Perspective Chapter: Probabilistic Modeling of Failure – Nonlinear Approximation

Abstract

The failure of systems to meet the specified requirements may have adverse effects on their integrity and reliability. The systems could be mechanical, electrical, structural, telecommunications, or electronic that are designed and built to satisfy certain technical specifications and operational requirements. Failure does not necessarily mean the occurrence of a disaster or damage to the system, but also the degraded performance of such systems is considered a failure. One of the essential indicators of the performance and reliability of a system is the probability of failure which is computed by probabilistic methods. One of these methods is the first-order reliability method (FORM). Using FORM to estimate the probability of failure of systems having a nonlinear or a higher-order performance function may provide inaccurate results that may lead to misleading conclusions. To resolve this issue, the second-order reliability method (SORM) is recommended to estimate the probability of failure. This chapter presents commonly used probabilistic approximation methods to estimate the probability of failure for nonlinear performance functions. Illustrative examples to demonstrate the application of these methods are provided at the end of the chapter.