Optimal Design of One-Sided Exponential Adaptive EWMA Scheme Based on Median Run Length
High-quality processes, characterized by low defect rates, typically exhibit an exponential distribution for time-between-events (TBE) data. To effectively monitor TBE data, one-sided exponential Adaptive Exponentially Weighted Moving Average (AEWMA) schemes are introduced. However, the run length (...
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2024-12-01
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| Online Access: | https://www.mdpi.com/1999-4893/18/1/5 |
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| author | Yulong Qiao Zixing Wu Qian Zhang Qin Xu Ge Jin |
| author_facet | Yulong Qiao Zixing Wu Qian Zhang Qin Xu Ge Jin |
| author_sort | Yulong Qiao |
| collection | DOAJ |
| description | High-quality processes, characterized by low defect rates, typically exhibit an exponential distribution for time-between-events (TBE) data. To effectively monitor TBE data, one-sided exponential Adaptive Exponentially Weighted Moving Average (AEWMA) schemes are introduced. However, the run length (RL) distribution varies with the magnitude of the process mean shift, rendering the median run length (MRL) a more pertinent performance metric. This paper investigates the RL properties of one-sided exponential AEWMA schemes using a Markov chain method. An optimal design procedure based on MRL is developed to enhance the one-sided exponential AEWMA scheme. Comparative analyses reveal that the one-sided exponential AEWMA scheme provides better balanced protection against both minor and major shifts in the process mean compared to EWMA-type and Shewhart schemes. Finally, two practical case studies illustrate the application of AEWMA schemes in manufacturing. |
| format | Article |
| id | doaj-art-9b7d24f978054a9aa69a174289cd30d5 |
| institution | Kabale University |
| issn | 1999-4893 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj-art-9b7d24f978054a9aa69a174289cd30d52025-01-24T13:17:25ZengMDPI AGAlgorithms1999-48932024-12-01181510.3390/a18010005Optimal Design of One-Sided Exponential Adaptive EWMA Scheme Based on Median Run LengthYulong Qiao0Zixing Wu1Qian Zhang2Qin Xu3Ge Jin4School of Information Technology, Jiangsu Open University, Nanjing 210036, ChinaSchool of Information Technology, Jiangsu Open University, Nanjing 210036, ChinaSchool of Information Technology, Jiangsu Open University, Nanjing 210036, ChinaSchool of Network Security, Jinling Institute of Technology, Nanjing 211169, ChinaSchool of Information Technology, Jiangsu Open University, Nanjing 210036, ChinaHigh-quality processes, characterized by low defect rates, typically exhibit an exponential distribution for time-between-events (TBE) data. To effectively monitor TBE data, one-sided exponential Adaptive Exponentially Weighted Moving Average (AEWMA) schemes are introduced. However, the run length (RL) distribution varies with the magnitude of the process mean shift, rendering the median run length (MRL) a more pertinent performance metric. This paper investigates the RL properties of one-sided exponential AEWMA schemes using a Markov chain method. An optimal design procedure based on MRL is developed to enhance the one-sided exponential AEWMA scheme. Comparative analyses reveal that the one-sided exponential AEWMA scheme provides better balanced protection against both minor and major shifts in the process mean compared to EWMA-type and Shewhart schemes. Finally, two practical case studies illustrate the application of AEWMA schemes in manufacturing.https://www.mdpi.com/1999-4893/18/1/5EWMAadaptive schemeexponential distributionmedian run lengthoptimal design |
| spellingShingle | Yulong Qiao Zixing Wu Qian Zhang Qin Xu Ge Jin Optimal Design of One-Sided Exponential Adaptive EWMA Scheme Based on Median Run Length Algorithms EWMA adaptive scheme exponential distribution median run length optimal design |
| title | Optimal Design of One-Sided Exponential Adaptive EWMA Scheme Based on Median Run Length |
| title_full | Optimal Design of One-Sided Exponential Adaptive EWMA Scheme Based on Median Run Length |
| title_fullStr | Optimal Design of One-Sided Exponential Adaptive EWMA Scheme Based on Median Run Length |
| title_full_unstemmed | Optimal Design of One-Sided Exponential Adaptive EWMA Scheme Based on Median Run Length |
| title_short | Optimal Design of One-Sided Exponential Adaptive EWMA Scheme Based on Median Run Length |
| title_sort | optimal design of one sided exponential adaptive ewma scheme based on median run length |
| topic | EWMA adaptive scheme exponential distribution median run length optimal design |
| url | https://www.mdpi.com/1999-4893/18/1/5 |
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