Adaptive multivariate EWMA charts for monitoring sparse mean shifts based on parameter optimization design

Abstract

High-dimensional data is becoming increasingly important in modern manufacturing environments, while brings difficulties for process monitoring at the same time, especially for the detection of sparse mean shifts. Several control schemes like VS-MEWMA and LEWMA have been proposed on basis of variable selection techniques recently. However, these schemes with constant smoothing parameters may perform poorly when the actual magnitude of mean shifts is significantly different from the assumed one. In this paper, to solve this problem, we focus on obtaining the optimal smoothing parameter of a specific shift range. It is proposed to minimize the expectation weighted run length (EWRL) by assigning a probability distribution to the shift magnitude. Therefore two improved MEWMA control charts that adaptively obtain the optimal parameters are proposed, leading to adaptive VS-MEWMA (AVS-MEWMA) and adaptive LEWMA (ALEWMA) schemes for succeeding in monitoring sparse mean shifts. The superiorities of the proposed scheme are illustrated by a real data example.