## 4 Discussion  
Results in the previous section suggest that the two revisited approaches based on simulations, namely, the normality polynomial and the multi-linear regression approaches, are effective in reducing the number of required simulations while adequately computing the reliability index, design point and sensitivity factors. It could be argued that still a relatively large number of simulations are required. However, the computing power is becoming higher every year, and these methods proposed at the end of the 1990s could become a feasible alternative for some complex models two or three decades later.  
The power law (Equations (19), (20), (23), and (24)), which describes the precision in computing \(\beta\) for the normality polynomial approach, was found very adequate for the three LSFs considered. Albeit it cannot be concluded that the underlaying error is based on the power law for every possible LSF, since one of LSFs studied here was a simple classical case using only one type of PDF, and the other LSFs were more complex (non-linear functions), with much more random variables and included several PDFs, as well as dependency between variables and the joint Longuet-Higgins distribution, it is reasonable to believe that the error for other LSFs for a wide range of coastal and structural engineering applications could follow the power law. A designer could opt to reduce the number of simulations while accepting an error level (including its uncertainty) by using the power laws as an aid.  
The multi-linear regression approach was originally developed to derive the design point and sensitivity factors not obtained when performing MCS; however, it is considered that it can be an alternative by itself to compute \(\beta\) in an accurate way, conditioned on performing enough simulations for a successful regression; the number of simulations can be reduced by increasing the tolerance _e._ Values reported in this study can be used as a guide.  
It is acknowledged that some differences with respect to the present study could be found when other LSFs and applications are used. However, the values reported in this study could be used for guidance, and it is believed that the power law may hold in many coastal and structural engineering applications, since the normality polynomials are based in strong mathematical foundations,as referenced before; nevertheless, future research to further inspect the findings in this study is recommended by using mathematical LSFs considered as benchmark in the literature, but also more ultimate and serviceability LSFs for other coastal and structural engineering applications. It is also believed that the revisited methods and the findings in this study can be exported to other engineering fields if practical applications can be posed as a capacity-demand problem and when extensive simulations are required, including system reliability (for instance for reinforced concrete frame buildings, among many other possibilities). Future research could also include a systematic study for the multi-linear regression approach by varying the tolerance, for given number of simulations, so that the number of MCS can be limited to a minimum while guaranteeing the obtaining of adequate reliability-related values.  
If more LSFs are investigated in future studies, perhaps it could be possible to infer general bounds for a wider applicability of the findings in the present study.