Application of dynamic evidential networks in reliability analysis of complex systems with epistemic uncertainty and multiple life distributions

  • Jinhua Mi
  • Yuhua ChengEmail author
  • Yufei Song
  • Libing Bai
  • Kai Chen
S.I.: Reliability Modeling with Applications Based on Big Data


With the modernization and intelligent of industrial equipment and systems, the challenges of dynamic characteristics, failure dependency and uncertainties have aroused by the increasing of system complexity. Besides, various types of components may follow different life distributions which bring the multiple life distributions problem in systems. In order to model the impact of time dependency and epistemic uncertainty on the failure behavior of system, this paper combines the flexible dynamic modeling with the uncertainty expression. Its advantages are intuitively graphical representation and reasoning that brought by evidential network (EN). After that, the discrete time dynamic evidential network (DT-DEN) is introduced to analyze the reliability of complex systems, and the network inference mechanism is clearly defined. The evidence theory and original definition and inference mechanism of conventional EN is firstly recommended, and the DT-DEN is further presented. Furthermore, the multiple life distributions are synthesized into the DT-DEN to tackle the epistemic uncertainty and mixed life distribution challenges. Specifically, the dynamic logic gates are converted into equivalent DENs with distinguished conditional mass tables, and then the belief interval of system reliability can be calculated by network forward reasoning. Finally, the availability and efficiency of the proposed method is verified by some numerical examples.


Evidence theory Dynamic evidential networks Epistemic uncertainty Multiple life distribution 

List of symbols

\( \varOmega \)

Frame of discernment

\( {2^{\varOmega}} \)

Power set

\( m\left( \cdot \right) \)

Mass function

\( Bel\left( \cdot \right) \)

Belief function

\( Pl\left( \cdot \right) \)

Plausibility function

\( \zeta \)

An evidential network (EN)


Node set of EN


Edge set of EN


Belief mass set of EN

\( \zeta_{ \to } \)

A dynamic evidential network (DEN)

\( N_{ \to } \)

Node set of DEN

\( E_{ \to } \)

Edge set of DEN

\( M_{ \to } \)

Belief mass set of DEN

\( M(X) \)

Belief mass assignment of variable X

\( \pi \left( \cdot \right) \)

Set of parent nodes

\( \Delta \)

Length of each time slice

\( {\mathbf{M}}\left( \cdot \right) \)

State transition matrix


Bayesian network


Credal network


Evidential network


Discrete time dynamic evidential network


Binary decision diagram


Dynamic fault tree


Probability box


Basic probability assignment


Conditional mass table


Conditional belief mass table


Directed acyclic graph


Cold spare gate


Hot spare gate


Functional dependent gate



This work was partially supported by the National Natural Science Foundation of China under contact Nos. 51805073 and 51607024, the Chinese Universities Scientific Fund under contact No. ZYGX2018J061, and the National Key Research and Development Program of China under contact No. 2017YFC1501005.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Automation Engineering, University of Electronic Science and Technology of ChinaChengduChina
  2. 2.Center for System Reliability and Safety, University of Electronic Science and Technology of ChinaChengduChina
  3. 3.Institute for Risk and Reliability, Leibniz University HannoverHannoverGermany

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