The effect of ignoring dependence between failure modes on evaluating system reliability
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Assuming independence between failure modes makes system reliability calculation simple but it adds approximation error. Interestingly, error due to ignoring dependence can be negligible for a highly reliable system. This paper investigates the reasons and the factors affecting the error. Error in system probability of failure (PF) is small for high reliability when tail-dependence is not very strong or the ratio between individual PFs is large. We created various conditions using copulas and observed the effect of ignoring dependence. Two reliability-based design optimization problems with a 2-bar and a 10-bar trusses are presented to show the effect of error on the optimum design and the system PF calculation. For the 10-bar truss, there were 5 % error in system PF and mass penalty less than 0.1 % in the optimum design for a target system PF of 10−7 even though five truss failures were strongly correlated.
KeywordsMultiple failure modes Tail-dependence System reliability Dependence Correlation Reliability-based design optimization
This work was supported by the National Science Foundation, under the grant CMMI-0856431 by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.
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