System Reliability Updating of Fatigue-induced Sequential Failures through Inspection and Repair

Structural systems are often subjected to the risk of fatigue-induced failures caused by repeated loadings during their service lifetime (Byers et al. 1997, Karamchandani et al. 1992). The reliability of such structural systems can be sustained through effective structural maintenance as well as proper structural design. It is thus essential to update the reliability of a structure against fatigue-induced sequential failures based on the actual observations from structural inspection and the further actions such as repair. Although much research effort has been dedicated to such structural reliability updating through inspection and repair, many existing studies have focused on updating the reliability of individual structural members. For accurate reliability updating of fatigue-induced sequential failure of structures, the reliability needs to be considered at a system level (Moan and Song 2000). For example, the common or correlated random variables involved with fatigue crack growth may result in significant statistical dependence between the failures of different structural members or between inspected and uninspected members. Furthermore, due to the nature of fatigue-induced sequential failure, a structural member can contribute to multiple important failure sequences. For these reasons, the reliability updating should be performed at the system level. For precise system reliability analysis of fatigue-induced sequential failures, a new Branch-and-Bound method employing system reliability Bounds (termed the B method) has been recently developed (Lee and Song 2011a). By describing failure sequences as disjoint cut-sets, the B method identifies critical sequences of fatigue-induced failure in the decreasing order of their likelihood, as it systematically updates lower and upper bounds of the system failure probability, which enables accurate risk estimation of fatigue-induced sequential failures. In addition, the method has been further developed through integration with sophisticated programs of finite element (FE) analysis and crack growth analysis for FEbased system reliability analysis of fatigue-induced sequential failures (Lee and Song 2011b). Through applications of the B method to numerical examples, it was successfully shown that the method allows efficient and accurate system reliability analysis of fatigue-induced sequential failures of continuum. This paper introduces a new system reliability updating method that employs the B method for fatigue-induced sequential failures. Since the B analysis identifies the most critical failure and non-failure cases, the probabilities updated by the proposed method can accurately update upper and lower bounds on system failure probability with a reasonable gap. In addition, the new method allows us to update the original probability efficiently because it reuses the results of the original B analysis. The proposed method is first demonstrated by a simple numerical example in which Monte Carlo simulation is performed for verifying the results. Furthermore, the method is applied to a more complex structural example, which shows that the method enables us to perform system reliability updating of fatigue-induced sequential failures efficiently and accurately. In these numerical examples, various scenarios with multiple times of inspection and repair are assumed, and the corresponding effects are