, Volume 94, Issue 2, pp 313-324

First online:

A verified realization of a Dempster–Shafer based fault tree analysis

  • Gabor RebnerAffiliated withUniversity of Duisburg-Essen Email author 
  • , Ekaterina AuerAffiliated withUniversity of Duisburg-Essen
  • , Wolfram LutherAffiliated withUniversity of Duisburg-Essen

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Fault tree analysis is a method to determine the likelihood of a system attaining an undesirable state based on the information about its lower level parts. However, conventional approaches cannot process imprecise or incomplete data. There are a number of ways to solve this problem. In this paper, we will consider the one that is based on the Dempster–Shafer theory. The major advantage of the techniques proposed here is the use of verified methods (in particular, interval analysis) to handle Dempster–Shafer structures in an efficient and consistent way. First, we concentrate on DSI (Dempster–Shafer with intervals), a recently developed tool. It is written in MATLAB and serves as a basis for a new add-on for Dempster–Shafer based fault tree analysis. This new add-on will be described in detail in the second part of our paper. Here, we propagate experts’ statements with uncertainties through fault trees, using mixing based on arithmetic averaging. Furthermore, we introduce an implementation of the interval scale based algorithm for estimating system reliability, extended by new input distributions.


Dempster–Shafer theory Fault tree analysis MATLAB INTLAB Interval analysis

Mathematics Subject Classification (2000)

65G30 60A99