John F. MacGregor

Exponentially weighted moving average control schemes: properties and enhancements

Roberts (1959) first introduced the exponentially weighted moving average (EWMA) control scheme. Using simulation to evaluate its properties, he showed that the EWMA is useful for detecting small shifts in the mean of a process. The recognition that an EWMA control scheme can be represented as a Markov chain allows its properties to be evaluated more easily and completely than has previously been done. In this article, we evaluate the properties of an EWMA control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value. A design procedure for EWMA control schemes is given. Parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process. In addition, several enhancements to EWMA control schemes are considered. These include a fast initial response feature that makes the EWMA control scheme more sensitive to start-up problems, a combined Shewhart EWMA that provides protection against both larg...

Multivariate SPC Charts for Monitoring Batch Processes

The problem of using time-varying trajectory data measured on many process variables over the finite duration of a batch process is considered. Multiway principal-component analysis is used to compress the information contained in the data trajectories into low-dimensional spaces that describe the operation of past batches. This approach facilitates the analysis of operational and quality-control problems in past batches and allows for the development of multivariate statistical process control charts for on-line monitoring of the progress of new batches. Control limits for the proposed charts are developed using information from the historical reference distribution of past successful batches. The method is applied to data collected from an industrial batch polymerization reactor.

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 ..

Multi-way partial least squares in monitoring batch processes

Multivariate statistical procedures for monitoring the progress of batch processes are developed. Multi-way partial least squares (MPLS) is used to extract the information from the process measurement variable trajectories that is more relevant to the final quality variables of the product. The only information needed is a historical database of past successful batches. New batches can be monitored through simple monitoring charts which are consistent with the philosophy of statistical process control. These charts monitor the batch operation and provide on-line predictions of the final product qualities. Approximate confidence intervals for the predictions from PLS models are developed. The approach is illustrated using a simulation study of a styrene-butadiene batch reactor.

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.

Fault diagnosis with multivariate statistical models part I: using steady state fault signatures

Abstract Multivariate statistical approaches to fault detection based on historical operating data have been found to be useful with processes having a large number of measured variables and when causal models are unavailable. For fault isolation or diagnosis they have been less powerful because of the non-causal nature of the data on which they are based. To improve the fault isolation with these methods, additional data on past faults have been used to supplement the models. A critical review of this fault isolation literature is given, and an improved approach capable of handling both simple and complex faults is presented. This approach extracts fault signatures that are vectors of movement of the fault in both the model space and the residual space. The directions of these vectors are then compared to the corresponding vector directions of known faults in the fault library. Isolation is then based on a joint plot of the angles between the vectors of the current fault and those of the known faults. Although the fault signatures are based on steady-state information, the methodology assumes that time varying disturbances due to common-cause sources are always present, and it is applied to dynamic data as soon as a fault is detected. The method is demonstrated using a simulated CSTR system with feedback control, and is shown to be effective in isolating both simple and complex faults.

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.

Missing data methods in PCA and PLS: Score calculations with incomplete observations

Abstract A very important problem in industrial applications of PCA and PLS models, such as process modelling or monitoring, is the estimation of scores when the observation vector has missing measurements. The alternative of suspending the application until all measurements are available is usually unacceptable. The problem treated in this work is that of estimating scores from an existing PCA or PLS model when new observation vectors are incomplete. Building the model with incomplete observations is not treated here, although the analysis given in this paper provides considerable insight into this problem. Several methods for estimating scores from data with missing measurements are presented, and analysed: a method, termed single component projection, derived from the NIPALS algorithm for model building with missing data; a method of projection to the model plane; and data replacement by the conditional mean. Expressions are developed for the error in the scores calculated by each method. The error analysis is illustrated using simulated data sets designed to highlight problem situations. A larger industrial data set is also used to compare the approaches. In general, all the methods perform reasonable well with moderate amounts of missing data (up to 20% of the measurements). However, in extreme cases where critical combinations of measurements are missing, the conditional mean replacement method is generally superior to the other approaches.