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This study aims to design a multivariate control chart that improves the applicability of the traditional Hotelling T² chart. This new type of multivariate control chart displays sufficient information about the states and relationships of the variables in the production process. It is used to make better quality control decisions during the production process.

Multivariate data are collected at an equal time interval and are represented by nodes of the graph. The edges connecting the nodes represent the sequence of operation. Each node is plotted on the control chart based on their Hotelling T² statistical distance. The changing behavior of each pair of input and output nodes is studied by the neural network. A case study from the cement industry is conducted to validate the control chart.

The finding of this paper is that the points and lines in the classic Hotelling T² chart are effectively substituted by nodes and edges of the graph respectively. Nodes and edges have dimension and color and represent several attributes. As a result, this control chart displays much more information than the traditional Hotelling T² control chart. The pattern of the plot represents whether the process is normal or not. The effect of the sequence of operation is visible in the control chart. The frequency of the happening of nodes is recognized by the size of nodes. The decision to change the product feature is assisted by finding the shortest path between nodes. Moreover, consecutive nodes have different behaviors, and that behavior change is recognized by neural network.

Modifying the classical Hotelling T² control chart by integrating with the concept of graph theory and neural network is new of its kind.