Multivariate Control Charts for Individual Observations

Tracy, Nola D.; Young, John C.; Mason, Robert L.

doi:10.1080/00224065.1992.12015232

Cited by 497 publications

(264 citation statements)

References 11 publications

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“…Nonetheless, in statistical monitoring [24,25], matrices T A and E A in (1) are used to develop control limits for incoming data. There -1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 [26,25].…”

Section: Pca Applicationsmentioning

confidence: 99%

Cross-validation in PCA models with the element-wise k-fold (ekf) algorithm: Practical aspects

Camacho

Ferrer

2014

Chemometrics and Intelligent Laboratory Systems

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ElsevierCamacho Páez, J.; Ferrer Riquelme, AJ. (2014). Cross-validation in PCA models with the element-wise k-fold (ekf) algorithm: Practical Aspects. Chemometrics and Intelligent Laboratory Systems. 131:37-50. doi:10.1016/j.chemolab.2013.12.003 . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 in the main commercial software packets for chemometrics. Finally, the choice of the missing data algorithm within ekf is also investigated.

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Section: Pca Applicationsmentioning

confidence: 99%

Cross-validation in PCA models with the element-wise k-fold (ekf) algorithm: Practical aspects

Camacho

Ferrer

2014

Chemometrics and Intelligent Laboratory Systems

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“…Three principal components were selected based on cross-validation results explaining 57% of total variation. Two monitoring charts, T 2 -Hotelling and SPE, were developed from the validated model, and also confidence limits were initially estimated from theoretical results [30,31]. In order to achieve a suitable performance of the monitoring charts, control limits for the SPE chart are readjusted using data in a leave-one-out basis.…”

Section: Resultsmentioning

confidence: 99%

Real-time synchronization of batch trajectories for on-line multivariate statistical process control using Dynamic Time Warping

González-Martínez

Ferrer

Westerhuis

2011

Chemometrics and Intelligent Laboratory Systems

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This paper addresses the real-time monitoring of batch processes with multiple different local time trajectories of variables measured during the process run. For Unfold Principal Component Analysis (U-PCA)-or Unfold Partial Least Squares (U-PLS)-based on-line monitoring of batch processes, batch runs need to be synchronized, not only to have the same time length, but also such that key events happen at the same time. An adaptation from Kassidas et al.'s approach [1] will be introduced to achieve the on-line synchronization of batch trajectories using the Dynamic Time Warping (DTW) algorithm. In the proposed adaptation, a new boundaries definition is presented for accurate on-line synchronization of an ongoing batch, together with a way to adapt mapping boundaries to batch length. A relaxed greedy strategy is introduced to avoid assessing the optimal path each time a new sample is available. The key advantages of the proposed strategy are its computational speed and accuracy for the batch process context. Data from realistic simulations of a fermentation process of the Saccharomyces cerevisae cultivation are used to illustrate the performance of the proposed strategy.

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“…Finally, a threshold of normal condition from the probability density function of the set of parameters is calculated. In literature [7], for the data set T 2 that follows a beta distribution, the threshold Upper Control Limit (UCL) is given by ( )…”

Section: Disturbances Detection Via Dpcamentioning

confidence: 99%

Loss-of-Main Monitoring and Detection for Distributed Generations Using Dynamic Principal Component Analysis

Guo¹,

Li²,

Laverty³

2014

JPEE

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In this paper, our previous work on Principal Component Analysis (PCA) based fault detection method is extended to the dynamic monitoring and detection of loss-of-main in power systems using wide-area synchrophasor measurements. In the previous work, a static PCA model was built and verified to be capable of detecting and extracting system faulty events; however the false alarm rate is high. To address this problem, this paper uses a well-known 'time lag shift' method to include dynamic behavior of the PCA model based on the synchronized measurements from Phasor Measurement Units (PMU), which is named as the Dynamic Principal Component Analysis (DPCA). Compared with the static PCA approach as well as the traditional passive mechanisms of loss-of-main detection, the proposed DPCA procedure describes how the synchrophasors are linearly auto-and cross-correlated, based on conducting the singular value decomposition on the augmented time lagged synchrophasor matrix. Similar to the static PCA method, two statistics, namely T 2 and Q with confidence limits are calculated to form intuitive charts for engineers or operators to monitor the loss-of-main situation in real time. The effectiveness of the proposed methodology is evaluated on the loss-of-main monitoring of a real system, where the historic data are recorded from PMUs installed in several locations in the UK/Ireland power system.

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Multivariate Control Charts for Individual Observations

Cited by 497 publications

References 11 publications

Cross-validation in PCA models with the element-wise k-fold (ekf) algorithm: Practical aspects

Cross-validation in PCA models with the element-wise k-fold (ekf) algorithm: Practical aspects

Real-time synchronization of batch trajectories for on-line multivariate statistical process control using Dynamic Time Warping

Loss-of-Main Monitoring and Detection for Distributed Generations Using Dynamic Principal Component Analysis

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