Optimizing settings by accounting for uncontrollable material and environmental variables

Process settings that work well for one batch may not work for another due to variation in the uncontrollable variables that characterize environmental and raw material properties, for example. This paper presents an optimization methodology to identify settings for a particular batch based on information about uncontrollable variables in the batch. Also, the methodology predicts whether the batch is likely to produce a successful output or if it should be scrapped. The batch process we consider, that is common in industries such as pharmaceuticals, petroleum, and food processing, is characterized by many, highly correlated input variables. Input variables include those that can be set, such as temperatures and flow rates, as well as the uncontrollable variables. A nonlinear mathematical program identifies the optimal process settings when the distribution of the uncontrollable variables is known. When the distribution is unknown, the optimal process settings are obtained by combining sequential sampling and a robust optimization procedure that takes into account the variability in the sample estimates. The work here is motivated by our research in multivariate process control for batch extrusion processes. We demonstrate the proposed methodology using an extrusion simulation.