Felipe Aguirre

Reliability assessment for multi-state systems under uncertainties based on the Dempster–Shafer theory

This article presents an original method for evaluating reliability indices for Multi-State Systems (MSSs) in the presence of aleatory and epistemic uncertainties. In many real- world MSSs, an insufficiency of data makes it difficult to estimate precise values for component state probabilities. The proposed approach applies the transferable belief model interpretation of the Dempster–Shafer theory to represent component state beliefs and to evaluate the MSS reliability indices. The example of an oil transmission system is used to demonstrate the proposed approach and it is compared with the universal generating function method. The value of the Dempster–Shafer theory lies in its ability to use several combination rules in order to evaluate reliability indices for MSSs that depend on the reliability of the experts’ opinions as well as their independence.

Transferable belief model for reliability analysis of systems with data uncertainties and failure dependencies

Abstract Dealing with uncertainty adds a further level of complexity to problems of reliability analysis. The uncertainties which impact reliability studies usually involve incomplete or imprecise reliability data and complex failure dependencies. This paper proposes an original methodology based on the transferable belief model (TBM) to include failure dependencies between components in the evaluation of the reliability of the whole system, given both epistemic and aleatory uncertainties. First, based on expert opinion and experimental data, basic probability assignments (BPAs) are assigned to reliability data components. TBM operations are then used to obtain the reliability of the whole system, for series, parallel, series–parallel, parallel–series, and bridge configurations. Implicit, explicit, and discounting approaches are presented for taking account of failure dependencies. Finally, the proposed model is applied to take into account common cause failures (CCFs) in a case study.

An evidential network approach to support uncertain multiviewpoint abductive reasoning

The paper proposes an approach to support human abductive reasoning in the diagnosis of a multiviewpoint system. The novelty of this work lies on the capability of the approach to treat the uncertainty held by the agent performing the diagnosis. To do so, we make use of evidential networks to represent and propagate the uncertain evidence gathered by the agent. Using forward and backward propagation of the information, the impact of the evidence over the different symptoms and causes of failure is quantified. The agent can then make use of this information as additional hints in an iterative diagnosis process until a desired degree of certainty is obtained. The model is compared with a deterministic one in which evidence is represented by binary states, that is, a symptom is either observed or not.

Construction of Belief Functions From Statistical Data About Reliability Under Epistemic Uncertainty

Probability theory is well adapted to handle aleatory uncertainties resulting from the variability of failure phenomena. Recently, several uncertainty theories such as belief function theory were introduced in reliability assessments to handle epistemic uncertainties resulting from the lack of knowledge or insufficient data. In this paper, we propose some methods to construct belief functions of reliability parameters of components from statistical data about reliability. The proposed methods consider the parametric estimation of reliability parameters.

Inclusion-exclusion principle for belief functions

The inclusion-exclusion principle is a well-known property in probability theory, and is instrumental in some computational problems such as the evaluation of system reliability or the calculation of the probability of a Boolean formula in diagnosis. However, in the setting of uncertainty theories more general than probability theory, this principle no longer holds in general. It is therefore useful to know for which families of events it continues to hold. This paper investigates this question in the setting of belief functions. After exhibiting original sufficient and necessary conditions for the principle to hold, we illustrate its use on the uncertainty analysis of Boolean and non-Boolean systems in reliability.

Application of evidential networks in quantitative analysis of railway accidents

Currently, a high percentage of accidents in railway systems are accounted to human factors. As a consequence, safety engineers try to take into account this factor in risk assessment. However, human reliability data are very difficult to quantify, thus, qualitative methods are often used in railway system’s risk assessments. Modeling of human errors through probabilistic approaches has shown some limitation concerning the quantification of qualitative aspects of human factors. The proposed article presents an original method to account for the human factor by using evidential networks and fault tree analysis.

A Quantitative Study of the Occurrence of a Railway Accident Based on Belief Functions

In the field of railway systems, there is a great interest to include the human factor in the risk analysis process. Indeed, a great number of accidents are consider to be triggered by the human factors interacting in the situation. Several attempts have been made to include human factors in safety analysis, but they generally attack the problem in a qualitative way. The choice of qualitative methods arises from the difficulty to elicit human behavior and the effects on systems safety. This paper presents a first attempt to account for the human factor by using the generalized bayesian theory and fault tree analysis.