Multivariate control charts based on Bayesian state space models

This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.Comment: 19 pages, 6 figure

Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

ADVANCES ON BILINEAR MODELING OF BIOCHEMICAL BATCH PROCESSES

[EN] This thesis is aimed to study the implications of the statistical modeling approaches proposed for the bilinear modeling of batch processes, develop new techniques to overcome some of the problems that have not been yet solved and apply them to data of biochemical processes. The study, discussion and development of the new methods revolve around the four steps of the modeling cycle, from the alignment, preprocessing and calibration of batch data to the monitoring of batches trajectories. Special attention is given to the problem of the batch synchronization, and its effect on the modeling from different angles. The manuscript has been divided into four blocks. First, a state-of- the-art of the latent structures based-models in continuous and batch processes and traditional univariate and multivariate statistical process control systems is carried out. The second block of the thesis is devoted to the preprocessing of batch data, in particular, to the equalization and synchronization of batch trajectories. The first section addresses the problem of the lack of equalization in the variable trajectories. The different types of unequalization scenarios that practitioners might finnd in batch processes are discussed and the solutions to equalize batch data are introduced. In the second section, a theoretical study of the nature of batch processes and of the synchronization of batch trajectories as a prior step to bilinear modeling is carried out. The topics under discussion are i) whether the same synchronization approach must be applied to batch data in presence of different types of asynchronisms, and ii) whether synchronization is always required even though the length of the variable trajectories are constant across batches. To answer these questions, a thorough study of the most common types of asynchronisms that may be found in batch data is done. Furthermore, two new synchronization techniques are proposed to solve the current problems in post-batch and real-time synchronization. To improve fault detection and classification, new unsupervised control charts and supervised fault classifiers based on the information generated by the batch synchronization are also proposed. In the third block of the manuscript, a research work is performed on the parameter stability associated with the most used synchronization methods and principal component analysis (PCA)-based Batch Multivariate Statistical Process Control methods. The results of this study have revealed that accuracy in batch synchronization has a profound impact on the PCA model parameters stability. Also, the parameter stability is closely related to the type of preprocessing performed in batch data, and the type of model and unfolding used to transform the three-way data structure to two-way. The setting of the parameter stability, the source of variability remaining after preprocessing and the process dynamics should be balanced in such a way that multivariate statistical models are accurate in fault detection and diagnosis and/or in online prediction. Finally, the fourth block introduces a graphical user-friendly interface developed in Matlab code for batch process understanding and monitoring. To perform multivariate analysis, the last developments in process chemometrics, including the methods proposed in this thesis, are implemented.[ES] La presente tesis doctoral tiene como objetivo estudiar las implicaciones de los métodos estadísticos propuestos para la modelización bilineal de procesos por lotes, el desarrollo de nuevas técnicas para solucionar algunos de los problemas más complejos aún por resolver en esta línea de investigación y aplicar los nuevos métodos a datos provenientes de procesos bioquímicos para su evaluación estadística. El estudio, la discusión y el desarrollo de los nuevos métodos giran en torno a las cuatro fases del ciclo de modelización: desde la sincronización, ecualización, preprocesamiento y calibración de los datos, a la monitorización de las trayectorias de las variables del proceso. Se presta especial atención al problema de la sincronización y su efecto en la modelización estadística desde distintas perspectivas. El manuscrito se ha dividido en cuatro grandes bloques. En primer lugar, se realiza una revisión bibliográfica de las técnicas de proyección sobre estructuras latentes para su aplicación en procesos continuos y por lotes, y del diseño de sistemas de control basados en modelos estadísticos multivariantes. El segundo bloque del documento versa sobre el preprocesamiento de los datos, en concreto, sobre la ecualización y la sincronización. La primera parte aborda el problema de la falta de ecualización en las trayectorias de las variables. Se discuten las diferentes políticas de muestreo que se pueden encontrar en procesos por lotes y las soluciones para ecualizar las variables. En la segunda parte de esta sección, se realiza un estudio teórico sobre la naturaleza de los procesos por lotes y de la sincronización de las trayectorias como paso previo a la modelización bilineal. Los temas bajo discusión son: i) si se debe utilizar el mismo enfoque de sincronización en lotes afectados por diferentes tipos de asincronismos, y ii) si la sincronización es siempre necesaria aún y cuando las trayectorias de las variables tienen la misma duración en todos los lotes. Para responder a estas preguntas, se lleva a cabo un estudio exhaustivo de los tipos más comunes de asincronismos que se pueden encontrar en este tipo de datos. Además, se proponen dos nuevas técnicas de sincronización para resolver los problemas existentes en aplicaciones post-morten y en tiempo real. Para mejorar la detección de fallos y la clasificación, también se proponen nuevos gráficos de control no supervisados y clasificadores de fallos supervisados en base a la información generada por la sincronización de los lotes. En el tercer bloque del manuscrito se realiza un estudio de la estabilidad de los parámetros asociados a los métodos de sincronización y a los métodos estadístico multivariante basados en el Análisis de Componentes Principales (PCA) más utilizados para el control de procesos. Los resultados de este estudio revelan que la precisión de la sincronización de las trayectorias tiene un impacto significativo en la estabilidad de los parámetros de los modelos PCA. Además, la estabilidad paramétrica está estrechamente relacionada con el tipo de preprocesamiento realizado en los datos de los lotes, el tipo de modelo a justado y el despliegue utilizado para transformar la estructura de datos de tres a dos dimensiones. El ajuste de la estabilidad de los parámetros, la fuente de variabilidad que queda después del preprocesamiento de los datos y la captura de las dinámicas del proceso deben ser a justados de forma equilibrada de tal manera que los modelos estadísticos multivariantes sean precisos en la detección y diagnóstico de fallos y/o en la predicción en tiempo real. Por último, el cuarto bloque del documento describe una interfaz gráfica de usuario que se ha desarrollado en código Matlab para la comprensión y la supervisión de procesos por lotes. Para llevar a cabo los análisis multivariantes, se han implementado los últimos desarrollos en la quimiometría de proc[CA] Aquesta tesi doctoral te com a objectiu estudiar les implicacions dels mètodes de modelització estadística proposats per a la modelització bilineal de processos per lots, el desenvolupament de noves tècniques per resoldre els problemes encara no resolts en aquesta línia de recerca i aplicar els nous mètodes a les dades dels processos bioquímics. L'estudi, la discussió i el desenvolupament dels nous mètodes giren entorn a les quatre fases del cicle de modelització, des de l'alineació, preprocessament i el calibratge de les dades provinents de lots, a la monitorització de les trajectòries. Es presta especial atenció al problema de la sincronització per lots, i el seu efecte sobre el modelatge des de diferents angles. El manuscrit s'ha dividit en quatre grans blocs. En primer lloc, es realitza una revisió bibliogràfica dels principals mètodes basats en tècniques de projecció sobre estructures latents en processos continus i per lots, així com dels sistemes de control estadístics multivariats. El segon bloc del document es dedica a la preprocessament de les dades provinents de lots, en particular, l' equalització i la sincronització. La primera part aborda el problema de la manca d'equalització en les trajectòries de les variables. Es discuteixen els diferents tipus d'escenaris en que les variables estan mesurades a distints intervals i les solucions per equalitzar-les en processos per lots. A la segona part d'aquesta secció es porta a terme un estudi teòric de la naturalesa dels processos per lots i de la sincronització de les trajectòries de lots com a pas previ al modelatge bilineal. Els temes en discussió són: i) si el mateix enfocament de sincronització ha de ser aplicat a les dades del lot en presència de diferents tipus de asincronismes, i ii) si la sincronització sempre es requereix tot i que la longitud de les trajectòries de les variables són constants en tots el lots. Per respondre a aquestes preguntes, es du a terme un estudi exhaustiu dels tipus més comuns de asincronismes que es poden trobar en les dades provinents de lots. A més, es proposen dues noves tècniques de sincronització per resoldre els problemes existents la sincronització post-morten i en temps real. Per millorar la detecció i la classificació de anomalies, també es proposen nous gràfics de control no supervisats i classificadors de falla supervisats dissenyats en base a la informació generada per la sincronització de lots. En el tercer bloc del manuscrit es realitza un treball de recerca sobre l'estabilitat dels paràmetres associats als mètodes de sincronització i als mètodes estadístics multivariats basats en l'Anàlisi de Components Principals (PCA) més utilitzats per al control de processos. Els resultats d'aquest estudi revelen que la precisió en la sincronització per lots te un profund impacte en l'estabilitat dels paràmetres dels models PCA. A més, l'estabilitat paramètrica està estretament relacionat amb el tipus de preprocessament realitzat en les dades provinents de lots, el tipus de model i el desplegament utilitzat per transformar l'estructura de dades de tres a dos dimensions. L'ajust de l'estabilitat dels paràmetres, la font de variabilitat que queda després del preprocessament i la captura de la dinàmica de procés ha de ser equilibrada de tal manera que els models estadístics multivariats són precisos en la detecció i diagnòstic de fallades i/o en la predicció en línia. Finalment, el quart bloc del document introdueix una interfície gràfica d'usuari que s'ha dissenyat e implementat en Matlab per a la comprensió i la supervisió de processos per lots. Per dur a terme aquestes anàlisis multivariats, s'han implementat els últims desenvolupaments en la quimiometria de processos, incloent-hi els mètodes proposats en aquesta tesi.González Martínez, JM. (2015). ADVANCES ON BILINEAR MODELING OF BIOCHEMICAL BATCH PROCESSES [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/55684TESISPremios Extraordinarios de tesis doctorale

Bilinear modeling of batch processes. Part III: Parameter Stability

A paramount aspect in the development of a model for a monitoring system is the so-called parameter stability. This is inversely related to the uncertainty, i.e., the variance in the parameters estimates. Noise affects the performance of the monitoring system, reducing its fault detection capability. Low parameters uncertainty is desired to ensure a reduced amount of noise in the model. Nonetheless, there is no sound study on the parameter stability in batch multivariate statistical process control (BMSPC). The aim of this paper is to investigate the parameter stability associated to the most used synchronization and principal component analysis-based BMSPC methods. The synchronization methods included in this study are the following: indicator variable, dynamic time warping, relaxed greedy time warping, and time linear expanding/compressing-based. In addition, different arrangements of the three-way batch data into two-way matrices are considered, namely single-model, K-models, and hierarchicalmodel approaches. Results are discussed in connection with previous conclusions in the first two papers of the series.This research work was partially supported by the Spanish Ministry of Economy and Competitiveness under the project DPI2011-28112-C04-02. Authors also acknowledge the anonymous reviewers for their comments to improve the article.González Martínez, JM.; Camacho Páez, J.; Ferrer, A. (2014). Bilinear modeling of batch processes. Part III: Parameter Stability. Journal of Chemometrics. 28(1):10-27. https://doi.org/10.1002/cem.2562S1027281Process analysis and abnormal situation detection: from theory to practice. (2002). IEEE Control Systems, 22(5), 10-25. doi:10.1109/mcs.2002.1035214Statistical monitoring of multistage, multiphase batch processes. (2002). IEEE Control Systems, 22(5), 40-52. doi:10.1109/mcs.2002.1035216Kourti, T. (2005). Application of latent variable methods to process control and multivariate statistical process control in industry. International Journal of Adaptive Control and Signal Processing, 19(4), 213-246. doi:10.1002/acs.859Wold, S., Kettaneh-Wold, N., MacGregor, J. F., & Dunn, K. G. (2009). Batch Process Modeling and MSPC. Comprehensive Chemometrics, 163-197. doi:10.1016/b978-044452701-1.00108-3Camacho, J., Picó, J., & Ferrer, A. (2008). Bilinear modelling of batch processes. Part I: theoretical discussion. Journal of Chemometrics, 22(5), 299-308. doi:10.1002/cem.1113Camacho, J., Picó, J., & Ferrer, A. (2008). Bilinear modelling of batch processes. Part II: a comparison of PLS soft-sensors. Journal of Chemometrics, 22(10), 533-547. doi:10.1002/cem.1179González-Martínez J Vitale R de Noord O Ferrer A Does synchronization matter in bilinear batch process monitoring?García-Muñoz, S., Kourti, T., MacGregor, J. F., Mateos, A. G., & Murphy, G. (2003). Troubleshooting of an Industrial Batch Process Using Multivariate Methods. Industrial & Engineering Chemistry Research, 42(15), 3592-3601. doi:10.1021/ie0300023Zarzo, M., & Ferrer, A. (2004). Batch process diagnosis: PLS with variable selection versus block-wise PCR. Chemometrics and Intelligent Laboratory Systems, 73(1), 15-27. doi:10.1016/j.chemolab.2003.11.009Wallace D Prosensus multivariate v12. 02 2010Louwerse, D. J., Tates, A. A., Smilde, A. K., Koot, G. L. M., & Berndt, H. (1999). PLS discriminant analysis with contribution plots to determine differences between parallel batch reactors in the process industry. Chemometrics and Intelligent Laboratory Systems, 46(2), 197-206. doi:10.1016/s0169-7439(98)00185-3Nomikos, P., & MacGregor, J. F. (1994). Monitoring batch processes using multiway principal component analysis. AIChE Journal, 40(8), 1361-1375. doi:10.1002/aic.690400809Kaistha, N., & Moore, C. F. (2001). Extraction of Event Times in Batch Profiles for Time Synchronization and Quality Predictions. Industrial & Engineering Chemistry Research, 40(1), 252-260. doi:10.1021/ie990937cRamsay, J. O., & Silverman, B. W. (1997). Functional Data Analysis. Springer Series in Statistics. doi:10.1007/978-1-4757-7107-7Andersen, S. W., & Runger, G. C. (2012). Automated feature extraction from profiles with application to a batch fermentation process. Journal of the Royal Statistical Society: Series C (Applied Statistics), 61(2), 327-344. doi:10.1111/j.1467-9876.2011.01032.xKassidas, A., MacGregor, J. F., & Taylor, P. A. (1998). Synchronization of batch trajectories using dynamic time warping. AIChE Journal, 44(4), 864-875. doi:10.1002/aic.690440412González-Martínez, J. M., Ferrer, A., & Westerhuis, J. A. (2011). Real-time synchronization of batch trajectories for on-line multivariate statistical process control using Dynamic Time Warping. Chemometrics and Intelligent Laboratory Systems, 105(2), 195-206. doi:10.1016/j.chemolab.2011.01.003Zhang Y Edgar TF A robust dynamic time warping algorithm for batch trajectory synchronization 2008 2864 2860Gins, G., Van den Kerkhof, P., & Van Impe, J. F. M. (2012). Hybrid Derivative Dynamic Time Warping for Online Industrial Batch-End Quality Estimation. Industrial & Engineering Chemistry Research, 51(17), 6071-6084. doi:10.1021/ie2019068Gurden, S. P., Westerhuis, J. A., Bijlsma, S., & Smilde, A. K. (2000). Modelling of spectroscopic batch process data using grey models to incorporate external information. Journal of Chemometrics, 15(2), 101-121. doi:10.1002/1099-128x(200102)15:23.0.co;2-vKourti, T. (2003). Multivariate dynamic data modeling for analysis and statistical process control of batch processes, start-ups and grade transitions. Journal of Chemometrics, 17(1), 93-109. doi:10.1002/cem.778Westerhuis, J. A., Kourti, T., & MacGregor, J. F. (1999). Comparing alternative approaches for multivariate statistical analysis of batch process data. Journal of Chemometrics, 13(3-4), 397-413. doi:10.1002/(sici)1099-128x(199905/08)13:3/43.0.co;2-iNomikos, P., & MacGregor, J. F. (1995). Multivariate SPC Charts for Monitoring Batch Processes. Technometrics, 37(1), 41-59. doi:10.1080/00401706.1995.10485888Wold, S., Kettaneh, N., Fridén, H., & Holmberg, A. (1998). Modelling and diagnostics of batch processes and analogous kinetic experiments. Chemometrics and Intelligent Laboratory Systems, 44(1-2), 331-340. doi:10.1016/s0169-7439(98)00162-2Chen, J., & Liu, K.-C. (2002). On-line batch process monitoring using dynamic PCA and dynamic PLS models. Chemical Engineering Science, 57(1), 63-75. doi:10.1016/s0009-2509(01)00366-9Ramaker, H.-J., van Sprang, E. N. M., Westerhuis, J. A., & Smilde, A. K. (2005). Fault detection properties of global, local and time evolving models for batch process monitoring. Journal of Process Control, 15(7), 799-805. doi:10.1016/j.jprocont.2005.02.001Lennox, B., Montague, G. A., Hiden, H. G., Kornfeld, G., & Goulding, P. R. (2001). Process monitoring of an industrial fed-batch fermentation. Biotechnology and Bioengineering, 74(2), 125-135. doi:10.1002/bit.1102Ündey, C., Ertunç, S., & Çınar, A. (2003). Online Batch/Fed-Batch Process Performance Monitoring, Quality Prediction, and Variable-Contribution Analysis for Diagnosis. Industrial & Engineering Chemistry Research, 42(20), 4645-4658. doi:10.1021/ie0208218Camacho, J., & Picó, J. (2006). Multi-phase principal component analysis for batch processes modelling. Chemometrics and Intelligent Laboratory Systems, 81(2), 127-136. doi:10.1016/j.chemolab.2005.11.003Rännar, S., MacGregor, J. F., & Wold, S. (1998). Adaptive batch monitoring using hierarchical PCA. Chemometrics and Intelligent Laboratory Systems, 41(1), 73-81. doi:10.1016/s0169-7439(98)00024-0Camacho, J., Picó, J., & Ferrer, A. (2009). 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MVBatch: A matlab toolbox for batch process modeling and monitoring

[EN] A novel user-friendly graphical interface for process understanding, monitoring and troubleshooting has been developed as a freely available MATLAB toolbox, called the MultiVariate Batch (MVBatch) Toolbox. The main contribution of this software package is the integration of recent developments in Principal Component Analysis (PCA) based Batch Multivariate Statistical Process Monitoring (BMSPM) that overcome modeling problems such as missing data, different speed of process evolution and length of batch trajectories, and multiple stages. An interactive user interface is provided, which aims to guide users in handling batch data through the main BMSPM steps: data alignment, data modeling, and the development of monitoring schemes. In addition, a small-scale non-linear dynamic simulator of the fermentation process of the Saccharomyces cerevisiae cultivation is available to generate realistic batch data under normal and abnormal operating conditions. This generator of synthetic data can be used for teaching purposes or as a benchmark to illustrate and compare the performance of new methods with sound techniques published in the field of BMSPM.This work is partially supported by the Spanish Ministry of Economy and Competitiveness and FEDER funds through the projects DPI2017-82896-C2-1-R and TIN2017-83494-R. Authors also acknowledge the volunteers to test MVBatch and report their impressions for this software tutorial.González Martínez, JM.; Camacho Paez, J.; Ferrer, A. (2018). MVBatch: A matlab toolbox for batch process modeling and monitoring. Chemometrics and Intelligent Laboratory Systems. 183:122-133. https://doi.org/10.1016/j.chemolab.2018.11.001S12213318

Intelligent Simulation Modeling of a Flexible Manufacturing System with Automated Guided Vehicles

Although simulation is a very flexible and cost effective problem solving technique, it has been traditionally limited to building models which are merely descriptive of the system under study. Relatively new approaches combine improvement heuristics and artificial intelligence with simulation to provide prescriptive power in simulation modeling. This study demonstrates the synergy obtained by bringing together the "learning automata theory" and simulation analysis. Intelligent objects are embedded in the simulation model of a Flexible Manufacturing System (FMS), in which Automated Guided Vehicles (AGVs) serve as the material handling system between four unique workcenters. The objective of the study is to find satisfactory AGV routing patterns along available paths to minimize the mean time spent by different kinds of parts in the system. System parameters such as different part routing and processing time requirements, arrivals distribution, number of palettes, available paths between workcenters, number and speed of AGVs can be defined by the user. The network of learning automata acts as the decision maker driving the simulation, and the FMS model acts as the training environment for the automata network; providing realistic, yet cost-effective and risk-free feedback. Object oriented design and implementation of the simulation model with a process oriented world view, graphical animation and visually interactive simulation (using GUI objects such as windows, menus, dialog boxes; mouse sensitive dynamic automaton trace charts and dynamic graphical statistical monitoring) are other issues dealt with in the study

Renewable Estimation and Incremental Inference with Streaming Health Datasets

The overarching objective of my dissertation is to develop a new methodology that allows to sequentially update parameter estimates and their standard errors along with data streams. The key technical novelty pertains to the fact that the proposed estimation method, termed as renewable estimation in my dissertation, uses current data and summary statistics of historical data, but no use of any historical subject-level data. To implement renewable estimation, I utilize the powerful Lambda architecture in Apache Spark to design a new paradigm that includes an inference layer in addition to the existing speed layer. This expanded architecture is named as the Rho architecture, which accommodates inference-related statistics and to facilitate sequential updating of quantities involved in estimation and inference. The first project focuses on the renewable estimation in the setting of generalized linear models (RenewGLM) in which I develop a new sequential updating algorithm to calculate numerical solutions of parameter estimates and related inferential quantities. The proposed procedure aggregates both score functions and information matrices over streaming data batches through some summary statistics. I show that the resulting estimation is asymptotically equivalent to the maximum likelihood estimation (MLE) obtained with the entire data once. I demonstrate this new methodology on the analysis of the National Automotive Sampling System-Crashworthiness Data System (NASS CDS) to evaluate the effectiveness of graduated driver licensing (GDL) in the USA. The second project focuses on a substantial extension of the first project to analyze streaming datasets with correlated outcomes, such as clustered data and longitudinal data. I establish the theoretical guarantees for the proposed renewable quadratic inference function (RenewQIF) for dependent outcomes and implement it within the Rho architecture. Furthermore, I relax the homogeneous assumption in the first project and consider regime-switching regression models with a structural change-point. I propose a real-time hypothesis testing procedure based on a goodness-of-fit test statistic that is shown to achieve both proper type I error control and desirable change-point detection power. The third project concerns data streams that involve both inter-data batch correlation and dynamic heterogeneity, arising typically from various types of electronic health records (EHR) and mobile health data. This project is built in the framework of state space models in which the observed data stream is driven by a latent state process that may incorporate trend, seasonal, or time-varying covariate effects. In this setting, calculating the online MLE is challenge due to the involvement of high-dimensional integrals and complex covariance structures. In this project, I develop a Kalman filter to facilitate a multivariate online regression analysis (MORA) in the context of linear state space mixed models. MORA enables to renew both point estimates and standard errors of the fixed effects. We also apply the MORA method to analyze an EHR data example, adjusting for some heterogeneous batch-specific effects.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163085/1/luolsph_1.pd

System overview of the NASA Dryden Integrated Test Facility

The Integrated Test Facility, built at the NASA Dryden Flight Research Facility, provides new real-time test capabilities for emerging research aircraft. An overview of the test facility and the real-time systems developed to operate this unique facility is presented. The facility will reduce flight test risk by minimizing the difference between the flight and ground test environments. This ground test environment is provided by combining real-time flight simulation with the actual aircraft. A brief introduction to the facility is followed by a discussion of the generic capabilities of its real-time systems. The simulation system with flight hardware and the remotely augmented vehicle system is described. An overview of many hardware systems developed for the facility follows. The benefits of applying simulation to hardware-in-the-loop testing on the X-31 Flight Research Program are presented

Integrated Projection and Regression Models for Monitoring Multivariate Autocorrelated Cascade Processes

This dissertation presents a comprehensive methodology of dual monitoring for the multivariate autocorrelated cascade processes using principal component analysis and regression. Principle Components Analysis is used to alleviate the multicollinearity among input process variables and reduce the dimension of the variables. An integrated principal components selection rule is proposed to reduce the number of input variables. An autoregressive time series model is used and imposed on the time correlated output variable which depends on many multicorrelated process input variables. A generalized least squares principal component regression is used to describe the relationship between product and process variables under the autoregressive regression error model. The combined residual based EWMA control chart, applied to the product characteristics, and the MEWMA control charts applied to the multivariate autocorrelated cascade process characteristics, are proposed. The dual EWMA and MEWMA control chart has advantage and capability over the conventional residual type control chart applied to the residuals of the principal component regression by monitoring both product and the process characteristics simultaneously. The EWMA control chart is used to increase the detection performance, especially in the case of small mean shifts. The MEWMA is applied to the selected set of variables from the first principal component with the aim of increasing the sensitivity in detecting process failures. The dual implementation control chart for product and process characteristics enhances both the detection and the prediction performance of the monitoring system of the multivariate autocorrelated cascade processes. The proposed methodology is demonstrated through an example of the sugar-beet pulp drying process. A general guideline for controlling multivariate autocorrelated processes is also developed