Comparative case study of finite mixture and T2-Hotelling control charts for multiple stream monitoring

The multiple stream process involves equipment with several modules producing the same items, but with respective random variables’ subpopulations. This particularity demands specific control charts for the statistical processes monitoring. Among the initiatives proposed are the finite mixture control chart and T2-Hotelling control chart, but there are no comparative studies between them. This article aims to study and compare the proposed use of a finite mixture control chart with the T2-Hotelling control chart for monitoring the multiple stream process (MSP). The modeling and simulation were performed using actual data from the dietary sector to develop an illustrative case. The results show that the T2-Hotelling charts’ performance was superior in detecting special causes and generating false alarms about the process and supplementary to having less mathematical difficulty in implementing. However, the finite mixture chart is a more recently used approach, considering the literature’s occurrence, compared with the T2-Hotelling chart. Furthermore, the finite mixture chart considering all streams and the variability between them in just one control chart is more straightforward in terms of sampling, but more difficult in mathematical terms for its application. In conclusion, the finite mixture and T2-Hotelling charts are suitable for solving MSP, monitoring with no losing information on each stream variability, and not masking effects from special causes in the process.