An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector
The special causes of variations, which is also known as a shift, can occur in a single or more than one related process characteristics. Statistical process control tools such as control charts are useful to monitor shifts in the process parameters (location and/or dispersion). In real-life situati...
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| Format: | Article |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/12/2025 |
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| author | Muhammad Riaz Babar Zaman Ishaq Adeyanju Raji M. Hafidz Omar Rashid Mehmood Nasir Abbas |
| author_facet | Muhammad Riaz Babar Zaman Ishaq Adeyanju Raji M. Hafidz Omar Rashid Mehmood Nasir Abbas |
| author_sort | Muhammad Riaz |
| collection | DOAJ |
| description | The special causes of variations, which is also known as a shift, can occur in a single or more than one related process characteristics. Statistical process control tools such as control charts are useful to monitor shifts in the process parameters (location and/or dispersion). In real-life situation, the shift is emerging in different sizes, and it is hard to identify it with classical control charts. Moreover, more than one process of characteristics required special attention because they must monitor jointly due to the association among them. This study offers two adaptive control charts to monitor the different sizes of a shift in the process mean vector. The novelty behind this study is to use dimensionally reduction techniques such as principal component analysis (PCA) and an adaptive method such as Huber and Bi-square functions. In brief, the multivariate cumulative sum control chart based on PCA is designed, and its plotting statistic is utilized as an input in the classical exponentially weighted moving average (EWMA) control chart. The run length (RL) properties of the proposed and other control charts are obtained by designing algorithms in MATLAB through a Monte Carlo simulation. For a single shift, the performance of the control charts is assessed through an average of RL, standard deviation of RL, and standard error of RL. Likewise, overall performance measures such as extra quadratic loss, relative ARL, and the performance comparison index are also used. The comparison reveals the superiority over other control charts. Furthermore, to emphasize the application process and benefits of the proposed control charts, a real-life example of the wind turbine process is included. |
| first_indexed | 2024-03-09T23:09:11Z |
| format | Article |
| id | doaj.art-c8551f1df71d46c28e56074af14920a4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:09:11Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c8551f1df71d46c28e56074af14920a42023-11-23T17:48:29ZengMDPI AGMathematics2227-73902022-06-011012202510.3390/math10122025An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean VectorMuhammad Riaz0Babar Zaman1Ishaq Adeyanju Raji2M. Hafidz Omar3Rashid Mehmood4Nasir Abbas5Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematics, University of Hafr Al Batin, Hafr Al Batin 39524, Saudi ArabiaDammam Community College, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematics, University of Hafr Al Batin, Hafr Al Batin 39524, Saudi ArabiaDepartment of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaThe special causes of variations, which is also known as a shift, can occur in a single or more than one related process characteristics. Statistical process control tools such as control charts are useful to monitor shifts in the process parameters (location and/or dispersion). In real-life situation, the shift is emerging in different sizes, and it is hard to identify it with classical control charts. Moreover, more than one process of characteristics required special attention because they must monitor jointly due to the association among them. This study offers two adaptive control charts to monitor the different sizes of a shift in the process mean vector. The novelty behind this study is to use dimensionally reduction techniques such as principal component analysis (PCA) and an adaptive method such as Huber and Bi-square functions. In brief, the multivariate cumulative sum control chart based on PCA is designed, and its plotting statistic is utilized as an input in the classical exponentially weighted moving average (EWMA) control chart. The run length (RL) properties of the proposed and other control charts are obtained by designing algorithms in MATLAB through a Monte Carlo simulation. For a single shift, the performance of the control charts is assessed through an average of RL, standard deviation of RL, and standard error of RL. Likewise, overall performance measures such as extra quadratic loss, relative ARL, and the performance comparison index are also used. The comparison reveals the superiority over other control charts. Furthermore, to emphasize the application process and benefits of the proposed control charts, a real-life example of the wind turbine process is included.https://www.mdpi.com/2227-7390/10/12/2025average run lengthcontrol chartsMonte Carlo simulationmultivariate CUSUMprincipal component |
| spellingShingle | Muhammad Riaz Babar Zaman Ishaq Adeyanju Raji M. Hafidz Omar Rashid Mehmood Nasir Abbas An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector Mathematics average run length control charts Monte Carlo simulation multivariate CUSUM principal component |
| title | An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector |
| title_full | An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector |
| title_fullStr | An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector |
| title_full_unstemmed | An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector |
| title_short | An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector |
| title_sort | adaptive ewma control chart based on principal component method to monitor process mean vector |
| topic | average run length control charts Monte Carlo simulation multivariate CUSUM principal component |
| url | https://www.mdpi.com/2227-7390/10/12/2025 |
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