An In-Depth Study of the Efficiency of Risk Evaluation Formulas for Multi-Fault Localization

A large amount of risk evaluation formulas have been proposed for spectrum-based fault localization (SBFL) in prior studies. A recent study by Xie et al. developed an innovative framework to theoretically analyze the effectiveness of those risk evaluation formulas in SBFL. Xie et al.'s study was based on the assumption that program has only one fault. In other words, they investigated SBFL in the context of single-fault SBFL. However, in practice, programs might have more than one faults. In this paper, we first propose a novel theoretical analysis framework for the risk evaluation formulas in the context of multi-faults SBFL. Our framework is based on a new effort cost evaluation L-Score. By applying our framework, we then conduct case studies to investigate the efficiency of existing formulas in the context of multi-faults SBFL.