# Consecutive Detecting Arrays for Interaction Faults

## TL;DR

This paper introduces consecutive detecting arrays (CDAs) for ordered interaction fault detection in software testing, establishing their optimality criteria and providing numerous optimal constructions, especially for systems with few factors.

## Contribution

It proposes a new family of detecting arrays considering interaction order, and links their optimality to orthogonal arrays, expanding the design space for fault detection tests.

## Key findings

- Established a criterion for CDA optimality.
- Demonstrated the equivalence between optimal CDAs and certain orthogonal arrays.
- Provided numerous constructions of optimal CDAs, especially for small systems.

## Abstract

The concept of detecting arrays was developed to locate and detect interaction faults arising between the factors in a component-based system during software testing. In this paper, we propose a family of consecutive detecting arrays (CDAs) in which the interactions between factors are considered to be ordered. CDAs can be used to generate test suites for locating and detecting interaction faults between neighboring factors. We establish a general criterion for measuring the optimality of CDAs in terms of their size. Based on this optimality criterion, the equivalence between optimum CDAs and consecutive orthogonal arrays with prescribed properties is explored. Using the advantages of this equivalence, a great number of optimum CDAs are presented. In particular, the existence of optimum CDAs with few factors is almost completely determined.