Improved drift handling in melamine resin production by ensemble partial least squares and incremental Page-Hinkley testing

Supervision of multivariate calibration models is pivotal in order to maintain process safety and product quality. Leverage (Hotelling’s T2-) and model miss-fit (Q-) statistics have gained wide popularity in statistical process control (SPC) applications owing to the complementary information they convey when predicting new samples1. However, mere violation of the typical control limits (e.g. 95% and 99% confidence limits) does not necessarily imply that model predictions are inaccurate and T2- and Q statistics might thus be of limited use to reliably determine the time-point when a model fails to extrapolate beyond the calibration samples. We here present a novel SPC tool which is based on the disagreement (variance) of a committee of partial least squares (PLS) models and its Page-Hinkley statistic2. For the latter we use incremental updates of first and second order statistics to derive dynamically adapting control limits, based on which changes/drifts can be identified at an early stage. We test our statistical change estimator on a dataset comprising Fourier Transform infrared (FT-NIR) spectra from a melamine resin batch process and compare its usefulness for drift detection with well-established measures for the assessment of model reliability. We further undertake a multivariate drift analysis in order to properly react to the underlying latent phenomenon. Therefore, we design a linear filter that - once the initial model significantly fails to make reliable predictions about batch maturity (i.e. the cloud point) - allows keeping predictions within the accuracy requirements of the company. This extends the lifespan of the calibration model for several months without requiring time-intensive off-line re-calibration cycles.