Mode importance measures under multiple failure modes and their solutions

For structural system with multiple failure modes extensively present in engineering practice, effects of failure modes on the system uncertainties need to be considered, upon which the design work can be improved. Enlightened by the concept of importance measures for basic variables, three mode importance measures are established to reflect the effects of failure modes on the system uncertainties, i. e. importance measures of failure modes on the system failure probability, importance measures of failure modes on the probabilistic distribution of the system response, and the correlation coefficient between the single failure mode and the system. Properties of these three mode importance measures are discussed, as well as the numerical simulation method employed to solve them. Based on the theories proposed here, the ranking of the contributions of failure modes can be obtained, thus providing design guidelines for engineers. Numerical and engineering examples are probed into later, to demonstrate the feasibility and rationality of the proposed mode importance measures.