SPECIAL ISSUE - RESEARCH ARTICLE Calibration model fusion Helene Fog Froriep Halberg 1 | Anette Yde Holst 2 | Niels Kaufmann 2 | Rasmus Bro 1 1 Department of Food Science, University of Copenhagen, Copenhagen, Denmark 2 Arla Foods amba, Viby, Denmark Correspondence Rasmus Bro, Department of Food Science, University of Copenhagen, Copenhagen, Denmark. Email: rb@life.ku.dk Abstract Calibration model maintenance is often overlooked but is a significant part of successful use of multivariate calibration models, for example, in process moni- toring and optimization. In some cases, companies are maintaining tens or even hundreds of calibration models. This could be partial least squares (PLS) calibra- tion models pertaining to different recipes or raw materials or neural network based models covering different production sites. Maintaining such a high num- ber of models is cumbersome and expensive. Sometimes, a solution presented for this problem is to merge all the models into one, but this often comes at the expense of significantly higher prediction errors. In this paper, we suggest a new approach for rationally merging calibration models in order to optimally balance the prediction error and maintenance workload. We do this by systematically merging models that lower the error as much as possible and hence provide a sort of optimal clustering or fusion of calibration models. We showcase the new approach on a case based on infrared spectroscopy applied to dairy production. 1 | INTRODUCTION Multivariate calibration is an omnipresent and critically important methodology in fields as diverse as food production, pharmaceutics, petrochemical industry, agriculture, and many other. 1,2 Maintenance of calibration models is an impor- tant aspect for assuring that the predictions are trustworthy. Many papers and standards have dealt with calibration transfer and instrument standardization, the subject of making sure that the calibration model will also work when essential conditions have changed. This could, for example, be when the model is applied on data from a new instru- ment, when sample constitution changes, or when production recipes are modified. Piece-wise direct standardization 3,4 or simple slope intercept corrections 5 are some of the methods commonly used for updating models. For a review on calibration model maintenance, see Workman (2018). 6 There are other aspects of calibration model maintenance though. One important aspect seems to have evaded sci- entific attention—if and how to combine calibration models. A typical scenario could be a situation where a company has a calibration model for each recipe/product. Many of those products may, in fact, be similar, and it would stand to reason that combining the models of two similar products could improve predictions while at the same time lowering the maintenance overhead. Maintaining one model instead of two will be less cumbersome all things equal. Imagine a case where there are not two but maybe hundreds of models. The potential gains may be significant. It may even be worth merging the models into one or a few models even though the predictions will have slightly worse quality. This will depend on the use case. In this paper, we develop a tool that can merge multivariate calibration models in a rational and scientific manner and allows the user to make an informed choice on how to merge models taking both simplicity and prediction quality into account. We call this calibration model fusion (CAMOFU). Received: 20 January 2021 Revised: 14 March 2021 Accepted: 3 May 2021 DOI: 10.1002/cem.3350 Journal of Chemometrics. 2021;e3350. wileyonlinelibrary.com/journal/cem © 2021 John Wiley & Sons, Ltd. 1 of 8 https://doi.org/10.1002/cem.3350