International Journal of Reliability and Safety 

Abstract: In this paper, a new variant of the Quickest Path Problem (QPP) is addressed with additional factors of risk and energy which leads to the evaluation of Risk-Energy Constrained Quickest Path Proble...

Abstract: Several inverse reliability measures (e.g. Probabilistic Performance Measure (PPM) and Probabilistic Sufficiency Factor (PSF)) that are essentially equivalent have been introduced in recent years as measures of safety. The different names for essentially the same measure reflect the fact that different researchers focused on different advantages of inverse measures. These advantages include improved computational efficiency of Reliability-Based Design Optimisation (RBDO), accuracy in Response Surface Approximations (RSAs) and easy estimates of resources needed for achieving target safety levels. This paper surveys these inverse measures and describes their advantages compared with the direct measures of safety such as probability of failure and reliability index. Methods to compute the inverse measures are also described. RBDO with inverse measure is demonstrated with a beam design example.

Abstract: Different representations of imprecise probabilities have been proposed, where interval-valued probabilities are used such that uncertainty is distinguished from variability. In this paper, we present a new form of imprecise probabilities for reliability assessment based on generalised intervals. Generalised intervals have group properties under the Kaucher arithmetic, which provides a concise representation and calculus structure as an extension of precise probabilities. With the separation between proper and improper interval probabilities, focal and non-focal events are differentiated based on the associated modalities and logical semantics. Focal events have the semantics of critical, uncontrollable, and specified in probabilistic analysis, whereas the corresponding non-focal events are complementary, controllable, and derived. A logic coherence constraint is proposed in the new form. Because of the algebraic properties of generalised intervals, conditional interval probability can be directly defined based on marginal interval probabilities. A Bayes' rule with generalised intervals allows us to interpret the logic relationship between interval prior and posterior probabilities. The imprecise Dirichlet model is also extended with the logic coherence constraint.

Abstract: This paper develops two algorithms that address the reliability evaluation of complex multidisciplinary engineering systems. In particular, systems with feedback coupling - a common characteristic of many multidisciplinary analyses - are considered. In such analyses, iterative convergence loops are needed to resolve inconsistencies in feedback variables. Assessing the reliability of such systems with a traditional 'black box' or fully coupled approach requires Multidisciplinary Analysis (MDA) convergence loops nested inside iterative loops for probabilistic analysis. The resulting computational effort is unacceptable for most high fidelity analyses. Therefore, this paper proposes two first-order reliability analysis methods that efficiently apply probabilistic analysis to multidisciplinary systems with feedback using a decoupling approach. The first method uses a First-Order Second Moment (FOSM) technique to characterise intermediate variables while applying more rigorous reliability analysis on the system as a whole. The second algorithm gives a specific solution to a decoupled first-order reliability analysis formulation as an optimisation problem. Each method is applied to an illustrative mathematical model and compared to otherwise equivalent coupled approaches with respect to accuracy and computational effort.