic procedure is developed to minimize the expected number of false positives and to control the missed discovery rate at given level. The procedure is statistically optimal and computationally efficient, and improves the diagnostic effectiveness by considering directional information, which provides insights to guide further decisions. Both theoretical and numerical results reveal the superiority of the new method.