Monitoring simple linear profiles in multistage processes by a MaxEWMA control chart

• An approach is proposed for monitoring simple linear profiles in multistage processes.
• All parameters in all stages are monitored simultaneously by one statistic at a time.
• The approach benefits from the diagnostic feature to identify out-of-control stage.
• The approach has also the diagnostic feature to identify out-of-control parameters.
• The proposed method performs well under various autocorrelation and shift scenarios.

In this paper, an approach is proposed for monitoring simple linear profiles in multistage processes in Phase II where, the effect of the cascade property involved in multistage processes is first removed using U statistic. Then, a MaxEWMA control scheme is constructed based on the adjusted parameters for simultaneous monitoring of all the parameters of simple linear profiles in all stages by plotting only one statistic at a time. The proposed chart also benefits from the diagnostic features to identify the out-of-control stage in addition to the out-of-control parameter after receiving a signal. The performance of the proposed control scheme is evaluated and compared to the competing methods for different autocorrelation coefficients and shift scenarios by extensive simulation experiments. The results show that the proposed method performs well in detecting process shifts and outperforms the competing methods in almost all shift scenarios. In addition, the diagnostic features of the proposed method provide accurate results in identifying the out-of-control stage and out-of-control parameter. The effect of parameter estimation on the performance of control charts is also investigated. Furthermore, two numerical illustrations are given at the end to show the application of the proposed scheme.