A two-step method for monitoring normally distributed multi-stream processes in high dimensions

This paper proposes a two-step method for monitoring high-dimensional normally distributed multi-stream processes. The first step consists of a single Hotelling chi-square chart, while the second includes a Shewhart chart for each stream to diagnose off-target streams. The second step is needed only if an alarm triggered in the first step. The required control limits and performance measures such as statistical power and ARLs are computed exactly and efficiently for both cases of independent and dependent streams. The new method performs well in detecting small shifts and has a competitive statistical performance relative to a recent method.