An approach to controlling two dependent process steps with autocorrelated observations

The observations from the process output are always assumed independent when using a control chart to monitor a process. However, for many processes the process observations are autocorrelated. This autocorrelation can have a significant effect on the performance of the control chart. This paper considers the problem of monitoring the mean of a quality characteristic X on the first process step and the mean of a quality characteristic Y on the second process step, in which the observations X can be modeled as an AR(1) model and observations Y can be modeled as a transfer function of X since the state of the second process step is dependent on the state of the first process step. To effectively distinguish and maintain the state of the two dependent process steps, the Shewhart control chart of residual and the cause-selecting control chart are proposed. The proposed control charts’ performance is measured by the rate of alarm on the proposed charts. From numerical analysis, it shows that the performance of the proposed control charts is much better than the misused Hotelling T² control chart and the individual Shewhart X and Y control charts.