Estimating resilience for water resources systems

Resilience characterizes the recovery capacity of repairable systems from the failure state to the safe state. Resilience has been recognized as a meaningful probabilistic indicator for evaluating risk‐cost trade‐offs in water resources systems. Traditionally, the resilience in the discrete time domain is estimated by sampling methods, which have a high computational expense. No single approximation approach has been well developed for estimating resilience, even under stationary conditions. This paper proposes two practical approximation methods for estimating the lag‐1 resilience in the discrete time domain. Both methods are theoretical developments, one based on a bivariate normal distribution, and the other based on a stochastic linear prediction of the performance function using the mean point of the failure domain. The foundations of both methods are the first‐order reliability method and the periodic vector autoregressive moving‐average time series model. The methods are robust for a wide range of problem characteristics and are applicable for systems facing stationary or nonstationary input conditions.