4 4.7. Conclusions 89 Table 4.5: Percentage of Minimal Cut Sets (MCSs) that were correctly encoded by the inferred Fault Tree (FT) per algorithm across all the case studies (evaluated 5 times) in Part I of this dissertation. |BEs| is the number of Basic Events; |F| is the FT size; |CD| is the number of MCSs in the ground truth problem. Q1, Q2, and Q3 are respectively the 25%, 50%, and 75% quantiles. Case |BEs||F| |CD| FT-EA FT-MOEA SymLearn FT-MOEA-CM Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3 CSD(a) 6 10 3 100%100%100%100%100%100% - - - 100%100%100% PT(b) 6 11 5 40% 100%100%100%100%100% - - - 100%100%100% COVID-19(c) 9 13 6 100%100%100%100%100%100% - - - 100%100%100% ddFT(d) 8 13 6 50% 50% 50% 17% 67% 100% - - - 100%100%100% MPPS(e) 8 23 7 57% 100%100%100%100%100% - - - 100%100%100% SMS(f) 13 25 13 100%100%100%100%100%100% - - - 100%100%100% gpt12(g1) 12 25 13 - - - 100%100%100% - - - 100%100%100% gpt15(g2) 15 27 10 - - - 90% 90% 100% - - - 100%100%100% SS(h1) 10 23 8 - - - 88% 94% 100%100%100%100% - - - SC(h2) 6 11 4 - - - 100%100%100%100%100%100% - - - TS1(h3) 10 34† 16 - - - 77% 84% 88% 62% 62% 62% 100%100%100% TS2(h4) 24 25† 26 - - - 35% 100%100%100%100%100% - - - TS3(h5) 20 63† 18 - - - 0% 0% 0% 100%100%100% - - - † Fault Trees associated to truss systems (Jimenez-Roa, Volk, and Stoelinga, 2022). (a)CSD: Container Seal Design (NASA, 2002); (b)PT: Pressure Tank (NASA, 2002); (c)COVID-19: COVID-19 FT (Jimenez-Roa, Heskes, Tinga, et al., 2023); (d)ddFT: Data-driven FT (Lazarova-Molnar, Niloofar, and Barta, 2020); (e)MPPS: Mono-propellant propulsion system (NASA, 2002); (f)SMS: Spread Monitoring System (Mentes and Helvacioglu, 2011); (g1)gpt12: GPT generated FT with 12 BEs (Jimenez-Roa, Rusnac, Volk, et al., 2024); (g2)gpt15: GPT generated FT with 15 BEs (Jimenez-Roa, Rusnac, Volk, et al., 2024); (h1)SS: symmetric toy-example (Jimenez-Roa, Volk, and Stoelinga, 2022); (h2)SC: symmetric toy-example (Jimenez-Roa, Volk, and Stoelinga, 2022); (h3)SC: Truss system case TS1 (Jimenez-Roa, Volk, and Stoelinga, 2022); (h4)SC: Truss system case TS2 (Jimenez-Roa, Volk, and Stoelinga, 2022); (h5)SC: Truss system case TS3 (Jimenez-Roa, Volk, and Stoelinga, 2022) achieves global optima. SymLearn often outperforms FT-MOEA when symmetries are present in the failure dataset. Notably, FT-MOEA-CM converges to the global optima four times faster than both FT-MOEA and SymLearn for the case TS1. 4.7 Conclusions In this chapter, we introduced FT-MOEA-CM (Chapter 2), an extension of the FT-MOEA algorithm, specifically designed for inferring Fault Tree models from failure datasets using the NSGA-II and Crowding Sorting algorithms for multiobjective optimisation. An important distinction of FT-MOEA-CM from its predecessor is the incorporation of features derived from the confusion matrix. We conducted a Principal Component Analysis on 17 available features, identifying 7 as the most important: Matthews correlation coe"cient, Specificity, Negative predictive value, Precision, Diagnostic odds ratio, FT size, and Accuracy.
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