Many of the most popular pre-processing methods for Affymetrix expression arrays, such as RMA, gcRMA, and PLIER, simultaneously analyze data across a set of predetermined arrays to improve precision of the final measures of expression. One problem associated with these algorithms is that expression measurements for a particular sample are highly dependent on the set of samples used for normalization and results obtained by normalization with a different set may not be comparable. A related problem is that an organization producing and/or storing large amounts of data in a sequential fashion will need to either re-run the pre-processing algorithm every time an array is added or store them in batches that are pre-processed together. Furthermore, pre-processing of large numbers of arrays requires loading all the feature-level data into memory which is a difficult task even with modern computers. We utilize a scheme that produces all the information necessary for pre-processing using a very large training set that can be used for summarization of samples outside of the training set. All subsequent pre-processing tasks can be done on an individual array basis. We demonstrate the utility of this approach by defining a new version of the Robust Multi-chip Averaging (RMA) algorithm which we refer to as refRMA.