Theodora Kourti

Statistical process control of multivariate processes

Abstract With process computers routinely collecting measurements on large numbers of process variables, multivariate statistical methods for the analysis, monitoring and diagnosis of process operating performance have received increasing attention. Extensions of traditional univariate Shewhart, CUSUM and EWMA control charts to multivariate quality control situations are based on Hotellings T 2 statistic. Recent approaches to multivariate statistical process control which utilize not only product quality data (Y), but also all of the available process variable data (X) are based on multivariate statistical projection methods (Principal Component Analysis (PCA) and Partial Least Squares (PLS)). This paper gives an overview of these methods, and their use for the statistical process control of both continuous and batch multivariate processes. Examples are provided of their use for analysing the operations of a mineral processing plant, for on-line monitoring and fault diagnosis of a continuous polymerization process and for the on-line monitoring of an industrial batch polymerization reactor.

Process analysis, monitoring and diagnosis, using multivariate projection methods

Abstract Multivariate statistical methods for the analysis, monitoring and diagnosis of process operating performance are becoming more important because of the availability of on-line process computers which routinely collect measurements on large numbers of process variables. Traditional univariate control charts have been extended to multivariate quality control situations using the Hotelling T2 statistic. Recent approaches to multivariate statistical process control which utilize not only product quality data (Y), but also all of the available process variable data (X) are based on multivariate statistical projection methods (principal component analysis, (PCA), partial least squares, (PLS), multi-block PLS and multi-way PCA). An overview of these methods and their use in the statistical process control of multivariate continuous and batch processes is presented. Applications are provided on the analysis of historical data from the catalytic cracking section of a large petroleum refinery, on the monitoring and diagnosis of a continuous polymerization process and on the monitoring of an industrial batch process.

Multivariate SPC Methods for Process and Product Monitoring

Statistical process control methods for monitoring processes with multivariate measurements in both the product quality variable space and the process variable space are considered. Traditional multivariate control charts based on X2 and T2 statistics ..

Analysis of multiblock and hierarchical PCA and PLS models

Multiblock and hierarchical PCA and PLS methods have been proposed in the recent literature in order to improve the interpretability of multivariate models. They have been used in cases where the number of variables is large and additional information is available for blocking the variables into conceptually meaningful blocks. In this paper we compare these methods from a theoretical or algorithmic viewpoint using a common notation and illustrate their differences with several case studies. Undesirable properties of some of these methods, such as convergence problems or loss of data information due to deflation procedures, are pointed out and corrected where possible. It is shown that the objective function of the hierarchical PCA and hierarchical PLS methods is not clear and the corresponding algorithms may converge to different solutions depending on the initial guess of the super score. It is also shown that the results of consensus PCA (CPCA) and multiblock PLS (MBPLS) can be calculated from the standard PCA and PLS methods when the same variable scalings are applied for these methods. The standard PCA and PLS methods require less computation and give better estimation of the scores in the case of missing data. It is therefore recommended that in cases where the variables can be separated into meaningful blocks, the standard PCA and PLS methods be used to build the models and then the weights and loadings of the individual blocks and super block and the percentage variation explained in each block be calculated from the results.

Analysis, monitoring and fault diagnosis of batch processes using multiblock and multiway PLS

Abstract Multivariate statistical procedures for the analysis and monitoring of batch processes have recently been proposed. These methods are based on multiway principal component analysis (PCA) and partial least squares (PLS), and the only information needed to exploit them is a historical database of past batches. In this paper, these procedures are extended to allow one to use not only the measured trajectory data on all the process variables and information on measured final quality variables but also information on initial conditions for the batch such as raw material properties, initial ingredient charges and discrete operating conditions. Multiblock multiway projection methods are used to extract the information in the batch set-up data and in the multivariate trajectory data, by projecting them onto low dimensional spaces defined by the latent variables or principal components. This leads to simple monitoring charts, consistent with the philosophy of SPC, which are capable of tracking the progress of new batch runs and detecting the occurrence of observable upsets. Powerful procedures for diagnosing assignable causes for the occurrence of a fault by interrogating the underlying latent variable model for the contributions of the variables to the observed deviation are also presented. The approach is illustrated with databases from two industrial batch polymerization processes.

Comparing alternative approaches for multivariate statistical analysis of batch process data

Batch process data can be arranged in a three‐way matrix (batch × variable × time). This paper provides a critical discussion of various aspects of the treatment of these multiway data. First, several methods that have been proposed for decomposing three‐way data matrices are discussed in the context of batch process data analysis and monitoring. These methods are multiway principal component analysis (MPCA)—also called Tucker1—parallel factor analysis (PARAFAC) and Tucker3. Secondly, different ways of unfolding, mean centering and scaling the three‐way matrix are compared and discussed with respect to their effects on the analysis of batch data. Finally, the role of the time variable in batch process data is considered and methods suggested to predict the per cent completion of batch runs with unequal duration are discussed. Copyright

Experiences with industrial applications of projection methods for multivariate statistical process control

With process computers routinely collecting measurements on large numbers of process variables, multivariate statistical methods for the analysis, monitoring and diagnosis of process operating performance have received increasing attention. Recent approaches to multivariate statistical process control, which utilize not only the product quality data (as traditional approaches have done) but also the available process data, are based on multivariate projection methods (Principal Component Analysis, PCA, and Partial Least Squares, PLS). These methods have been rapidly accepted and utilized by industry. This paper gives a brief overview of these methods and illustrates their use for process monitoring and fault diagnosis with applications to a wide range of industrial batch and continuous processes. Emphasis is placed on the practical issues that arise when dealing with process data. Several of these issues are discussed and solutions are suggested for a successful outcome of the application of these methods in an industrial setting.

Process Analytical Technology Beyond Real-Time Analyzers: The Role of Multivariate Analysis

Process analytical chemistry was recognized by Callis et al. (Analytical Chemistry, 59 (1987): 624A–635A) (1) as a field that extends well beyond real time measurements of process parameters. Process Analytical Technology is taking central stage with the 2004 guidance from the Food and Drug Administration, with a mandate much wider than real time measurements. The pharmaceutical industry is entering a new era. Chemometrics has played an integral part for the real time development of process analytical measurements (multivariate calibration) and it is ready to face the challenge of Process Analytical Technology in this wider definition. The scope of this paper is to demonstrate that multivariate, data based statistical methods, can play a critical role in process understanding, multivariate statistical process control, abnormal situation detection, fault diagnosis, process control and process scale-up, as linked to process analytical technology.

Abnormal situation detection, three-way data and projection methods; robust data archiving and modeling for industrial applications

Abstract Three-way data collected from batch processes and from transitions of continuous processes (start ups, grade to grade transitions, re-starts) are dynamic in nature. The process variables in such processes are both auto correlated and cross correlated. Empirical models developed for the statistical process control of these processes should be capable of capturing the auto and cross correlation of the process variables. Data acquisition and storage should also be performed in a way that preserves these correlations. This paper addresses issues related to acquisition and compression of multivariate data and to modeling of three-way data using projection methods, such as principal component analysis (PCA) and partial least squares (PLS). Other issues such as trajectory alignment, direction of unfolding and modeling data collected from complicated multistage configurations are also discussed.

Analysis, Monitoring and Fault Diagnosis of Industrial Processes Using Multivariate Statistical Projection Methods

Abstract Multivariate statistical procedures based on various versions of principle component analysis (PCA), and partial least squares (PLS), have recently been proposed for the analysis monitoring and diagnosis of industrial processes. These methods are capable of treating processes with large numbers of highly correlated process and quality variables, and can easily handle missing data. The only information needed to exploit them is a good database on historical process operations. In this paper, industrial experiences with these methods based on recent applications in many different industries are presented. Both continuous and batch processes are treated. Multi-block methods are shown to be very useful for treating large continuous processes or multistage batch operations, and multi-way methods are used to treat batch processes where one has time-varying trajectory data on many variables.