Traditionally, assessment of human health risk caused by contamination of a water supply focuses on the maximum risk to an individual. Here, we introduce a time-dependent risk assessment method and adapt and explore the reliability, resilience, and vulnerability (RRV) criteria from the surface-water literature as possible tools for assessing this risk. Time-dependent risk assessment, including RRV, is applied to two synthetic examples where water quality at a well varies over time. We calculate time-dependent health risks for discrete periods of exposure to the contaminated water for a variable population. The RRV criteria provide information about time-dependent risk: probability of an acceptable risk, probability of system recovery, maximum risk, and average exceedance of a prescribed risk threshold. The results demonstrate that episodic contamination events produce fundamentally different time-dependent risks than long-term events: these differences, such as generally lower risks for the episodic contamination, can be captured via plots of the risk and the RRV criteria. Furthermore, the evaluation of time-dependent health risk and the RRV criteria demonstrates significant sensitivity to the shape of the contaminant breakthrough curve, length of exposure, and variability within the population. Overall, analysis of time-dependent health risks provides substantial insight into the structure of risk, with RRV providing a reasonable framework for the evaluation of these risks.