## 1 Introduction
MCS can be incorporated with variance reduction techniques, e.g., Latin hypercube sampling (LHS), weighted Latin hypercube sampling (WLHS), importance sampling, subset simulation, etc. [19; 20; 45; 52]. The stochastic expansion consists of intrusive and non-intrusive formulations. An intrusive formulation is one whereby the representation of uncertainty is expressed explicitly within the analysis of the system. Practically, this refers to methods that use Karhunen-Leove expansion (K-L) and polynomial chaos expansion (PCE) to directly modify the stiffness matrix of a finite element analysis procedure, such as SSFEM (spectral stochastic FEM) and stochastic Galerkin FEM. On the other hand, non-intrusive formulations, such as stochastic response surface methods [46; 49], represent uncertainties in a non-explicit way and treat the analysis code as a \"black box\" without requiring access to the source code. Both methods employed in this research constitute non-intrusive formulations. The first method studied in this paper accounts for the use of a commercial tool (ANSYS DesignXplorer(c)), which considers randomness in input variables (such as material properties, boundary conditions, loads, and geometry) and characterizes them by the joint probability density function of the input variables. Mixed moments of order higher than two are assumed to be negligible, which means that the joint probability density function can be described by the marginal distribution functions and the correlation structure. Available tools offer several statistical distribution functions to specify the marginal distribution. The probabilistic methods implemented in the DesignXplorer(c) include Latin hypercube sampling, all versions of the central composite design of experiment (DOE) type,Box-Behnken design DOE type, variational technology, and Monte Carlo simulations on the response surface [53; 54]. More information on these probabilistic methods can be found in References [48; 54]. The benefit of the tool is in its user-friendly interface and direct link with FEM modeling. However, it relies on direct simulations, which is a limitation for the order of magnitude probabilities of interest for offshore and marine applications, and which cannot be generalized and integrated with more specialized tools for more advanced analysis. The second approach, which was developed by the authors, proposes a non-intrusive stochastic formulation, which links the structural model to a reliability analysis algorithm through approximation modeling. In this case, quadratic response surface modeling is adopted in order to map the response of the structure in the domain of stochastic variables. The benefit of this approach is that it allows for high-fidelity computational tools to be employed for the analysis in a modular way, thereby extending its applicability to various engineering problems requiring advanced modeling techniques, and further permitting coupling with analytical reliability methods such as FORM and SORM, allowing for low values of probability of failure to be calculated. This work aims to carry out a comparison of the two methods described above for a typical OWT jacket-type support structure considering various design constraints and stochastic variables. This paper is the first of its kind to study the structural reliability of an OWT jacket-type support structure using two methods and then comparing the results, as there is no work which reported the use of the post-processing tool inbuilt in ANSYS applied to an OWT jacket-type support structure to determine the probability of failure, nor any work comparing results from the probabilistic FEA in ANSYS to a non-intrusive stochastic formulation, which is also documented in this paper.