Optimal multivariate control charts based on linear combination of normal variables

In some productive processes where normal variables intervene, it is necessary to control specific directions of shifts (increments or decrements) in the mean vector. Many multivariate control charts base their statistics on quadratic forms and do not rapidly detect a shift in a specific direction. In this paper, we propose two charts based on the linear combination of correlated normal variables, the linear combination of normal variables (LCN) and linear combination of principal components (LCPC). These charts were designed to detect a specific shift in the process. To analyse the performances of these charts, we have developed a friendly program that finds the best parameters through genetic algorithms (GA). This algorithm minimises the out-of-control average run length (ARL) for a proposed shift in the mean vector under the restriction of a desired in-control ARL value. The proposed control charts are Shewhart type, which show better performances than the Hotelling T 2 chart.