« In the realm of binary systems, Chiacchio [22] combined binary logistic regression with
nonsequential Monte Carlo simulation for reliability assessment. Imakhlaf [13] employed
binary decision diagrams for reliability analysis of non-coherent systems, while Tan [21]
developed algorithms for multiple-trigger binary systems with concurrent failures.
Concerning multi-state systems, Huang [12] proposed a dynamic Bayesian network approach
combined with evidence theory to integrate imprecise observations across hierarchical
multistate systems. Xia [24] introduced the Universal Generating Function (UGF) technique
for analyzing reliability in complex electromechanical multi-state systems, accounting for
cascade failures and multiple functional states. Various studies have utilized UGF for
different reliability applications in MSS, such as Wang [23]'s Interval-valued Multi-state
Sliding Window System (IMSWS-ST) for sequential tasks, Li [15]'s GO-FLOW methodology
combined with UGF for reliability analysis of phased mission systems with cold standby
configurations, Babaei [19]'s narrow reliability bounds evaluation, Qiu [2]'s fuzzy UGF
method, and Ding [8]'s fuzzy Universal Generating Functions. Jafary [7] extended UGF for
modeling MSS performance with correlated failures. Markov chain-based methods have also
been prevalent, including Che [14]'s use of Piecewise Deterministic Markov Process (PDMP),
Bo [1]'s deep neural network-based method considering semi-Markovian processes, Tan
[20]'s resilience modeling framework based on Markov processes, Nop [5]'s multi-state
Markov chain model for optimal operation of rainwater harvesting systems, Ding [9]'s Hidden
Markov Model-based method for event-triggered output consensus in Markov jump
multiagent systems, and Gao [25]'s finite Markov chain embedding method. Fuzzy
approaches have been employed by Chachra [11] with an intuitionistic fuzzy approach using
Triangular Intuitionistic Fuzzy Numbers (TIFN), and by Qiu [2] and Ding [8] with their
respective fuzzy methods UGF. Neural networks and machine learning methods have also
been explored. Zhou [3] used Physics-Informed Neural Networks (PINN) to handle complex
dependencies and uncertainties in MSS, Cheng [8] developed a hybrid framework based on
deep learning, and Wang [18] applied XGBoost in substitution modeling to evaluate fatigue
reliability under multi-source uncertainty. Levitin [26] optimized MSS survival with multi-
level protection using genetic algorithms, and Essadqi [10] proposed a genetic algorithm-
oriented redundancy allocation in MSS. Finally, Monte Carlo simulations were applied by Zio
[4] for assessing MSS availability with operational dependencies and by Campos [20] for
evaluating reliability in binary systems. Other articles might include those focusing on
stochastic hybrid automaton models for dynamic reliability assessment [18], as well as those
studying resilience of multi-state systems through various modeling approaches [20]. »
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