Variable Selection Methods for Process Monitoring

Abstract

In the first stage of a manufacturing process a large number of variables might be available. Then, a smaller number of measurements should be selected for process monitoring. At this point in time, variable selection methods for process monitoring have focused mainly on explained variance performance criteria. However, explained variance efficiency is a minimal notion of optimality and it does not necessarily result in an economically desirable selected subset, as it makes no statement about the measurement cost or other engineering criteria. Without measuring cost many decisions will be impossible to make. In this article, we propose two new methods to select a reduced number of relevant variables for multivariate statistical process control that makes use of engineering, cost and variability evaluation criteria. In the first method we assume that a two-class system is used to classify the variables as primary and secondary based on different criteria. Then a double reduction of dimensionality is applied to select relevant primary variables that represent well the whole set of variables. In the second methodology a cost-utility analysis is used to compare different variable subsets that may be used for process monitoring. The objective of carrying out a cost–utility analysis is to compare one use of resources with other possible uses. To do this, to any process monitoring procedure is assigned a score calculated as ratio of the cost at which it might be obtained to explained variance that it might provide. The subset of relevant variables is selected in a manner that retains, to some extent, the structure and information carried by the full set of original variables.