46 Chapter 2. Automatic Inference of Fault Tree Models via Multi-Objective Evolutionary Algorithms 2.4 Methodology Case study (FT*) (Section 2.6.2) Parameters to evaluate (Section 2.5.5) The Monte Carlo method (Section 2.6.1) The Failure Dataset (Section 2.4.1) FT-MOEA (Section 2.5) Inferred FT Parametric analysis (Section 2.6.4) Figure 2.3: General methodology followed in this chapter. Figure 2.3 depicts the general methodology we followed in this chapter. First, we selected some case studies of existing FTs (Section 2.7.2), these FTs act as ground truth. Then, we selected some parameters of interest (Section 2.7.4) to be evaluated in the parametric analysis. We used the Monte Carlo method (Section 2.7.1) to generate synthetic failure datasets (Section 2.5) based on selected case studies. Then we used our FT-MOEA algorithm (Section 2.6) to infer the FT based on the provided failure dataset. Finally, we compared the ground truth with the inferred FTs and evaluate the experiment (Section 2.7). 2.5 The failure dataset We formally defined the failure dataset in Section I.4.2. For this chapter, we also assume the following: - Labelled: The dataset contains combinations of BE and their corresponding TE. - Binary: Both BE and TE are binary, allowing for the use of Boolean operations, which enhances algorithm e"ciency. Here, 0 and 1 represent non-faulty and faulty states, respectively. - Monotonic/consistent: For any set of BE, if a BE changes from 0 to 1, TE may change from 0 to 1 but will never change from 1 to 0. - Complete: The number of unique BE combinations in the failure dataset matches the space complexity O(2w), where wis the number of unique BE for a given FT. - Noise-free: The failure dataset contains no corrupted information; the relationship BE↑TE is always accurate for a given FT. Table 2.2 illustrates an example dataset corresponding to the FT depicted in Figure 2.2. This dataset was generated using the Monte Carlo method outlined in Section 2.7.1, with N=250,000 data points and a failure rate of pi =0.5 for each BE. Ob. denotes the observation associated with a unique combination of BE values and the corresponding TE. The columns BE1, BE2, ..., BE7 represent the states of the BE set, while TE indicates the top event. The final column shows the count of each observation in the failure dataset.
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