Estimating resilience for water resources systems

[1] 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.