A model-free-based control chart for batch process using U-statistics

Renan Faraon Cintra

doi:10.1016/j.jprocont.2023.103097

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A model-free-based control chart for batch process using U-statistics

2023-12-01

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Renan Faraon Cintra

Valk, Marcio

Danilo Marcondes Filho *

DOI：10.1016/j.jprocont.2023.103097

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Abstract

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Batch processes are known to generate time series of successive measurements of many process variables in each run and the main challenge is to capture and accommodate the variability in the batch domain (batch -to-batch variability) and in the time domain (data with serial correlation). Classical approaches are focused on the first goal by applying multivariate techniques in the columns of a data matrix, in which each row has the data for the entire batch run. Those approaches are grounded in the traditional Multiway Principal Component Analysis (MPCA). Recent approaches are focused on the balance between the two sources, taking into account the time series nature of the data mainly by using time series models and neural network methods to directly accommodate the variability in the time domain. This paper proposes a model-free approach based on U-statistics theory. Through this theory, we can build a group of control charts (named V charts) capable of monitoring batch processes considering both sources of variability. In general, the new batch under monitoring is evaluated according to a group of reference in-control samples, based on the distance measures from those batches. The proposed approach is really flexible since we avoid model identification, parameter estimates issues and it is able to accommodate the within and between batch variability. Additionally, our method is suitable to deal with a wide range of batch data features, since under weak conditions, the distribution of the V statistics remains well known. It makes the V-based charts able to be used in different kinds of processes. We are focused here on controlling changes caused by data drifts (including trends) and by data serial correlation (data dynamics). Through the simulated and real batch process, we show that the V charts work well, including a scenario with very few reference batches available.

Keywords:

Batch process

U-statistics

Control charts

High dimensional

Features detection

Fault diagonis