An adaptive CUSUM chart for robust monitoring of multivariate processes

Abstract

Statistical process control (SPC) charts are widely utilized in various fields to identify distributional shifts of sequential processes. Conventional SPC charts are designed for cases when in-control (IC) process observations are independent and identically distributed at different observation times and the IC process distribution belongs to a parametric family. In practice, however, these assumptions are rarely valid. To address this issue, there have been some existing discussions in the SPC literature for handling cases where these assumptions are not valid. Although many existing charts are effective for detecting shifts across a wide spectrum when their model assumptions are valid, their optimal performance for detecting shifts depends on the pre-specified parameters. Additionally, further analysis is often required to estimate the time of shift after a signal is given. In this article, we propose a new multivariate online monitoring scheme, where process observations are first preprocessed, including data decorrelation and transformation. Subsequently, this preprocessed data is projected onto a one-dimensional space, and finally, a univariate adaptive control chart is applied to the projected data for online monitoring. The design and implementation of the new method is relatively simple, since it eliminates the need for pre-specifying control chart parameters and provides a formula for determining control limit. Moreover, it can provide an estimate of the shift’s location immediately after a shift is detected. Numerical studies demonstrate that the proposed online monitoring scheme is robust to the IC process distribution and short-range serial correlation, and effective in detecting shifts of various magnitudes.

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