Nonprobabilistic reliability analysis method for series-parallel structural systems with correlated uncertainties

Traditionally, nonprobabilistic methods for reliability problems evaluate the reliability level of single failure modes, lacking the capability to perform comprehensive reliability analysis series–parallel systems formed by multiple failure modes. In this paper, the nonprobabilistic systematic reliability method (NSRM) is proposed to evaluate the reliability of series–parallel systems within the nonprobabilistic framework. Firstly, the correlation propagation analysis is introduced to quantify the ellipsoidal uncertain domain of limit state functions, upon which all subsequent reliability analyses are based. Subsequently, an equivalence-based method based is proposed to determine the equivalent limit state functions of parallel subsystems, accompanied by the establishment of an optimal equivalence strategy. The NSRM is further established by combining the second order reliability bound techniques. Lastly, the paper presents two numerical examples and an engineering application, showcasing the efficacy and precision of the proposed NSRM in practical scenarios.