Monitoring of Multivariate Processes

If the process is out-of-control, the next step is to find the source cause of the deviation (fault diagnosis) and then to remedy the situation. Fault diagnosis can be conducted by associating process behavior patterns to specific faults or by relating the process variables that have significant deviations from their expected values to various equipment that can cause such deviations as discussed in Chapter 7. If the latter approach is used, univariate charts provide readily the information about process variables with significant deviation. Since multivariate monitoring charts summarize the information from many process variables, the variables that inflate 

To include the information about process d3mamics in the models, the data matrix can be augmented with lagged values of data vectors, or model identification techniques such as subspace state-space modeling can be used (Section 4.5). Negiz and Cinar [209] have proposed the use of state variables developed with canonical variates based realization to implement SPM to multivariable continuous processes. Another approach is based on the use of Kalman filter residuals [326]. MSPM with dynamic process models is discussed in Section 5.3. The last section (Section 5.4) of the chapter gives a brief survey of other approaches proposed for MSPM. 

Sometimes, plots of individual PC scores can be used for preliminary analysis of variables that contribute to an out-of-control signal. The control limits for new t scores under the assumption of Normality at significance level a at any time interval k is given by [100] 

Hotelling s plot detects the small shifts and deviations from normal operation defined by the model since it includes contributions of all variables that can become significant faster than the deviation of an individual 

If the observation vector x is not independent of the estimators x and S, but is included in their computation, then follows a Beta distribution with m/2 and n — m— l)/2 degrees of freedom [190]  

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K. Pollanen, A. Hakkinen, S-P. Reinikinen, J. Rantanen, M. Kaijalainen, M. Louhi-Kultanen and L. Nystrom, IR spectroscopy together with multivariate data analysis as a process analytical tool for in-hne monitoring of crystallization process and solid-state analysis of crystalline product, J. Pharm. Biomed. Anal., 38, 275-284 (2005). 

The appeal of multivariate process monitoring techniques is based on... 

A Negiz and A Cinar. Statistical monitoring of multivariable dynamic processes with state-space models. AIChE J., 43(8) 2002-2020, 1997. 

A Negiz and A Cinar. Monitoring of multivariable dynamic processes and sensor auditing. J. Process Control, 8(5-6) 375-380, 1998. 

Traditionally, product quality is based on direct product quality measurements. Such measurements are usually infrequent and tedious to perform. In modem process industry, many process variables are measured on line, such as pressure, temperature, flows, liquid levels, concentrations. It is also possible to monitor such variables in order to verify the quality of the process. The underlying assumption is that if all the process variables have a constant behavior then the product quality will still be on specification. The process variables are used detecting common variation or special variation. Hence, the full machinery of multivariate process monitoring for detecting deviating process behavior can also be applied in this situation. 

Albert S, Kinley RD, Multivariate statistical monitoring of batch processes an industrial case study of fermentation supervision, Trends in Biotechnology, 2001, 19, 53-62. 

Multivariate process monitoring and diagnosis of a full-scale industrial wastewater treatment plant... 

Piovoso, M. J., and Kosanovich, K. A., Applications of multivariate statistical methods to process monitoring and controller design, Int. J. Control 59(3), 743-765 (1994). 

A data matrix is the structure most commonly found in environmental monitoring studies. In these data tables or matrices, the different analyzed samples are placed in the rows of the data matrix, and the measured variables (chemical compound concentrations, physicochemical parameters, etc.) are placed in the columns of the data matrix. The statistical techniques necessary for the multivariate processing of these data are grouped in a table or matrix, or use tools, formulations, and notations of the lineal algebra. 

Finally, the use of PAT should not be limited to existing processes and products but is especially attractive in the R D and scale-up of new processes and products. PAT is especially effective in scale-up. As PAT involves consideration of all monitored variables and not only an empirical selection of some of those variables, and since in-process monitoring techniques are normally multiparametric (e.g., near-infrared spectra of a whole sample), they will be more suited to capture scale effects present in the sample s matrix that show up clearly in a consolidated multivariate analysis of quality and operating variables, thus helping the skillful engineer or scientist to pinpoint and solve scale-up problems thus resulting in a much faster process prototyping and scale-up. 

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