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...

Full description

Saved in:
Bibliographic Details
Main Authors: Ce Shi, Tatsuhiro Tsuchiya, Chengmin Wang
Format: Article
Language:English
Published: AIMS Press 2024-12-01
Series:AIMS Mathematics
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/math.20241657
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832590782100406272
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