A Sparse LeadingEigenvalueDriven Control Chart for Phase I Analysis of HighDimensional Covariance Matrices In statistical process control (SPC), a proper Phase I analysis is essential to the success of Phase II monitoring. With recent progresses in sensor technology and data collection systems, Phase I analysis of highdimensional (HP) 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 HP process variability. Motivated by this, this paper develops a Sparse Leading Eigenvalue Driven control chart for retrospectively monitoring HP 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 L xe2x88x9e 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.

Principal Component Analysis for High Dimension Stochastic Gaussian Process Model Fitting Stochastic Gaussian Process models are widely used in stochastic simulation metamodeling to predict the response of noisy simulations. Often, many realworld engineering problems are highdimensional (more than 10 dimensions), and the Gaussian Process modelsu0027 prediction for such highdimensional inputs are computationally expensive due to multiple inversions of the covariance matrix. Therefore, the xe2x80x9ccurse of dimensionalityxe2x80x9d on these models prevent them from being used in a highdimensional setting. To overcome this problem, a methodology for highdimensional stochastic Gaussian Process modelsu0027 fitting is proposed in this paper. The input data is first projected onto a reduced set of dimensions found by Principal Component Analysis before being used to fit the model. Numerical experiments prove that the method helps significantly in reducing the computation time.