Some Important Issues on First Order Reliability Analysis With Nonprobabilistic Convex Models

Abstract

Compared with the probability model, the convex model approach only requires the bound information on the uncertainty, and can make it possible to conduct the reliability analysis for many complex engineering problems with limited samples. Presently, by introducing the wellestablished techniques in probabilitybased reliability analysis, some methods have been successfully developed for convex model reliability. This paper aims to reveal some different phenomena and furthermore some severe paradoxes when extending the widely used firstorder reliability method (FORM) into the convex model problems, and whereby provide some useful suggestions and guidelines for convexmodelbased reliability analysis. Two FORMtype approximations, namely, the meanvalue method and the designpoint method, are formulated to efficiently compute the nonprobabilistic reliability index. A comparison is then conducted between these two methods, and some important phenomena different from the traditional FORMs are summarized. The nonprobabilistic reliability index is also extended to treat the system reliability, and some unexpected paradoxes are found through two numerical examples.