Performance assessment and improvement of control charts for statistical batch process monitoring

Abstract

This paper describes the concepts of statistical batch process monitoring and the associated problems. It starts with an introduction to process monitoring in general which is then extended to batch process monitoring. The performance of control charts for batch process monitoring is discussed by means of two performance indices: the overall type I error and the action signal time. Problems associated with the existing approach are discussed and highlighted. Improvements are suggested and checked with the performance indices. To evaluate the effect of the proposed improvements as well as to assess the performance of the existing approach, an industrial batch production process is used.

Multi‐phase analysis framework for handling batch process data

“…Now let us focus on the performance indices of the on-line monitoring system developed for every model (lower part of Table III). The results confirmed that the OTI is closer to the ISL for incoming data when using a leave-one-out strategy in the correction of the limits [11,31] than when this strategy is not used in the correction (the latter result not shown). Nonetheless, the batchwise approach presents a very low OTI value for the D-statistic.…”

“…condition in (iii.5) is satisfied and M 2 is selected, so that at this point the MP model has two phases with one LV. The first phase is divided once again yielding phases [1,31] and [32,44] and then this branch of the recursion is stopped. The second phase is also split up, yielding phases [45, 109] and [110,144].…”

“…This can be seen in the fact that the OTI for incoming data-that is data not used for calibration-is very different to the ISL. The OTI-ISL mismatch is greatly relaxed if the control limits are readjusted using a leave-one-out procedure [11,31]. Following this procedure, a batch is separated each time and the model and control limits are computed from the remaining batches.…”

The best approaches in the on-line monitoring of batch processes based on PCA: Does the modelling structure matter?

“…In the monitoring charts, the control limits are initially estimated from theoretical results [17,18] and then adjusted using a leave-one-out approach [13,27] for an imposed significance level (ISL) of 1%. This value is the expected percentage of faults for a batch under NOC.…”

Using warping information for batch process monitoring and fault classification

“…Typically, two Shewhart control charts based on the Hotelling-T 2 and Squared Prediction Error (SPE) statistics are designed. Their control limits (thresholds) are estimated from normal operating conditions (NOC) process data and later adjusted using cross-validation techniques for an imposed significance level (ISL) [12,13]. Once the scheme is designed, new measurements from a new batch data can be projected onto the data model, yielding to the aforementioned multivariate statistics, to check for the correct performance of the process.…”