Hotelling T² chart using the generalized multiple dependent state sampling scheme

This research proposes a multivariate control chart, whose parameters are optimized using genetic algorithms (GA) in order to accelerate the detection of a change in the vector of means.

This chart is based on a variation of the Hotelling T² chart using a sampling scheme called generalized multiple dependent state sampling. For the analysis of performances of this chart, the out-of-control average run length (ARL) values were used for different scenarios. In this comparison, it was considered the classic Hotelling T² chart and the T² chart using the scheme called multiple dependent state sampling.

It was observed that the new chart with its optimized parameters is more efficient to detect an out-of-control process. Additionally, a sensitivity analysis was performed, and it was concluded that the best yields are obtained when the change to be considered in the optimization is small. An application in the resolution of a real problem is given.

In this research, a multivariate control chart is proposed based on the Hotelling T² statistic but adding a sampling scheme. This makes this control chart more efficient than the classic T² chart because the new chart not only uses the current information of the T² statistic but also conditions the decision to consider a process as “in- control” on the statistic's previous information. The practitioner can obtain the optimal parameters of this new chart through a friendly program developed by the authors.