Multivariate statistical process

Chen, J., Bandoni, A., and Romagnoli, J. A. (1996). Robust PCA and normal region in multivariable statistical process monitoring. AIChE J. 42, 3563-3566. 

Martin, E. B., Morris, A. J., and Zhang, J. (1996). Process performance monitoring using multivariate statistical process control. IEE Proc. Control Theory 143, 132. 

QA, quality attributes SPC/MSPC, statistical process control/multivariate statistical process control CPPs, critical process parameters. 

All experiments were set np so as to be realistic scenarios with respect to multivariate statistical process control (MSPC). The pilot plant grannlator is operated exactly as the industrial scale counterpart, but most of the experiments inclnded mnch more severe variation than will usually be found in an otherwise stable industrial production sitnation of similar duration (e.g. it is normally not necessary to change nozzle types, or to change prodnct types within snch short intervals). 

DRIFT-IR) spectroscopy was also used for polymorphic characterization. The authors detail the application of multivariate techniques, multivariate statistical process control (MSPC), PC A and PLS, to the spectroscopic data for a simple yet powerful, rapid evaluation of the given crystalhzation process. ... 

At-line PAT data nsed directly without conversion back to the original variables space - e.g., MVI (Mnltivariate Identification), MSPC (multivariate statistical process control). 

MSPC multivariate statistical process PCR principal component regression... 

The control can be enabled by multivariate statistical process control (MSPC) using process models, control charts and the like. 

A technique known as multivariate statistical process control (MVSPC). 

A bioprocess system has been monitored using a multi-analyzer system with the multivariate data used to model the process.27 The fed-batch E. coli bioprocess was monitored using an electronic nose, NIR, HPLC and quadrupole mass spectrometer in addition to the standard univariate probes such as a pH, temperature and dissolved oxygen electrode. The output of the various analyzers was used to develop a multivariate statistical process control (SPC) model for use on-line. The robustness and suitability of multivariate SPC were demonstrated with a tryptophan fermentation. 

Cimander, C. Mandenius, C.-F., Online monitoring of a bioprocess based on a multi-analyser system and multivariate statistical process modelling /. Chem. Technol. Biotechnol. 2002, 77, 1157-1168. 

M Kano, S Hasebe, I Hashimoto, and H Ohno. Evolution of multivariate statistical process control Independent component analysis and external analysis. Comput. Chem. Engg., 28(6-7) 1157-1166, 2004. 

RL Mason and JC Young. Multivariate Statistical Process Control with Industrial Applications. ASA-SIAM, Philadelphia, 2002. 

GC Runger and FB Alt. Choosing principal components for multivariate statistical process control. Commun. Statist. - Theory Methods, 25(5) 909-922, 1996. 

E Tatara and A Cinar. An intelligent system for multivariate statistical process monitoring and diagnosis. ISA Trans., 41 255-270, 2002. 

M Weighell, EB Martin, M Bachmann, AJ Morris, and J Friend. Multivariate statistical process control applied to an industrial production facility. In Proc. of ADCHEM 91, pages 359-364, 1997. 

BM Wise, DJ Veltkamp, NL Ricker, BR Kowalski, SM Barnes, and V Arakali. Application of multivariate statistical process control (M-SPC) to the West Valley slurry-fed ceramic melter process. In Proceedings of Waste Management 91, pages 169-176, Tucson, AZ, 1991. 

Kourti, T., and J. F. MacGregor, 1996. Multivariate Statistical Process Control methods for Monitoring, Diagnosing Process and Product Performance. J. Qual. Tech. 28 409-428. 

Examples of this type of data are, e.g., from the field of process modeling and multivariate statistical process control. Suppose that process measurements are taken from a chemical reactor during a certain period of time. In the same time period, process measurements are taken from the separation column following that reactor as a unit operation. The composition of the product leaving the column is also measured in the same time period and with the same measurement frequency as the process measurements. This results in three blocks of data, with one mode in common. Relationships between these blocks can be sought and, e.g., used to develop control charts [Kourti et al. 1995, MacGregor et al. 1994],... 

Three-way two-block data can be encountered, e.g., in modeling and multivariate statistical process control of batch processes. The first block contains the measured process variables at certain points in time of different batch runs. The second block might contain the quality measurements of the end products of the batches. Creating a relationship between these blocks through regression analysis or similar, can shed light on the connection of the variation in quality and the variation in process measurements. This can be used to build control charts [Boque Smilde 1999, Kourti et al. 1995], Another application is in multivariate calibration where, for example, fluorescence emission/excitation data of samples are used to predict a property of those samples [Bro 1999],... 

An example of a three-way multiblock problem was published in the area of multivariate statistical process control of batch processes [Kourti et al. 1995], Suppose, e.g., that the feed of a batch process is characterized by a composition vector of length L. If / different batch runs have been completed this results in a matrix X (I x L) of feed characteristics. The process measurements are collected in Z (I x J x K) having I batches, J variables and measured at K time points each. The M different end product quality measurements are collected in Y (/ x M). Investigating if there is a connection between X, Z and Y is a common task in process analysis. 

The middle part of Table 7.4 is about more formal statistical tests, where the distributional properties of the residual data are calculated from the residuals themselves. This is more demanding and often requires knowledge of degrees of freedom, which is a difficult subject for three-way residuals. If the residuals are centered around zero, then the sum of squared residuals is approximately x2 distributed [Box 1954], The degrees of freedom can be estimated from the data [Box 1954, Jackson Mudholkar 1979], The resulting statistics are used in multivariate statistical process control (see Chapter 10). 

TVT is diagonal and contains the R largest eigenvalues of X X on its diagonal. It is readily seen that the squared Mahalanobis distance is closely related to Hotelling s T2 statistic, the only difference being a scalar correction. This distance is used extensively for outlier detection, e.g. in multivariate statistical process control (see Chapter 10). 

Louwerse DJ, Smilde AK, Multivariate statistical process control of batch processes based on three-way models, Chemical Engineering Science, 2000, 55, 1225-1235. 

Tates AA, Louwerse DJ, Smilde AK, Koot GLM, Berndt H, Monitoring a PVC batch process with multivariate statistical process control charts, Industrial and Engineering Chemistry Research, 1999, 38, 4769 1776. 

Westerhuis JA, Gurden SP, Smilde AK, Generalized contribution plots in multivariate statistical process monitoring, Chemometrics and Intelligent Laboratory Systems, 2000a, 51, 95-114. 

Kourti, T. Process analytical technology and multivariate statistical process control. Wellness index of process and product— part 1. Process Analytical Technology, 1 (1), 13-19, 2004. 

B.R. Bakshi, Multiscale PCA with Application to Multivariate Statistical Process Monitoring, AlCliE Journal. 44(7) (1998). 1596-1610,... 

Ferrer A.. Multivariate Statistical Process Control based on Principal Component Analysis (MSPC-PCA) Some Reflections and a Case Study in an Autobody Assembly Process Quality Engineering. 2007 19 311-325. 

M. Reis, P. Saraiva, Heteroscedastic latent variable modelling with applications to multivariate statistical process control, Chemometrics and Intelligent Laboratoy Systems 80 (2006) 57-66. 

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