Batch process monitoring for consistent production

The goal of engineering process control (EPC) is to minimize variability by adjusting some manipulative process variables. The goal of statistical process control (SPC) is to reduce variability by monitoring and eliminating assignable causes of variation. As suggested by Box and Kramer and others, it is possible to reduce both special cause and common cause variations by integrating EPC and SPC. In the integrated multivariate EPC (MEPC) and multivariate SPC (MSPC) charts, we propose some statistical and economic criteria, such as the average Euclidean distance from the target vector and the average quality cost (AQC) to evaluate the performance of the MEPC/MSPC charts. The traditional average run length (ARL), average Euclidean distance and AQC of three MSPC charts are investigated and compared. The results of the simulations show that the MEPC/MGWMA chart is more effective and more economical than both the MEPC/MEWMA chart and the MEPC/Hotelling multivariate chart in detecting small shifts of the mean vector. Copyright © 2006 John Wiley & Sons, Ltd.

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 Control limits for the proposed charts are developed using information from the historical reference distribution of past successful batches.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

Multivariate modelling of fish freshness index based on ion mobility spectrometry measurements

Similar to the univariate CUSUM chart, a multivariate CUSUM (MCUSUM) chart can be designed to detect a particular size of the mean shift optimally based on the scheme of a sequential likelihood ratio test for the noncentrality parameter. However, in multivariate case, the probability ratio of a sequential test is intractable mathematically and the test statistic based on the ratio does not have a closed form expression which makes it impractical for real application. We drive an approximate log-likelihood ratio and propose a multivariate statistical process control chart based on a sequential χ2 test to detect a change in the noncentrality parameter. The statistical properties of the proposed test statistic are explored. The average runs length (ARL) performance of the proposed charts is compared with other MCUSUM charts for process mean monitoring. The experimental results reveal that the proposed charts achieve superior, both zero-state and steady-state, ARL performance over a wide range of mean shifts, especially when the dimension of measurements is large.

Multivariate statistical process control (MSPC) charts are particularly useful when there is a need to simultaneously monitor several quality characteristics of a process. Most of the control charts in MSPC assume that the quality characteristics follow some parametric multivariate distribution, such as the normal. This assumption is almost impossible to be justified in practice. Distribution-free MSPC charts are attractive, as they can overcome this hurdle by guaranteeing a stable (or in-control (IC)) performance of the control chart without the assumption of a parametric multivariate process distribution. Utilizing an existing distribution-free multivariate tolerance interval, we propose a Phase II Shewhart-type distribution-free MSPC chart for individual observations, with control limits based on Phase I order statistics. In addition to being easy to interpret, the proposed chart preserves the original scale of measurements and can easily identify out-of-control variables after a signal. The exact in-control performance based on the conditional and unconditional perspectives is presented and examined along with the control limits determination. The out-of-control performance of the chart is studied by simulation for data from a number of multivariate distributions. Illustrative examples are provided for chart implementation, using both real and simulated data, along with a summary and conclusions.

Application of in-line near infrared spectroscopy and multivariate batch modeling for process monitoring in fluid bed granulation

Tapping is a widely employed but complex manufacturing process in which a multi-toothed tool, known as a tap, cuts a mating thread when driven into a hole. In this paper, the experiments, statistical analysis and the on-line implementation of a new thread quality monitoring system are presented for a tapping process in high-speed conditions. A multivariate statistical process control chart, for each tap, is presented based on the principal components of the torque directly measured from spindle motor drive. The on-line implementation of the multivariate chart provides tap wear warnings and alarms before the process starts producing unacceptable screw threads. The system is cost-effective since the tapping process can be run automatically without any operator intervention, does not require intrusive sensors, does not result in false negatives (defects) and provides an acceptable number of false positives.

A multivariate T 2 chart is developed based on the Generalized Likelihood Ratio Test (GLRT) without a priori information about potential mean deviations. Identification of response variables from a T 2 chart is challenging and has received considerable attention recently. By highlighting the intrinsic relationship between various multivariate control charts and statistical hypothesis testing, this paper presents a theoretical framework for various individual multivariate control charts including the T 2 chart, regression-adjusted chart and M chart. The performance of these control charts is compared under different correlation structures among variables and different mean deviations. A hybrid control chart is also proposed based on the GLRT and union-intersection test, which can serve as a complementary diagnosis tool for the T 2 chart.

Batch process monitoring in the original measurement's space

Multivariate Statistical Process Control (MSPC) techniques are effective tools for detecting the abnormalities of multivariate process variation. MSPC techniques are based on overall statistics; this has caused the difficulties in interpretation of the alarm signal, that is, MSPC charts do not provide the necessary information about which process variables (or subset of them) are responsible for the signal, and this task is left up to the quality engineers in production field. This article proposes a model based on LS-SVM pattern recognizer to diagnose the bivariate process abnormality in covariance matrix. The main property of this model is a supplement of MSPC |S| chart to identify the variable(s) which is (are) responsible for the process abnormality when |S| chart issue a warning signal. Through simulation experiment, the performance of the model is evaluated by accuracy rate of pattern recognition. The results indicate that the proposed model is an effective method to interpret the root causes of the process abnormality. A bivariate example is presented to illustrate the application of the proposed model.

Chemometric quality control of chromatographic purity

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] There are many areas where optimal designs are applied to, for example, the development of a new drug, where a conventional dose- finding study involves learning about the dose-response curve in order to bring forward right doses of drug to late-stage development. The first part of this dissertation focus on three pharmacodynamics sigmoid Emax models, we derive the corresponding simple formats of the adaptive optimal designs regardless of the optimality criteria or parameters of interest. An algorithm for deriving a specific adaptive optimal design is developed. A simulation study comparing the adaptive optimal designs and the uniform designs is also performed. The second part of this dissertation focuses on the statistical process control, we proposed an adaptive approach for the multivariate CUSUM statistical process control chart for signaling a range of location shifts. This method is based on the multivariate CUSUM control chart proposed by Pignatiello and Runger in 1990. We used the exponentially moving weighted average (EMWA) statistic to estimate the current process mean shift and change the reference value adaptively in each run. By specifying the minimal magnitude of the mean shift through the non-centrality parameter, our proposed control chart can achieve an overall good performance for detecting a range of shifts rather than a single value.

Multivariable Analysis Methods have been used widely in Spectroscopy Analysis. Partial least square (PLS) and principal component analysis (PCA) are the two most popular methods due to their excellent ability in data components analysis and results prediction. This work derived 1D/2D PLS and 1D/2D PCA based on the viewpoint of three-layer artificial neural networks, and uses theoretical proving to figure out the essences of these two methods. Two 2D experimental dataset was used to verify the calibration and prediction ability, furthermore, the similarity and dissimilarity of PLS and PCA. The finding showed that both the 1D/2D PLS and 1D/2D PCA methods use maximum covariance and minimum sum of square error to figure out the relationship between independent and dependent variables. The dissimilarity is that, weight vectors calibration of PLS is cross-correlation, and that of PCA is autocorrelation. The difference causes that the PCA method would keep more principal characters than PLS under insufficient sample among and provides better calibration ability. PLS would provide higher performance in prediction under sufficient sample among. For the needs of system implementation of spectroscopic measurement and analysis, this study designed "Multivariate Analysis Toolkits for LabVIEW" for the convenient implementation in automatic measurement system integration.

Use of ultrasound and NIRs as tools for monitoring ice formation in superchilled meat

Batch processes are very important to the chemical and manufacturing industries. Techniques for monitoring these batch processes to ensure their safe operation and that they produce consistent high quality products are needed. Nomikos and MacGregor (1994) present a multi-way principal component analysis (MPCA) approach for monitoring batch processes, and test results show that the method is simple, powerful, and effective. However MPCA is a linear method, and most batch processes are nonlinear. In this paper a nonlinear principal component analysis (NLPCA) method (Dong-McAvoy, 1993) is used for batch process monitoring. The main focus of this paper is on multi-stage batch process monitoring. The proposed approach and special problems for multi-stage batch processes are illustrated through a detailed simulation study.