Reliability, vulnerability, and resilience provide measures of the frequency, magnitude, and duration of the failure of water resources systems, respectively. Traditionally, these measures have been estimated using simulation. However, this can be computationally intensive, particularly when complex system-response models are used, when many estimates of the performance measures are required, and when persistence among the data needs to be taken into account. In this paper, an efficient method for estimating reliability, vulnerability, and resilience, which is based on the First-Order Reliability Method (FORM), is developed and demonstrated for the case study of managing water quality in the Willamette River, Oregon. Reliability, vulnerability, and resilience are determined for different dissolved oxygen (DO) standards. DO is simulated using a QUAL2EU water quality response model that has recently been developed for the Oregon Department of Environmental Quality (ODEQ) as part of the Willamette River Basin Water Quality Study (WRBWQS). The results obtained indicate that FORM can be used to efficiently estimate reliability, vulnerability, and resilience. ¿ 2001 American Geophysical Union