Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions
Quick detection of an assignable cause is necessary for process accuracy with respect to the specifications. The aim of this study is to monitor the time and magnitude processes based on unit-interval data. To this end, maximum exponentially weighted moving average (Max-EWMA) control chart for simul...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/7951748 |
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| _version_ | 1849308101813993472 |
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| author | Muhammad Farhan Akram Sajid Ali Ismail Shah Giulia Marcon |
| author_facet | Muhammad Farhan Akram Sajid Ali Ismail Shah Giulia Marcon |
| author_sort | Muhammad Farhan Akram |
| collection | DOAJ |
| description | Quick detection of an assignable cause is necessary for process accuracy with respect to the specifications. The aim of this study is to monitor the time and magnitude processes based on unit-interval data. To this end, maximum exponentially weighted moving average (Max-EWMA) control chart for simultaneous monitoring time and magnitude of an event is proposed. To be precise, beta and unit gamma distributions are considered to develop the Max-EWMA chart. The chart’s performance is accessed using average run length (ARL), the standard deviation of run length (SDRL), and different quantiles of the run length distribution through extensive Monte Carlo simulations. Besides a comprehensive simulation study, the proposed charting methodology is applied to a real data set. The results show that the proposed chart is more efficient in detecting small to medium-sized shifts. The results also indicate that simultaneous shifts are detected more quickly as compared to the pure shift. |
| format | Article |
| id | doaj-art-135aa2f357d947fa9fe1cc086e790c05 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-135aa2f357d947fa9fe1cc086e790c052025-08-20T03:54:33ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/7951748Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma DistributionsMuhammad Farhan Akram0Sajid Ali1Ismail Shah2Giulia Marcon3Department of StatisticsDepartment of StatisticsDepartment of StatisticsDepartment of EngineeringQuick detection of an assignable cause is necessary for process accuracy with respect to the specifications. The aim of this study is to monitor the time and magnitude processes based on unit-interval data. To this end, maximum exponentially weighted moving average (Max-EWMA) control chart for simultaneous monitoring time and magnitude of an event is proposed. To be precise, beta and unit gamma distributions are considered to develop the Max-EWMA chart. The chart’s performance is accessed using average run length (ARL), the standard deviation of run length (SDRL), and different quantiles of the run length distribution through extensive Monte Carlo simulations. Besides a comprehensive simulation study, the proposed charting methodology is applied to a real data set. The results show that the proposed chart is more efficient in detecting small to medium-sized shifts. The results also indicate that simultaneous shifts are detected more quickly as compared to the pure shift.http://dx.doi.org/10.1155/2022/7951748 |
| spellingShingle | Muhammad Farhan Akram Sajid Ali Ismail Shah Giulia Marcon Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions Journal of Mathematics |
| title | Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions |
| title_full | Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions |
| title_fullStr | Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions |
| title_full_unstemmed | Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions |
| title_short | Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions |
| title_sort | unit interval time and magnitude monitoring using beta and unit gamma distributions |
| url | http://dx.doi.org/10.1155/2022/7951748 |
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