Confidence Bounds for Multivariate Process Performance Monitoring Charts

Martin, E.B.; Morris, A.J.; Papazoglou, M. C.

doi:10.1016/s1474-6670(17)45399-7

Cited by 8 publications

(7 citation statements)

References 7 publications

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“…Multivariable warning and alarm limits are set which test whether a new set of measurements is within the normal bounds captured by the calibration model. 4,25,26 The work in this paper, like refs 10-22, concerns the discovery of structures in a data set and ascertains the items that belong together. It achieves multidimensional visualization of a complete data set and gains insights by exploration of the structures within the data set.…”

Section: Background and Contextmentioning

confidence: 99%

“…There is no calibration model representing normal process operation with which abnormal days are compared. Therefore, the SPE (also called the Q statistic) and Hotelling T 2 measures 4,25,26 which are useful in online multivariate statistical process control are not appropriate for the detection of the abnormal days in the application presented here. The SPE (or Q) for the plant profile of the ith day is |e′ i | 2 , where e′ i is the ith row of E in (2).…”

Section: Outlier Detection (A) Definition Of An Outliermentioning

confidence: 99%

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Multidimensional Visualization and Clustering of Historical Process Data

Thornhill

Melbø

Wiik

2006

Ind. Eng. Chem. Res.

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Multivariate statistical analysis using principal components can reveal patterns and structures within a data set and give insights into process performance and operation. The output medium is usually a two dimensional screen, however, so it is a challenge to visualize the multidimensional structure of a data set by means of a two-dimensional plot. A method of visualization is described in the form of a hierarchical classification tree that can be used to view the structure within a multivariate principal component model of three or more dimensions. The tree is generated from an unsupervised agglomerative hierarchical clustering algorithm which operates in the score space of the principal component model, and a recursive algorithm to draw the tree. It is readily adaptable to a wide range of multivariate analysis applications including process performance analysis and process or equipment auditing. Its application are illustrated with industrial data sets.

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Section: Background and Contextmentioning

confidence: 99%

Section: Outlier Detection (A) Definition Of An Outliermentioning

confidence: 99%

Multidimensional Visualization and Clustering of Historical Process Data

Thornhill

Melbø

Wiik

2006

Ind. Eng. Chem. Res.

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“…In this case, the control limits can be estimated using nonparametric density estimation techniques, such as kernel density estimation. 24…”

Section: Monitoring Statisticsmentioning

confidence: 99%

Fault Detection Based on a Maximum-Likelihood Principal Component Analysis (PCA) Mixture

Choi

Martin

Morris

et al. 2005

Ind. Eng. Chem. Res.

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Multivariate statistical process control (MSPC) that is based on principal component analysis (PCA) has been applied to many industrial processes. Such an approach assumes that the process signals are normally distributed and exhibit stationary behavior. These assumptions significantly limit the range of applicability of the methodology. In this paper, a monitoring scheme based on a maximum-likelihood PCA (MLPCA) mixture is proposed. The main idea behind the approach is that complex data patterns obtained from a process can be described by several local models. A learning algorithm that helps determine model structure, i.e., the number of local PCA models to be constructed and the number of principal components to be included in each local model, is proposed, resulting in the efficient determination of a MLPCA mixture model. Two monitoring statistics used in the MLPCA-based monitoring scheme are then derived and a two-step fault detection method is proposed. Several mathematical models that describe different process features, including multiple steady states, nonlinearity, and process dynamics, are used to demonstrate the potential of the proposed method. The approach is compared with previous approaches, including nonlinear PCA and dynamic PCA, and it is confirmed that the developed methodology is a good alternative. Finally, the method is applied for fault detection on a continuously stirred tank reactor process, and its performance for detecting six types of faults, in terms of false alarm rate, missed alarm rate, and detection delay, is shown to outperform current approaches.

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“…In the second approach, the density function is estimated using an unstructured approach. In this work, the non parametric approach is adopted based on kernel density estimation (Martin and Morris, 1996). Kernel estimator with kernel K is defined by:…”

Section: Fault Detection and Identificationmentioning

confidence: 99%