Non-Probabilistic Reliability Bounds for Series Structural Systems

Most of the current non-probabilistic reliability methods are applicable for an individual component of a structure. However, a system consisting of interconnected components is involved in many engineering problems and its non-probabilistic reliability analysis remains a major challenge. In this paper, a non-probabilistic reliability method using upper and lower bound techniques is proposed for a series structural system. Based on the failure areas and the joint failure areas of two failure modes, the bounds of the non-probabilistic failure degree for a series system are firstly formulated. A judgement criterion is then presented to determine the joint failure areas of two failure modes. An analytical solution for the joint failure area of two failure modes is further given to simplify the calculation of the bounds. Four numerical examples are used to demonstrate the validity and effectiveness of the presented method.