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 Control limits for the proposed charts are developed using information from the historical reference distribution of past successful batches.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.

[1]  Ralph B. D'Agostino,et al.  Goodness-of-Fit-Techniques , 2020 .

[2]  S. Wold,et al.  Multi‐way principal components‐and PLS‐analysis , 1987 .

[3]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[4]  George E. P. Box,et al.  Statistical process monitoring and feedback adjustment: a discussion , 1992 .

[5]  J. Macgregor,et al.  The exponentially weighted moving variance , 1993 .

[6]  John F. MacGregor,et al.  ASQC Chemical Division Technical Conference 1971 Prize Winning Paper Some Problems Associated with the Analysis of Multiresponse Data , 1973 .

[7]  D. W. Osten,et al.  Selection of optimal regression models via cross‐validation , 1988 .

[8]  W. T. Tucker,et al.  Algorithmic statistical process control: concepts and an application , 1992 .

[9]  M. Stone.  Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[10]  Toshiomi Yoshida,et al.  Real-time qualitative analysis of the temporal shapes of (bio) process variables , 1992 .

[11]  Benjamin C. Kuo,et al.  AUTOMATIC CONTROL SYSTEMS , 1962, Universum:Technical sciences.

[12]  S. Wold,et al.  Principal component analysis of multivariate images , 1989 .

[13]  B. Efron.  How Biased is the Apparent Error Rate of a Prediction Rule , 1986 .

[14]  Gerald J. Hahn,et al.  Adapting control charts to meet practical needs: a chemical processing application , 1987 .

[15]  Bruce H. Krogh,et al.  On-Line Trajectory Encoding for Discrete-Observation Process Monitoring , 1992 .

[16]  John F. MacGregor,et al.  Monitoring Batch Processes , 1996 .

[17]  T. W. Tucker,et al.  Application of SPC techniques to batch units , 1989 .

[18]  B. Kowalski,et al.  Tensorial resolution: A direct trilinear decomposition , 1990 .

[19]  G. Box.  Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification , 1954 .

[20]  H. Lilliefors.  On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown , 1967 .

[21]  B. Efron.  Estimating the Error Rate of a Prediction Rule: Improvement on Cross-Validation , 1983 .

[22]  J. Macgregor,et al.  Monitoring batch processes using multiway principal component analysis , 1994 .

[23]  Age K. Smilde,et al.  Three‐way methods for the calibration of chromatographic systems: Comparing PARAFAC and three‐way PLS , 1991 .

[24]  B. Skagerberg,et al.  Multivariate data analysis applied to low-density polyethylene reactors , 1992 .

[25]  Dominique Bonvin,et al.  Target factor analysis for the identification of stoichiometric models , 1990 .

[26]  Victor Chew,et al.  Simultaneous Prediction Intervals , 1968 .

[27]  S. Wold.  Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models , 1978 .

[28]  D. G. Watts,et al.  Spectral analysis and its applications , 1968 .

[29]  Paul Geladi,et al.  Analysis of multi-way (multi-mode) data , 1989 .

[30]  W. T. Tucker,et al.  Algorithmic Statistical Process Control: An Elaboration , 1993 .

[31]  O. Prinz,et al.  MONITORING DISCONTINUOUS REACTORS USING FACTOR-ANALYTICAL TECHNIQUES , 1992 .

[32]  Philip K. Hopke,et al.  Methodological study applying three-mode factor analysis to three-way chemical data sets , 1990 .

[33]  J. E. Jackson.  A User's Guide to Principal Components , 1991 .

[34]  Peter Bauer,et al.  An Extension of the MOSUM Technique for Quality Control , 1980 .

[35]  Wojtek J. Krzanowski,et al.  Cross-validatory choice in principal component analysis; some sampling results , 1983 .

[36]  D. R. Jensen,et al.  A Gaussian Approximation to the Distribution of a Definite Quadratic Form , 1972 .

[37]  J. Stuart Hunter,et al.  The exponentially weighted moving average , 1986 .

[38]  Thomas E. Marlin,et al.  Multivariate statistical monitoring of process operating performance , 1991 .

[39]  Wojtek J. Krzanowski,et al.  Cross-Validation in Principal Component Analysis , 1987 .

[40]  John F. MacGregor,et al.  Process monitoring and diagnosis by multiblock PLS methods , 1994 .

[41]  J. E. Jackson,et al.  Control Procedures for Residuals Associated With Principal Component Analysis , 1979 .

[42]  Stephen Warwick Looney,et al.  A comparison of tests for multivariate normality that are based on measures of multivariate skewness and kurtosis , 1992 .

[43]  Nola D. Tracy,et al.  Multivariate Control Charts for Individual Observations , 1992 .