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 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.