An efficient procedure on the evaluation of the probability distribution function of the cumulative seismic loss

•Literature is mainly limited to the evaluation of the expected lifetime seismic losses.•A straightforward and cost-efficient procedure is developed to assess probability distribution of the lifetime losses.•The procedure is compatible with PEER loss assessment framework.•Superior consistency is observed in the results of the proposed procedure and the scenario-based approach.•Using the expected lifetime loss assessed by conventional methods may lead to an uneconomical design. The existing loss assessment frameworks in the literature are mainly limited to the evaluation of the expected lifetime seismic losses, and do not assess the probability distribution of the long-term losses. The long-term loss is defined as the cumulative seismic loss of the structures over the service life. However, the probability distribution of the long-term losses can also be informative for decision-making under uncertain seismic consequences. This paper proposes an efficient procedure to calculate the probability distribution of the long-term losses. The procedure is based on the discretization of continuous random variables and performing two sets of recursive convolutions. The proposed method is compatible with PEER loss assessment framework, such that it can be readily implemented in engineering practice. The main contribution of the developed method is its simplicity compared to the existing analytical procedures and its computational efficiency compared to the Monte Carlo-based simulation methods. An illustrative example is provided to demonstrate the details of the procedure. A precise consistency is observed between the results of the proposed procedure and the scenario-based sampling method as the benchmark. The results show that among the common distribution functions, the log-logistic distribution has a better relative fit with the probability distribution of lifetime repair cost. It the studied cases, the difference between the median and expected lifetime loss turn out to be significant. Therefore, when dealing with similar scenarios, relying on the expected lifetime loss calculated using the conventional methods may result in an uneconomical design.