Reducing sampling costs in multivariate SPC with a double-dimension T2 control chart

In some real situations there is the need of controlling p variables of a multivariate process, where p1 out of these p variables are easy and inexpensive to monitor, while the p2=p–p1 remaining variables are difficult and/or expensive to measure. However, this set of p2 variables is important to quickly detect the process shifts. This paper develops a control chart based on the T2 statistic where normally only the set of p1 variables is monitored, and only when the T2 value falls in a warning area the rest of variables (p2) are measured and combined with the sample values from the p1 variables, in order to obtain a new T2 statistic. This new chart is the double dimension T2 (DDT2) control chart. The ARL of the DDT2 chart is obtained and the chart's parameters are optimized using genetic algorithms with the aim of maximizing the performance in detecting a given process shift. The optimized DDT2 chart is compared against the standard T2 chart when all the variables are monitored. The results show that the DDT2 clearly outperforms T2 chart in terms of cost, and in some cases even detects process shifts faster than the latter. In addition, friendly software has been developed with the objective of promoting the real application of this new control chart.