Multivariate Pattern Recognition in MSPC Using Bayesian Inference
Multivariate Statistical Process Control (MSPC) seeks to monitor several quality characteristics simultaneously. However, it has limitations derived from its inability to identify the source of special variation in the process. In this research, a proposed model that does not have this limitation is...
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| Format: | Article |
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MDPI AG
2021-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/4/306 |
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| author | Jose Ruiz-Tamayo Jose Antonio Vazquez-Lopez Edgar Augusto Ruelas-Santoyo Aidee Hernandez-Lopez Ismael Lopez-Juarez Armando Javier Rios-Lira |
| author_facet | Jose Ruiz-Tamayo Jose Antonio Vazquez-Lopez Edgar Augusto Ruelas-Santoyo Aidee Hernandez-Lopez Ismael Lopez-Juarez Armando Javier Rios-Lira |
| author_sort | Jose Ruiz-Tamayo |
| collection | DOAJ |
| description | Multivariate Statistical Process Control (MSPC) seeks to monitor several quality characteristics simultaneously. However, it has limitations derived from its inability to identify the source of special variation in the process. In this research, a proposed model that does not have this limitation is presented. In this paper, data from two scenarios were used: (A) data created by simulation and (B) random variable data obtained from the analysed product, which in this case corresponds to cheese production slicing process in the dairy industry. The model includes a dimensional reduction procedure based on the centrality and data dispersion. The goal is to recognise a multivariate pattern from the conjunction of univariate variables with variation patterns so that the model indicates the univariate patterns from the multivariate pattern. The model consists of two stages. The first stage is concerned with the identification process and uses Moving Windows (<b>MWs</b>) for data segmentation and pattern analysis. The second stage uses Bayesian Inference techniques such as conditional probabilities and Bayesian Networks. By using these techniques, the univariate variable that contributed to the pattern found in the multivariate variable is obtained. Furthermore, the model evaluates the probability of the patterns of the individual variables generating a specific pattern in the multivariate variable. This probability is interpreted as a signal of the performance of the process that allows to identify in the process a multivariate out-of-control state and the univariate variable that causes the failure. The efficiency results of the proposed model compared favourably with respect to the results obtained using the Hotelling’s <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula> chart, which validates our model. |
| first_indexed | 2024-03-09T05:45:22Z |
| format | Article |
| id | doaj.art-b8bf47a4d66643ea8cddc395d23f573b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:45:22Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b8bf47a4d66643ea8cddc395d23f573b2023-12-03T12:21:45ZengMDPI AGMathematics2227-73902021-02-019430610.3390/math9040306Multivariate Pattern Recognition in MSPC Using Bayesian InferenceJose Ruiz-Tamayo0Jose Antonio Vazquez-Lopez1Edgar Augusto Ruelas-Santoyo2Aidee Hernandez-Lopez3Ismael Lopez-Juarez4Armando Javier Rios-Lira5Tecnologico Nacional de Mexico/Instituto Tecnologico de Celaya, Celaya 38010, MexicoTecnologico Nacional de Mexico/Instituto Tecnologico de Celaya, Celaya 38010, MexicoInstituto Tecnologico Superior de Irapuato, Irapuato 36821, MexicoSistema Avanzado de Bachillerato y Educacion Superior, Celaya 38010, MexicoCentro de Investigacion y de Estudios Avanzados del IPN (CINVESTAV), Ramos Arizpe 25900, MexicoTecnologico Nacional de Mexico/Instituto Tecnologico de Celaya, Celaya 38010, MexicoMultivariate Statistical Process Control (MSPC) seeks to monitor several quality characteristics simultaneously. However, it has limitations derived from its inability to identify the source of special variation in the process. In this research, a proposed model that does not have this limitation is presented. In this paper, data from two scenarios were used: (A) data created by simulation and (B) random variable data obtained from the analysed product, which in this case corresponds to cheese production slicing process in the dairy industry. The model includes a dimensional reduction procedure based on the centrality and data dispersion. The goal is to recognise a multivariate pattern from the conjunction of univariate variables with variation patterns so that the model indicates the univariate patterns from the multivariate pattern. The model consists of two stages. The first stage is concerned with the identification process and uses Moving Windows (<b>MWs</b>) for data segmentation and pattern analysis. The second stage uses Bayesian Inference techniques such as conditional probabilities and Bayesian Networks. By using these techniques, the univariate variable that contributed to the pattern found in the multivariate variable is obtained. Furthermore, the model evaluates the probability of the patterns of the individual variables generating a specific pattern in the multivariate variable. This probability is interpreted as a signal of the performance of the process that allows to identify in the process a multivariate out-of-control state and the univariate variable that causes the failure. The efficiency results of the proposed model compared favourably with respect to the results obtained using the Hotelling’s <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula> chart, which validates our model.https://www.mdpi.com/2227-7390/9/4/306Multivariate Statistical Process Controlcontrol chartsBayesian NetworkBayesian Inferencemoving windows |
| spellingShingle | Jose Ruiz-Tamayo Jose Antonio Vazquez-Lopez Edgar Augusto Ruelas-Santoyo Aidee Hernandez-Lopez Ismael Lopez-Juarez Armando Javier Rios-Lira Multivariate Pattern Recognition in MSPC Using Bayesian Inference Mathematics Multivariate Statistical Process Control control charts Bayesian Network Bayesian Inference moving windows |
| title | Multivariate Pattern Recognition in MSPC Using Bayesian Inference |
| title_full | Multivariate Pattern Recognition in MSPC Using Bayesian Inference |
| title_fullStr | Multivariate Pattern Recognition in MSPC Using Bayesian Inference |
| title_full_unstemmed | Multivariate Pattern Recognition in MSPC Using Bayesian Inference |
| title_short | Multivariate Pattern Recognition in MSPC Using Bayesian Inference |
| title_sort | multivariate pattern recognition in mspc using bayesian inference |
| topic | Multivariate Statistical Process Control control charts Bayesian Network Bayesian Inference moving windows |
| url | https://www.mdpi.com/2227-7390/9/4/306 |
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