Separable detecting arrays
This paper aimed to address the issue of potential noise or measurement errors in component-based systems by utilizing separable detecting arrays (SDAs) to identify interaction faults and assess whether the number of faulty interactions exceeded a predefined threshold. In this paper, we established...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241657 |
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| author | Ce Shi Tatsuhiro Tsuchiya Chengmin Wang |
| author_facet | Ce Shi Tatsuhiro Tsuchiya Chengmin Wang |
| author_sort | Ce Shi |
| collection | DOAJ |
| description | This paper aimed to address the issue of potential noise or measurement errors in component-based systems by utilizing separable detecting arrays (SDAs) to identify interaction faults and assess whether the number of faulty interactions exceeded a predefined threshold. In this paper, we established a comprehensive lower bound on the size of SDAs and explored an equivalence between optimum SDAs and orthogonal arrays with specific properties. By leveraging this equivalence, numerous optimum SDAs were derived from known results of orthogonal arrays. Additionally, optimum SDAs constructed from difference matrices (DMs) possessing the 'super-simple' property were presented. Several infinite classes of such DMs were provided. Specifically, the existence of super-simple DMs with four rows was fully determined. Our study's findings offer practical implications for improving the reliability and accuracy of fault detection in component-based systems. |
| format | Article |
| id | doaj-art-e0791a8f1bbf42ccb64bb29349718464 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-e0791a8f1bbf42ccb64bb293497184642025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912348063482610.3934/math.20241657Separable detecting arraysCe Shi0Tatsuhiro Tsuchiya1Chengmin Wang2School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, ChinaGraduate School of Information Science and Technology, Osaka University, Suita 565-0871, JapanDepartment of Mathematics, Taizhou University, Taizhou 225300, ChinaThis paper aimed to address the issue of potential noise or measurement errors in component-based systems by utilizing separable detecting arrays (SDAs) to identify interaction faults and assess whether the number of faulty interactions exceeded a predefined threshold. In this paper, we established a comprehensive lower bound on the size of SDAs and explored an equivalence between optimum SDAs and orthogonal arrays with specific properties. By leveraging this equivalence, numerous optimum SDAs were derived from known results of orthogonal arrays. Additionally, optimum SDAs constructed from difference matrices (DMs) possessing the 'super-simple' property were presented. Several infinite classes of such DMs were provided. Specifically, the existence of super-simple DMs with four rows was fully determined. Our study's findings offer practical implications for improving the reliability and accuracy of fault detection in component-based systems.https://www.aimspress.com/article/doi/10.3934/math.20241657separable detecting arrayssuper-simple orthogonal arrayssuper-simple difference schemeoptimality |
| spellingShingle | Ce Shi Tatsuhiro Tsuchiya Chengmin Wang Separable detecting arrays AIMS Mathematics separable detecting arrays super-simple orthogonal arrays super-simple difference scheme optimality |
| title | Separable detecting arrays |
| title_full | Separable detecting arrays |
| title_fullStr | Separable detecting arrays |
| title_full_unstemmed | Separable detecting arrays |
| title_short | Separable detecting arrays |
| title_sort | separable detecting arrays |
| topic | separable detecting arrays super-simple orthogonal arrays super-simple difference scheme optimality |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241657 |
| work_keys_str_mv | AT ceshi separabledetectingarrays AT tatsuhirotsuchiya separabledetectingarrays AT chengminwang separabledetectingarrays |