Regional importance analysis under multiple failure modes

For structural system with multiple failure modes extensively present in engineering practice, two regional mode importance measures are proposed on the basis of the existing mode importance measures, i.e., the regional mode importance measure based on failure probability and the regional mode importance measure based on sample mean of output response. Compared with the existing global mode importance measures, the proposed regional importance measures can not only provide the inter-mode importance information, but also reflect the effects of different regions of input variables on the importance of a single mode or a group of modes, thus providing useful information to improve and optimize the reliability model. Numerical and engineering examples are used to demonstrate the feasibility and rationality of the proposed indices.