An effective approach to detect the source(s) of out-of-control signals in productive processes by vector error correction (VEC) residual and Hotelling’s T2 decomposition techniques

Ueda, Renan Mitsuo; Souza, Adriano Mendonça

doi:10.1016/j.eswa.2021.115979

Cited by 7 publications

(4 citation statements)

References 56 publications

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“…As an example, in bivariate process quality y = (y 1 , y 2 ) T , the basic idea of the MYT orthogonal decomposition method [17][18][19][20] is to decompose the T 2 statistic into the following form:…”

Section: Diagnosis Methods Based On Correlation and Orthogonal Decomp...mentioning

confidence: 99%

Algorithm for Correlation Diagnosis in Multivariate Process Quality Based on the Optimal Typical Correlated Component Pair Group

Niu,

Cheng,

Qiu

2024

Processes

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Correlation diagnosis in multivariate process quality management is an important and challenging issue. In this paper, a new approach based on the optimal typical correlated component pair group (OTCCPG) is proposed. Firstly, the theorem of correlation decomposition is proved to decompose the correlation of all the quality components as serial correlations of component pairs, and then according to the transitivity of correlations of component pairs, the decomposition result is represented by a correlation set of typical correlated component pairs. Finally, an algorithm for OTCCPG based on the maximum correlation spanning tree (MCST) is proposed, and T2 control charts to monitor the correlations of component pairs in OTCCPG are established to form the correlation diagnostic system. Theoretical analysis and practice prove that the proposed method could reduce the space complexity of the diagnostic system greatly.

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Section: Diagnosis Methods Based On Correlation and Orthogonal Decomp...mentioning

confidence: 99%

Algorithm for Correlation Diagnosis in Multivariate Process Quality Based on the Optimal Typical Correlated Component Pair Group

Niu,

Cheng,

Qiu

2024

Processes

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show abstract

“…Then, according to the statistical distribution of the conditional and unconditional terms, the corresponding control limits are established, so as to diagnose the specific cause(s) when the manufacturing process is abnormal. As an example, in bivariate process quality y=(y 1 , y 2 ) T , the basic idea of the MYT orthogonal decomposition method [17][18][19][20] is to decompose the T 2 statistic into the following form: T , called the unconditional term, is related only to the quality component y 1 and is used to measure the contribution shift in y 1 to the T 2 statistic, and…”

Section: Diagnosis Methods Based On Correlation Orthogonal Decompositionmentioning

confidence: 99%

Algorithm for Correlation Diagnosis in Multivariate Process Quality Based on Optimal Typical Correlated Component Pairs Group

Niu,

Cheng,

Qiu

2023

Preprint

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Correlation diagnosis in multivariate process quality management is an important and challenging issue. In this paper, a new approach based on the optimal typical correlated component pairs group (OTCCPG) is proposed. Firstly, theorem of correlation decomposition is proved to decompose the correlation of all the quality components as serial correlations of component pairs, and then according to the transitivity of correlations of component pairs, the decomposition result is represented by a correlation set of typical correlated component pairs. Finally, algorithm of OTCCPG based on the maximum correlation spanning tree (MCST) is proposed, and T2 control charts to monitor the correlations of component pairs in OTCCPG are established to form the correlation diagnosis system. Theoretical analysis and practice prove that the proposed method could reduce the space complexity of the diagnosis system greatly.

show abstract

“…As an example, in bivariate process quality y = ( y 1 , y 2 ) T , the basic idea of the MYT orthogonal decomposition method 21 – 24 is to decompose the T 2 statistic into the following form: where , called the unconditional term, is related only to the quality component y 1 and is used to measure the contribution shift in y 1 to the T 2 statistic; and , called the conditional term, whose value is related to the conditional probability P ( y 2 | y 1 ) and is used to measure the contribution in the correlation between y 1 and y 2 to the T 2 statistic.…”

Section: Introductionmentioning

confidence: 99%

A multivariate process quality correlation diagnosis method based on grouping technique

Niu,

Cheng,

Qiu

2024

Sci Rep

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Correlation diagnosis in multivariate process quality management is an important and challenging issue. In this paper, a new diagnostic method based on quality component grouping is proposed. Firstly, three theorems describing the properties of the covariance matrix of multivariate process quality are established based on the statistical viewpoint of product quality, to prove the correlation decomposition theorem, which decomposes the correlation of all the quality components into a series of correlations of components pairs, and then by using the factor analysis method, all quality components are grouped in order to maximize the correlations in the same groups and minimize the ones between different groups. Finally, on the basis of correlations between different groups are ignored, T2 control charts of component pairs in the same groups are established to form the diagnostic model. Theoretical analysis and practice prove that for the multivariate process quality whose the correlations between different components vary considerably, the grouping technique enables the size of the correlation diagnostic model to be drastically reduced, thus allowing the proposed method can be used as a generalized theoretical model for the correlation diagnosis.

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An effective approach to detect the source(s) of out-of-control signals in productive processes by vector error correction (VEC) residual and Hotelling’s T2 decomposition techniques

Cited by 7 publications

References 56 publications

Algorithm for Correlation Diagnosis in Multivariate Process Quality Based on the Optimal Typical Correlated Component Pair Group

Algorithm for Correlation Diagnosis in Multivariate Process Quality Based on the Optimal Typical Correlated Component Pair Group

Algorithm for Correlation Diagnosis in Multivariate Process Quality Based on Optimal Typical Correlated Component Pairs Group

A multivariate process quality correlation diagnosis method based on grouping technique

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