Group control charts for monitoring the average of correlated streams

Abstract

In many manufacturing processes, multiple identical parts are made in parallel during a single run. Different inspectors may inspect similar parts, and several assembly lines may produce similar products. These scenarios involve multiple stream processes, where a different set of control charts is traditionally required to monitor the performance of each stream over time. As the number of streams increases, applications become unrealistic. Group control charts offer a more viable alternative. A basic assumption in the traditional application of multiple stream processes charting techniques is that the observations from the multiple stream process under investigation are normally and independently distributed. When these assumptions are satisfied, conventional control charts may be applied. In a practical setting, correlation may be present and may impact the performance of charting scheme. The lack of care provided to the correlation between the streams results in a higher ARL. The in-control ARL associated with the traditional group charts is approximately 370/m, where m is the number of streams. This research investigated the effect of correlation on the rate of false alarms and proposed appropriate values of the half-width (L) to be used in designing group control charts for monitoring the process average. The number of streams (m), level of correlation (r), subgroup size and the half-width are design factors. Results were used to fit a mathematical model representing the relationship between the four factors and the proposed half-width. Additionally, several simulated scenarios were generated and used to evaluate the long-term performance in terms of the average run length (ARL1). Statistical analysis of the results indicated that the corrected half-width correction has an advantage over the traditional group chart in terms of the rate of false alarms.