Yayılan hataların bulunduğu ve sistem bilgisinin eksik olduğudurumlarda çoklu arıza tespiti problemi için bir dal kesi yöntemi

Failure detection in complex systems is a crucial task that attracts significant attention from both industry and academia. Accurate detection of the failed component(s) and equally importantly the failure spread path(s) are critical to take corrective actions (in time) to restore a malfunctioning system and improve its design. In this thesis, we focus on multiple failure detection that relaxes the simplifying assumption of a single component failure, at the time of inspection, which is difficult to justify for many real world problems that involve fault-tolerant systems with little opportunity of maintenance during their operation. We also aim to relax the commonly used perfect information assumption (accurately detecting all the symptoms) and consider the cases where only a (random) subset of possible symptoms can be successfully detected, due to possible failures in the sensors as well. To address this urgent yet challenging problem we introduce a novel approach that uses graph theory concepts to model the diagnosis problem with an Integer programming formulation and devise a branch-and-cut algorithm to solve it efficiently. Extensive numerical experiments on realistic problem instances attests to the superior performance of our approach, in terms of both computational efficiency and prediction accuracy, compared to the state-of-the-art in the literature.