Max-EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions
The recent industrial revolution is a result of modern technological advancement and industrial improvements require quick detection of assignable causes in a process. This study presents a monitoring scheme for unit interval data assuming beta and unit Nadarajah and Haghighi distributions. To this...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9374740 |
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| _version_ | 1849408615609270272 |
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| author | Muhammad Farhan Akram Sajid Ali Ismail Shah Syed Muhammad Muslim Raza |
| author_facet | Muhammad Farhan Akram Sajid Ali Ismail Shah Syed Muhammad Muslim Raza |
| author_sort | Muhammad Farhan Akram |
| collection | DOAJ |
| description | The recent industrial revolution is a result of modern technological advancement and industrial improvements require quick detection of assignable causes in a process. This study presents a monitoring scheme for unit interval data assuming beta and unit Nadarajah and Haghighi distributions. To this end, a maximum exponentially weighted moving average (Max-EWMA) chart is introduced to jointly monitor unit interval bounded time and magnitude data. The performance of the proposed chart is evaluated by using average run length and other characteristics of run length distribution using extensive Monte Carlo simulations. Besides a comprehensive simulation study, a real data set is also used to assess the performance of the chart. The results supplementing the proposed chart are efficient for joint monitoring time and magnitude, and simultaneous shifts are detected more quickly than separate shifts in the process parameters. |
| format | Article |
| id | doaj-art-7c07191de45f43fba933ecd30f814bfb |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-7c07191de45f43fba933ecd30f814bfb2025-08-20T03:35:44ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9374740Max-EWMA Chart Using Beta and Unit Nadarajah and Haghighi DistributionsMuhammad Farhan Akram0Sajid Ali1Ismail Shah2Syed Muhammad Muslim Raza3Department of StatisticsDepartment of StatisticsDepartment of StatisticsDepartment of Economics and StatisticsThe recent industrial revolution is a result of modern technological advancement and industrial improvements require quick detection of assignable causes in a process. This study presents a monitoring scheme for unit interval data assuming beta and unit Nadarajah and Haghighi distributions. To this end, a maximum exponentially weighted moving average (Max-EWMA) chart is introduced to jointly monitor unit interval bounded time and magnitude data. The performance of the proposed chart is evaluated by using average run length and other characteristics of run length distribution using extensive Monte Carlo simulations. Besides a comprehensive simulation study, a real data set is also used to assess the performance of the chart. The results supplementing the proposed chart are efficient for joint monitoring time and magnitude, and simultaneous shifts are detected more quickly than separate shifts in the process parameters.http://dx.doi.org/10.1155/2022/9374740 |
| spellingShingle | Muhammad Farhan Akram Sajid Ali Ismail Shah Syed Muhammad Muslim Raza Max-EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions Journal of Mathematics |
| title | Max-EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions |
| title_full | Max-EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions |
| title_fullStr | Max-EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions |
| title_full_unstemmed | Max-EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions |
| title_short | Max-EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions |
| title_sort | max ewma chart using beta and unit nadarajah and haghighi distributions |
| url | http://dx.doi.org/10.1155/2022/9374740 |
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