An EWMA control chart for the mean of individual streams in multiple stream processes

Abstract

In a multiple stream process (MSP) a product is manufactured in a number of streams in parallel. The traditional tool for monitoring MSPs, the group control chart (GCC), does not take into account that typically the value of the quality variable in each stream is the sum of a component common to all streams and an individual component, of the particular stream. This may render the GCC ineffective in detecting shifts in the mean of individual streams. Based on this two-components model, we propose an exponentially weighted moving average (EWMA) GCC to monitor the means of the individual streams components. We optimize its design (minimizing the ARL for given shifts in the mean of a stream) and compare their ARLs with the ones of other existing charts devised for two-components MSPs. For this comparison, we needed to obtain optimal designs of these previous charts too, which were not available in the literature; this is an additional contribution of our work. The ARLs of the charts were obtained by simulation, with a number of runs sufficiently large to ensure precise results. The results show that the proposed chart outperforms the previous ones, becoming thus recommended for the statistical control of MSPs.