On the variable contributions to the D-statistic

Alvarez, Carlos R.; Brandolin, Adriana; Sánchez, Mabel

doi:10.1016/j.chemolab.2007.04.007

Cited by 11 publications

(16 citation statements)

References 10 publications

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“…Following a similar procedure, we can prove that for all other variables x new,i , C (1) xnew,i = C (2) xnew,i (i = 2, 3, · · · , m) also holds.…”

Section: Potential Shortcomings Of the Existing Algorithms For Contrimentioning

confidence: 88%

“…(5) are also given in Refs. [1][2], but they are the same as Eq. (5) if r is set as m, so they can be regarded as special cases of Eq.…”

Section: Introductionmentioning

confidence: 84%

“…x new,i ) to the D-statistic can be further calculated to identify the contributing variables of the fault. The following algorithms for calculating the contributions of x new to the D-statistic, denoted as C (1) x new,k and C (2) x new,k respectively in this paper, were proposed in Refs. [2,12].…”

Section: Introductionmentioning

confidence: 99%

“…D-statistic measures the deviation from the principal component space online and is often used in fault detection [1] . A variable's contribution to Dstatistic can be viewed as the influence of the variable to the D-statistic and therefore can be used to indicate whether a variable is responsible to a detected faulty event [2] .…”

Section: Introductionmentioning

confidence: 99%

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Improved algorithm for calculating contributions to D-statistic

Hao

Wan

2011

J. Shanghai Jiaotong Univ. (Sci.)

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D-statistic contribution analysis has been frequently used in practice for fault diagnosis. Existing algorithms for computing contributions to D-statistic tend to distribute cross-term contribution equally between two correlated variables. This leads to increased variance in contribution estimation and hence poor separability of faulty and normal variables. A new method for contribution calculation to D-statistic is proposed here which introduces a weighting scheme capable of distinguishing the contributions of two correlated variables. Simulation examples show that the proposed approach achieves improved resolution for distinguishing faulty and normal conditions.

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“…Following a similar procedure, we can prove that for all other variables x new,i , C (1) xnew,i = C (2) xnew,i (i = 2, 3, · · · , m) also holds.…”

Section: Potential Shortcomings Of the Existing Algorithms For Contrimentioning

confidence: 88%

“…(5) are also given in Refs. [1][2], but they are the same as Eq. (5) if r is set as m, so they can be regarded as special cases of Eq.…”

Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improved algorithm for calculating contributions to D-statistic

Hao

Wan

2011

J. Shanghai Jiaotong Univ. (Sci.)

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“…Because of the combinatorial nature of the formulation, a great number of decompositions are obtained, increasing the complexity of the identification procedure. A straightforward method to decompose the D statistic as a unique sum of each variable contribution was recently developed by Alvarez et al,15 which is called OSS (original‐space strategy). It provides a clear understanding of positive and negative variable contributions and estimates a bound for the negative ones.…”

Section: Introductionmentioning

confidence: 99%

A multivariate statistical process control procedure for BIAS identification in steady‐state processes

2008

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in Wiley InterScience (www.interscience.wiley.com).In this article, a multivariate statistical process control (MSPC) strategy, devoted to bias identification and estimation for processes operating under steady-state conditions, is presented. The technique makes use of the D statistic to detect the presence of biases. Besides, it uses a new decomposition of this statistic to identify the faulty sensors. The strategy is based only on historical process data. Neither process modeling nor assumptions about the probability distribution of measurement errors are required. In contrast to methods based on fundamental models, both redundant and nonredundant measurements can be examined to identify the presence of biases. The performance of the proposed technique is evaluated using data-reconciliation benchmarks. Results indicate that the technique succeeds in identifying single and multiple biases and fulfills three paramount issues to practical implementation in commercial software: robustness, uncertainty, and efficiency.

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Statistics Decomposition and Monitoring in Original Variable Space

Jing

Zhou

Chen

2022

Intelligent Control and Learning Systems

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The traditional process monitoring method first projects the measured process data into the principle component subspace (PCS) and the residual subspace (RS), then calculates $$\mathrm T^2$$ T 2 and $$\mathrm SPE$$ S P E statistics to detect the abnormality. However, the abnormality by these two statistics are detected from the principle components of the process. Principle components actually have no specific physical meaning, and do not contribute directly to identify the fault variable and its root cause. Researchers have proposed many methods to identify the fault variable accurately based on the projection space. The most popular is contribution plot which measures the contribution of each process variable to the principal element (Wang et al. 2017; Luo et al. 2017; Liu and Chen 2014). Moreover, in order to determine the control limits of the two statistics, their probability distributions should be estimated or assumed as specific one. The fault identification by statistics is not intuitive enough to directly reflect the role and trend of each variable when the process changes.

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On the variable contributions to the D-statistic

Cited by 11 publications

References 10 publications

Improved algorithm for calculating contributions to D-statistic

Improved algorithm for calculating contributions to D-statistic

A multivariate statistical process control procedure for BIAS identification in steady‐state processes

Statistics Decomposition and Monitoring in Original Variable Space

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