Multivariate one-sided control charts

Process knowledge can be exploited to improve the performance of control charts and it is not unusual to know that a specific variable shifts above or below its mean under an assignable cause. In such a case, a one-sided control chart is common. The available statistical theory for the one-sided tests is used to provide a reasonable compromise for a numerical procedure to design and implement multivariate solutions. Although simulation is used in the analysis, it is not a direct estimate of performance through simulation. Instead, weights are estimated and these are used to easily set a desired on-target average run length. Furthermore, an interesting quadratic programming solution is incorporated into the analysis. Then the statistical results are extended to a partial one-sided case where only some (not all) variables are known to shift in one direction and the numerical procedure is extended to design and implement the charts. A modern method can blend theory and algorithms into a practical solution. We conclude that modern computer software permits an efficient solution to this problem with meaningful performance advantages over traditional multivariate control charts.