## 1 Introduction  
In the seismic probabilistic risk assessment (SPRA) of nuclear power plants (NPP), it is common practice to represent seismic hazards using the uniform hazard response spectrum (UHRS) [1], as observed in the relevant literature [2; 3; 4; 5]. The UHRS was constructed by reading spectral accelerations corresponding to the same annual frequency of exceedance from seismic hazard curves for different natural frequencies. The seismic hazard curve was calculated by combining the seismic source model and the ground motion prediction equation (GMPE). The correlation between spectral accelerations at different frequencies is not considered by the UHRS because the GMPE has been derived for different frequencies independently as well. Therefore, it is unlikely that spectral accelerations at different frequencies are distributed in the shape of the UHRS in a single earthquake. Therefore, the seismic response of a structure calculated for ground motion matched to the UHRS tends to be overestimated compared to the actual seismic response [6]. The conditional spectrum (CS) may be considered an alternative to UHRS with inherent conservatism. The CS is anchored to the UHRS at a specific control frequency and has probable spectral acceleration at other frequencies, where the probability distribution of the spectral acceleration is defined by considering the correlation to the spectral acceleration at the control frequency. In general, the spectral acceleration of the median CS is lower than that of the UHRS at the remaining frequencies, except for the control frequency [6]. The CS has been used in the seismic design of building structures as an alternative to the UHRS because it can predict a more realistic shape of the response spectrum for a given combination of seismic magnitude and epicentral distance [7; 8; 9; 10; 11]. For the same reason, several attempts to apply the CS to NPP structures have been conducted [12; 13; 14; 15]. In past SPRA, irregular peaks and valleys that inevitably appear in the shape of the response spectrum for individual earthquakes were regarded as a type of randomness (i.e., aleatory uncertainty). Thus, a logarithmic standard deviation in seismic response due to randomness was combined with a logarithmic standard deviation due to uncertainty (i.e., epistemic uncertainty) to evaluate seismic fragility and other seismic risk assessment criteria [16]. However, in recent years, all types of randomness, including the peaks and valleys of the response spectrum, have been considered to be included in the probabilistic definition of the seismic hazard curve, so that the UHRS is deemed to be a median spectrum and no logarithmic standard deviation is introduced [1]. For the CS, it is necessary to consider the randomness of the spectral acceleration at frequencies other than the control frequency where the CS and UHRS meet and share the annual frequency of exceedance based on probabilistic seismic hazard analysis (PSHA). Therefore, the randomness inherent in the CS makes it difficult to predict whether a lower seismic risk will be derived by applying the CS rather than the UHRS, although the spectral acceleration of the median CS tends to be lower than that of the UHRS at most frequencies. Unlike existing literature [7; 8; 9; 10; 11; 12; 13; 14; 15], this study aims to present a procedure for seismic fragility assessment of NPPs by applying ground motion compatible with the probability distribution of CS, and to examine the impact of inelastic behavior on the selection of control frequencies. For a rigorous assessment of the seismic fragility, a Monte Carlo simulation based on incremental dynamic analysis (IDA) was performed with consideration of both randomness in the seismic demand and uncertainty in the seismic capacity of NPPs. Nonlinear dynamic analysis was performed using a simplified model for the containment building in an NPP to directly reflect the influence of inelastic energy absorption behavior.