Control Limits for Monitoring the Average of Correlated Streams

Purpose – An increasing number of manufacturing processes involve multiple streams where the same type of item is produced in a parallel fashion. Traditionally, streams need to be monitored using separate control charts. The number of charts becomes unrealistic as the number of streams increases. This research proposes modified limits for individual measurement group charts to control the average of multiple streams and account for the level of correlation between them.
Methodology – Results of simulation studies were used to develop a mathematical model representing the relationship between the in-control average run length (ARL0), the number of streams, the level of correlation between them, and the half-width of the control limits. The fitted model was confirmed and used to generate tables of recommended values of the half-width to be used in constructing group control charts to achieve a specified level of the ARL0. A similar approach was used to characterize the shift detection capability of the proposed charts.
Findings – The fitted model was confirmed and used to generate tables for modified values of the half-width factor based on the number of streams and the level of correlation between them.
Research limitations – Simulated measurements were generated from the normal distribution assuming that the process variability is in-control and that the streams are equally correlated.
Value – Research findings offer a solution for implementing group control charts to monitor the average of multiple stream processes.

Multiple Stream Processes, Group Control Charts, Charts for Individual
Measurements, Average Run Length