A fragility curve based on the transformation of a random variable

There are two failure criteria in seismic probabilistic risk assessment of a nuclear power plant to define component failure caused by an earthquake. The first is in terms of peak ground acceleration and peak ground acceleration capacity. The second is in terms of seismic response and component capacity. These criteria are closely related, but they are not equivalent. One can derive a different fragility curve from the second criterion. First, this study analytically shows the relation of these failure criteria, pointing out that a fragility curve may not represent the uncertainty of a failure probability derived from the second criterion. In addition, we propose a probability density function of a failure probability based on the second criterion using the transformation of a random variable method applied to probability density functions of seismic response and component capacity. Then, we derive a new fragility curve based on the derived probability density function. Also, we show that the derived probability density function links to a likelihood function based on a mean fragility curve used in the literature. Finally, we discuss the non-identifiability of uncertainties of response and capacity, and we propose a Bayesian model utilizing a local response to overcome the non-identifiability. (author)