## 1 Introduction  
In line with the quest to battle against the energy crisis and global climate change, wind energy is found to provide a technically and economically feasible solution, making it the most promising renewable energy technology in Europe and beyond (i.e., China, United States of America (USA), etc.) [1]. Today, the vast majority of wind energy is generated from onshore wind farms. However, there is a limitation in the further growth of onshore wind farms as a result of visual impact and limited space available to deploy wind turbines. In comparison to land, there is more available space to deploy wind turbines at sea, and the wind shear is stronger at offshore locations, driving the wind industry to move offshore, currently aiming for offshore wind in Europe to reach 64.8 GW by 2030 [1; 2; 3; 4]. With few exceptions, most of the existing offshore wind turbines (OWTs) are installed on monopile foundations in shallow waters (depths \(<\) 50 m). However, as turbines become larger (\(>\)5 MW) and as water depth increases beyond 35-50 m, monopiles become progressively uneconomical, primarily because of modal requirements that force structural dimensions to grow even beyond fabrication and installation capabilities currently available [5]. State-of-the-art research on monopile foundations can be found in References [6; 7]. Space frame structures such as jackets, widely used in the petroleum industry, offer a lighter and yet stiff alternative to monopiles. Effective design of these structures from a turbine system dynamics perspective is a demanding task. Although jacket-type support structures could contribute to further developments in the offshore wind industry, research is still required to support their basic design and analysis [5; 8], as well as to take into account the requirement for optimization due to both the serial production required and the nature of these unmanned structures. As a result of application-based research, several new methods and patents were developed aiming to resolve some of these issues [9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. In a conventional structural analysis, the environmental loads, geometric dimensions, material properties, and parameters are treated as deterministic quantities, which are often expressed in the design through characteristic values incorporating partial safety factors for consideration of uncertainties. This type of analysis is adequate in cases where randomness is relatively small. However, structures used for offshore deployment are generally complex and subjected to high uncertainties introduced by the environment, manufacturing, and operational processes. Randomness in design parameters for such systems should be systematically accounted for via stochastic modeling, allowing for a better informed and potentially optimized design that would take into consideration the life cycle of the structure and associated time-variant mechanisms of damage. Reliability analysis enables an efficient approach to better understand the response of the system to variation of an input parameter, enabling the systematic modeling of uncertainties occurring from highly complex models, loading conditions, etc. [19]. In particular, for offshore jacket foundations, soil-structure interactions and particularities of marine environments introduce considerable uncertainties (e.g., soil properties, wind, wave, and current loads, etc. ), leading to the requirement of employing proper reliability analysis methods. A structural reliability model of OWT support structures requires two key components, i.e., (1) a structural model describing the structural behavior of OWT support structures, and (2) a suitable reliability assessment method which finds the reliability index \(\beta\) (or the probability of failure \(P_{f}\)) of critical members with respect to the constraints [20]. Structural models for OWT support structures can be roughly classified into two groups, i.e., one-dimensional (1D) beam models and three-dimensional (3D) finite element analysis (FEA) models.