Phase I analysis of high-dimensional covariance matrices based on sparse leading eigenvalues

Abstract

In statistical process control (SPC), a proper Phase I analysis is essential to the success of Phase II monitoring. With recent advances in sensing technology and data acquisition systems, Phase I analysis of high-dimensional data is increasingly encountered. However, the high dimensionality presents a new challenge to the traditional Phase I techniques. A literature review reveals nearly no Phase I techniques in existence for analyzing high-dimensional process variability. Motivated by this, this paper develops a sparse-leading-eigenvalue-driven control chart for retrospectively monitoring high-dimensional covariance matrices in Phase I, denoted as the SLED control chart. The key idea of it is to track changes in the sparse leading eigenvalue between two covariance matrices. Compared to the L 2-type and -type methods, the proposed method can extract stronger signal with less noise. It is shown that the proposed method can gain high detection power, especially when the shift is weak and is not very dense, which is often the case in practical applications.