## 1 Introduction  
Simulations are often used to estimate the probability of failure of structural elements and systems because they are a very versatile option which is not restricted by complex and implicit limit state functions (LSF), the use of sophisticated methods (e.g., finite element method), and/or highly non-linear structural behavior. However, millions of crude Monte Carlo simulations (MCS) could be required to adequately estimate structural probabilities of failure, which may not be feasible; also, the results could differ from a set of simulations to another. To cope with this issue, modified versions of the crude simulation approach, surrogate modeling, subset simulation, and other techniques have emerged and been used in the last decades not only for structural engineering but also in other fields. To mention only a few studies which employ some of these techniques, optimization using surrogate modeling, reliability analysis of deteriorating structural systems and the reliability assessment of a structure affected by chloride attack are reported in the studies by [1; 2; 3], respectively. Importance sampling has also been used to estimate the system reliability of deteriorating pipelines [4]. Other kind of approaches are also reported in the literature to compute reliabilities [5]. The different reliability methods can be applied not only to different fields in structural and geotechnical engineering, as for the case of sudden column removal in reinforced concrete buildings and rockfall protection structures [6; 7; 8], but also to many other research and engineering fields, for instance to artic oil and gas facilities [9] and to coastal engineering applications [10]. This last case is used in the present study to show the applicability of two revisited methods to obtain the reliability of coastal structures. Other simulation-based reliability methods have not been given so much attention. In this study a couple of these alternatives are revisited to inspect their feasibility and adequacy to estimate reliability indices. One of them employs polynomial transformations of a nonnormal variable to a normal one by fitting simulated data with fractile constraints and can be referred to as normality polynomial approach [11]. The second approach was developed to derive the design point and sensitivity factors (in the FORM, first order reliability method, perspective) from simulated data [12] and it is referred to as the multi-linear regression approach in this study. A similar approach to the normality polynomial method was previously developed by [PERSON] and [PERSON] [13] and named normal polynomial approach (note that the names are slightly different); unlike the normality polynomial approach, the normal polynomial approach has been paid much more attention (judging by number of citations), even very recently (e.g., [14]). Both methods are based on the fact [15; 16] that a fractile of a random variable can be expressed as polynomial of a fractile of a standard normal variable (normal polynomial), and that a fractile of a standard normal variable can be expressed as a polynomial of a fractile of a random variable (normality polynomial). Although the normal polynomial approach [13] is not considered in the present study (we prefer to focus in the less explored alternative), the findings here could be extended to do so. To inspect the adequacy of the normality polynomial approach and the multi-linear regression approach (the methods revisited in the present study), three LSFs are considered. One is based on a very simple classical case; other one is based on a structural application from a previous study and the last one is related to the reliability of a coastal structure. Extensive simulations are performed to estimate the error level by using the normality polynomial approach and its associated uncertainty; neither of these was thoroughly carried out in previous studies, nor the application to coastal engineering.