Chapters authored
Probabilistic Modeling of Failure
Failure of a system or a component of a system is and has been a major concern to systems’ operators and owners. Failure could be traced back to different causes and may take different forms and shapes. It may result from software malfunction, hardware degraded performance, human error, sabotage, environmental as well as other external factors. There are various techniques found in the literature that can assist in the analysis of failure. These techniques comprise deterministic and probabilistic techniques. Deterministic techniques ignore the variability and uncertainties of the variables in the analysis which may lead to unsatisfactory and inaccurate results. While probabilistic techniques produce accurate and an all-inclusive result because they incorporate the variabilities and uncertainties in the analysis. The focus of this chapter is to present commonly used probabilistic failure analysis techniques and their mathematical derivations. Examples to enhance the understanding of the concept of failure analysis are also presented.
Part of the book: Failure Analysis
Perspective Chapter: Probabilistic Modeling of Failure – Nonlinear Approximation
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.
Part of the book: Failure Analysis