Article ID: | iaor20106061 |
Volume: | 42 |
Issue: | 10 |
Start Page Number: | 746 |
End Page Number: | 752 |
Publication Date: | Oct 2010 |
Journal: | IIE Transactions |
Authors: | Castillo Enrique del, Runger George, Lian Zilong |
Keywords: | programming: dynamic |
A bounded adjustment strategy is an important link between statistical process control and engineering process control (or closed-loop feedback adjustment). The optimal bounded adjustment strategy for the case of a single variable has been reported in the literature and recently a number of publications have enhanced this relationship (but still for a single variable). The optimal bounded adjustment strategy for a multivariate processes (of arbitrary dimension) is derived in this article. This uses optimization and exploits a symmetry relationship to obtain a closed-form solution for the optimal strategy. Furthermore, a numerical method is developed to analyze the adjustment strategy for an arbitrary number of dimensions with only a one-dimensional integral. This provides the link between statistical and engineering process control in the important multivariate case. Both infinite- and finite-horizon solutions are presented along with a numerical illustration.