Monitoring multistage processes with autocorrelated observations
针对多阶段制造过程中时间自相关导致传统控制图失效的问题，提出基于投影和条件选择的多元控制图CBAM和条件MEWMA，有效检测均值偏移，尤其对小偏移敏感。
In multistage manufacturing processes, autocorrelations within stages over time are prevalent and the classical control charts are often ineffective in monitoring such processes. In this paper, we derive a linear state space model of an autocorrelated multistage process as a vector autoregressive process, and construct novel multivariate control charts, CBAM and Conditional-based MEWMA, for detecting the mean changes in a multistage process based on a projection scheme by incorporating in-control stage information. When in-control stages are unknown, finding in-control stages is a challenging issue due to the autocorrelations over time and the sequential correlations between stages. To overcome this difficulty, we propose a conditional-based selection that chooses stages with strong evidences of in-control stage using the cascading property of multistage processes. The information of selected stages is effectively utilised in obtaining powerful test statistics for detecting a mean change. The performance of the proposed charts is compared with other existing procedures under different scenarios. Both simulation studies and a real example show the effectiveness of the conditional-based charts in detecting a wide range of small mean shifts compared with the other existing control charts.