Statistical Process Monitoring

Monitoring and control of batch processes are crucial tasks in a wide variety of industrial processes such as pharmaceutical processes, specialty chemicals production, polymer production and fermentation processes. Batch processes are characterized by prescribed processing of raw materials for a finite duration to convert them to products. A high degree of reproducibility is necessary to obtain successful batches. With the advent of process computers and recent developments in on-line sensors, more data have become available for evaluation. Usually, a history of the past successful and some unsuccessful batches exist. Data from successful batches characterize the normal process operation and can be used to develop empirical process models and process monitoring systems.

The goal of statistical process monitoring (SPM) is to detect the existence, magnitude, and time of occurrence of changes that cause a process to deviate from its desired operation. The methodology for detecting changes is based on statistical techniques that deal with the collection, classification, analysis, and interpretation of data. Traditional statistical process control (SPC) has focused on monitoring quality variables at the end of a batch and if the quality variables are outside the range of their specifications, making adjustments (hence control the process) in subsequent batches. An improvement of this approach is to monitor quality variables during the progress of the batch and make adjustments if they deviate from their expected ranges. Monitoring quality variables usually delays the detection of abnormal process operation because the appearance of the defect in the quality variable takes time. Information about quality variations is encoded in process variables. The measurement of process variables is often highly automated and more frequent, enabling speedy refinement of measurement information and inferencing about product quality. Monitoring of process variables is useful not only for assessing the status of the process, but also for controlling product quality. When process monitoring indicates abnormal process operation, diagnosis activities are initiated to determine the source causes of this abnormal behavior.

This chapter starts with a review of statistical monitoring techniques for a single variable system. Shewhart charts, cumulative sum (CUSUM), moving average (MA) and exponentially weighted moving average (EWMA) methods are discussed in Section 6.1. Monitoring of multivariable batch processes by using multivariate statistical process monitoring (MSPM) methods is discussed in the subsequent sections of the Chapter. Most MSPM techniques rely on empirical process models developed from process data using methods discussed in Chapter 4. Empirical models based on principal components analysis (PCA), partial least squares (PLS), functional data analysis, multiscale analysis, and artificial neural networks (ANNs) can be used for monitoring batch or continuous processes. It is usually easier to visualize these methods in terms of data from continuous processes operating around a steady state value. Consequently, the discussion in Section 6.2 focuses first on the application of these methods to generic continuous processes. Then, the determination of landmarks that separate different phases of a batch process and equalization of batch data lengths are discussed in Section 6.3. The application of multivariable statistical monitoring (MSPM) methods to batch process data is introduced in Section 6.4. The multiway PCA (MPCA) method is discussed first. Other modeling and monitoring techniques such as the multivariate covariates regression method, the multiblock MPCA and MPLS, various three-way methods, and multiscale SPM techniques based on wavelets are introduced in Section 6.4.6. On-line monitoring of batch processes during the progress of the batch is discussed in Section 6.5. Techniques based on estimation of variable trajectories, hierarchical PCA and estimation of final product quality are presented. Section 6.6 introduces a framework for monitoring successive batch runs for disturbances that evolve through several batches, leading to gradual drifts in product quality.

For the sake of simplicity and realism, it will be assumed that each measurement will be made only once (no repeated measurements) except for Section 6.1. For multivariable continuous processes, the index i will denote the variables and j the samples (measurements) with the upper limits indicated by m and n, respectively. For multivariable batch processes, traditionally i denotes the number of batches, j the number of variables, and k the number of samples, with the upper limits indicated by I, J, K, respectively. This notation will be followed in the text.

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