(202p) Control Limits for Variable Contributions to the Hotelling Statistic. Applications to a Fed-Batch Fermentation Process

During the last decades batch processes experienced a renaissance as products-on-demand and first-to-market strategies impel the need for flexible and specialized production methods. They are mainly devoted to the production of high added value products such as polymers, pharmaceuticals, foods, bio-chemicals and semiconductors.

 Online process performance monitoring and product quality prediction in real time ensure safe and profitable operation of batch processes since they provide the opportunity to take corrective actions before the effects of excursions from normal operation ruin the batch.

 Many successful applications of Multivariate Statistical Process Control for the monitoring and diagnostic of batch processes have been presented. In general, batch progress is monitored by exploiting the information contained in a historical database of successful batches using projection techniques. 

 Monitoring approaches that work in the original measurements space have been successfully applied for batch processes if the number of variables involved is not extremely high and there exist strong non-linear relationships among them that prevent the measurements from being linear combinations. For these cases, original space strategies can perform as well as, o even better than some projection-based techniques (Alvarez et al., 2010). They apply only the Hotelling statistic for detecting the faulty state.

From the monitoring standpoint, determining whether the process can be considered as in-control at a given time is just one step in the procedure. Whenever one observation is believed to show an abnormal behavior, all the effort must be oriented towards finding what the root cause of the deviation is. The activities related to isolating the variables that indicate the faulty state conform what is known as the identification stage, which is frequently performed by calculating the variable contributions to the inflated statistic. The main purpose of evaluating those contributions is to compare the relative influence of each measured variable on the statisticvalue. It is considered that the largest contributions help to reveal the faulty state.

 Recently, a new approach to identify the suspicious measurements when the Hotelling statistic exceeds its critical value was proposed (Cedeño et al., 2012). The methodology consists in finding the Nearest In-Control Neighbour of the observation point by solving a minimization problem. The distance between these points is used to evaluate the relative influence of each measured variable on the Hotelling statistic value. Those variables whose distance measures exceed a certain threshold value help to isolate the root cause of the fault.

 In this work, the Nearest In-Control Neighbour methodology is extended to monitor the operation of batch processes. The calculation of the variable-contributions control limits to the inflated Hotelling statistic for each time interval is a main topic for the industrial application of the strategy. Different formulations of those control limits are proposed and an analysis of their performances is conducted based on identification measures such as: number of precise - ambiguous – incorrect and void identifications (Alvarez et al., 2010) for a fed-batch penicillin fermentation benchmark (Birol et al., 2002).

 References

Alvarez R, Brandolin A, Sánchez M. Batch Process Monitoring in the Original Measurement’s Space, J. of Process Control 2010; 20: 716-725.

Birol G, Ündey C, Çinar A. A Modular Simulation Package for Fed-Batch Fermentation: Penicillin Production. Comp. Chem. Eng. 2002; 26: 1553-1565.

Cedeño M, Rodriguez L, Alvarez R, Sánchez M. A New Approach to Estimate Variable Contributions to the Hotelling’s Statistic. Chem. & Intell. Lab. Sys. 2012; 118: 120-126.