An economic nxà-chart approach to the joint control of the means of independent quality characteristics

In controlling the mean of a multivariate normally distributed quality characteristic the main disadvantage of the global T²-control charts is that they don’t indicate the component of the quality characteristic which gives rise to an alarm. To avoid this disadvantage the joint use of nx-charts is proposed in this paper, where-for the sake of simplicity-the investigations are restricted to the case of independent components and to one-sided nx-charts. On the basis of an economic objective function an approximation to the optimal design of the nx-charts procedure is derived and discussed. It turns out that at least in the bivariate case the nearly optimal economic design is very close to the exact solution.