Using imprecise continuous time Markov chains for assessing the reliability of power networks with common cause failure and non-immediate repair.

We explore how imprecise continuous time Markov chains can improve traditional reliability models based on precise continuous time Markov chains. Specifically, we analyse the reliability of power networks under very weak statistical assumptions, explicitly accounting for non-stationary failure and repair rates and the limited accuracy by which common cause failure rates can be estimated. Bounds on typical quantities of interest are derived, namely the expected time spent in system failure state, as well as the expected number of transitions to that state. A worked numerical example demonstrates the theoretical techniques described. Interestingly, the number of iterations required for convergence is observed to be much lower than current theoretical bounds

Robust Inference of Trees

This paper is concerned with the reliable inference of optimal tree-approximations to the dependency structure of an unknown distribution generating data. The traditional approach to the problem measures the dependency strength between random variables by the index called mutual information. In this paper reliability is achieved by Walley's imprecise Dirichlet model, which generalizes Bayesian learning with Dirichlet priors. Adopting the imprecise Dirichlet model results in posterior interval expectation for mutual information, and in a set of plausible trees consistent with the data. Reliable inference about the actual tree is achieved by focusing on the substructure common to all the plausible trees. We develop an exact algorithm that infers the substructure in time O(m^4), m being the number of random variables. The new algorithm is applied to a set of data sampled from a known distribution. The method is shown to reliably infer edges of the actual tree even when the data are very scarce, unlike the traditional approach. Finally, we provide lower and upper credibility limits for mutual information under the imprecise Dirichlet model. These enable the previous developments to be extended to a full inferential method for trees.Comment: 26 pages, 7 figure

Bayesian reliability analysis with imprecise prior probabilities

The Bayesian framework for statistical inference offers the possibility of taking expert opinions into account, and is therefore attractive in practical problems concerning reliability of technical systems. Probability is the only language in which uncertainty can be consistently expressed, and this requires the use of prior distributions for reporting expert opinions. In this paper an extension of the standard Bayesian approach based on the theory of imprecise probabilities and intervals of measures is developed. It is shown that this is necessary to take the nature of experts knowledge into account. The application of this approach in reliability theory is outlined. The concept of imprecise probabilities allows us to accept a range of possible probabilities from an expert for events of interest and thus makes the elicitation of prior information simpler and clearer. The method also provides a consistent way for combining the opinions of several experts

FRAM for systemic accident analysis: a matrix representation of functional resonance

Due to the inherent complexity of nowadays Air Traffic Management (ATM) system, standard methods looking at an event as a linear sequence of failures might become inappropriate. For this purpose, adopting a systemic perspective, the Functional Resonance Analysis Method (FRAM) originally developed by Hollnagel, helps identifying non-linear combinations of events and interrelationships. This paper aims to enhance the strength of FRAM-based accident analyses, discussing the Resilience Analysis Matrix (RAM), a user-friendly tool that supports the analyst during the analysis, in order to reduce the complexity of representation of FRAM. The RAM offers a two dimensional representation which highlights systematically connections among couplings, and thus even highly connected group of couplings. As an illustrative case study, this paper develops a systemic accident analysis for the runway incursion happened in February 1991 at LAX airport, involving SkyWest Flight 5569 and USAir Flight 1493. FRAM confirms itself a powerful method to characterize the variability of the operational scenario, identifying the dynamic couplings with a critical role during the event and helping discussing the systemic effects of variability at different level of analysis

On the reliability of multistate systems with imprecise probabilities

Розглядається обчислення надійності в складних системах за наявності випадкового набору оцінок працездатності елементів. Виявлено, що підхід Демпстер-Шефера є відповідним математичним інструментом, який відповідає поставленим задачам. Для випадку, коли взаємозалежності елементів невідомі, наведено також оцінки ефективності системи переконань і правдоподібність функції.Рассматривается вычисления надежности в сложных системах при наличии случайного набора оце- нок работоспособности элементов. Выявлено, что подход Демпстер-Шефера является соответствующим математическим инструментом, который соответствует поставленным задачам. Для случая, когда взаимозависимости элементов неизвестны, приведены также оценки эффективности системы убеждений и правдоподобность функции.We consider the computation of multistate systems reliabilities in the presence of random set estimations for the elements' working abilities. It turns out that the Dempster-Shafer approach is a suitable mathematical tool. For the case that the interdependence of the elements is unknown, bounds for the system's performance belief and plausibility functions are given as well