2 2.2. Fault Tree Analysis 43 OR BE1 AND Top event TE G1 Logic Gate BE2 BE3 Basic Event 3 Basic Event 1 Basic Event 2 Figure 2.1: Inferred FTF from toy dataset in Table 2.1. Thus, for this failure dataset, we want to find the FT structure F that best encodes the logic that describes the failure propagation in the system. Moreover, we are interested in the FT F composed of a minimal amount of elements. The desired output is presented in Figure 2.1, where the inferred FT is composed of basic events BE1, BE2, connected to an AND-gate (G1), which together with BE3, is connected with an OR-gate to the top event TE. Here the gates, which connect the basic events and the top event, result from the inference process following the logic described by the failure dataset. And although for this example the solution is rather simple, for larger failure datasets (i.e., with more basic events) the solution is not straightforward. Contributions. This chapter o!ers: (i) A demonstration that Multi-Objective Evolutionary Algorithms (MOEAs) can achieve more consistent and e"cient FT structures by optimising multiple criteria simultaneously. (ii) A new metric for comparing FT structures using Minimal Cut Sets and the RV-coe!cient. (iii) A parametric analysis elucidating the algorithm’s performance under varying conditions. (iv) Evidence that compact FTs improve convergence speed. Data and implementation are available at zenodo.org/record/5536431. Outline. The remaining part of this chapter is organised as follows. Section 2.2 provides background on Fault Tree Analysis (FTA). Section 2.3 provides the technical background of Multi-Objective Evolutionary Algorithms (MOEAs). Section 2.4 explains our methodology. Section 2.6 presents how we apply the NSGA-II (an MOEA) to infer FTs. Section 2.7 presents the results of our thorough parametric analysis. Section 2.8 discusses our findings and conclusions. 2.2 Fault Tree Analysis Fault Tree Analysis (FTA) is a widely recognised method in reliability engineering that supports design and maintenance decisions for complex systems. FTA enables both qualitative and quantitative analyses. The qualitative analysis, based on an FT structure, identifies critical system components, with a focus on Minimal
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