## 1 Introduction
In order to develop fragility curves, the structural demands, the earthquake intensity measures, and uncertainties regarding demand and capacity have to be defined. Focused on the development of analytical fragility curves non-linear dynamic analysis procedures have to be performed. Thus, the influence of the record-to-record variability on structural seismic response is taken into account, as the structural model is subjected to a wide range of ground motions. The characteristics of ground motions are described through intensity measures (IMs) while the structural behavior through engineering demand parameters (EDPs). Nonlinear dynamic analysis procedures, such as cloud analysis (CA) [31; 32; 33], incremental dynamic analysis (IDA) [34], and multi-stripe analysis (MSA) [35; 36], can be performed to generate samples of EDPs-IMs pairs. Thereafter, the discrete probability data points for each level of earthquake intensity can be defined incorporating directly the results of the nonlinear analyses (e.g., IDA) in order to provide a form of empirical cumulative distribution function (CDF) of fragility curve. A key parameter for the development of a fragility curve is the definition of the median (\(\upmu\)) and the dispersion (\(\beta\)) of the EDP-IM values, and thus different approaches have been reported in the literature. Among them, the moment method, the method of maximum likelihood estimation, the IM percentiles method, and the concept of the probabilistic seismic demand model (PSDM) are widely used [37; 38; 39; 40]. For the moment method (also known as Method A by Porter) [37], parameters of the fragility curves occur based on the earthquake intensities of the observed data. [PERSON] [38] introduced the method of maximum likelihood estimation where the parameters of the fragility curves are deduced through maximizing the likelihood of producing the observed data. The IM percentiles [39] incorporate results of the IDA and are based on the summarized 16%, 50%, and 84% IDA curves, respectively. [PERSON] et al. [31] introduced the relationship between the IM and EDP that provides a closed form solution of fragility curves. In this method, the variation of the structural demand for a wide range of earthquake intensities can be described through regression models known as the probabilistic seismic demand model (PSDM). In this context, the linear regression model is commonly used. Nevertheless, when nonlinear seismic demands have to be described, the use of bilinear PSDM is suggested [40]. [PERSON] et al. [41] developed fragility curves based on linear and bilinear PSDMs for the vulnerability assessment of RC buildings and the evaluation of retrofitted strategy. [PERSON] et al. [42] developed linear and bilinear PSDMs in order to achieve a better representation of the demand for the examined range of the IM. [PERSON] et al. [43] used bilinear PSDM to describe the local EDPs of low-ductility RC frames. [PERSON] et al. [44] used bilinear PSDM to study the influence of ground motion sequences on the fragility of RC moment-resisting frames. Other researchers developed fragility curves based on a Bayessian approach for the formulation of PSDMs [41; 42; 45; 46]. Furthermore, [PERSON] et al. [47] introduced a robust fragility assessment approach for the RC moment-resisting frame using Markov Chain Monte Carlo (MCMC) simulation. Recently, fragility curves have also been used for the probabilistic evaluation of the bounding effect between adjacent buildings. [PERSON] et al. [40] developed fragility curves for the assessment of the seismic bounding risk of singe-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems, based on linear and bilinear PSDMs. [PERSON] et al. [48] developed fragility curves in terms of maximum interstory drift vs. PGA to study the structural bounding effect between the adjacent RC frames, taking into account the available separation distance and the structural irregularities. The results of the assessment were based on the IDA method.