The effect of ignoring dependence between failure modes on evaluating system reliability

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 even though five truss failures were strongly correlated.