Monitoring multistage processes with autocorrelated observations

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.