Estimation of health risks from exposure to contaminated groundwater traditionally focuses on the maximum risk. As such, the traditional approach does not provide insight into the time evolution of risk. Here, a continuous time-dependent method is developed and explored that allows estimation of chronic, carcinogenic risk as a function of when exposure to contaminated groundwater starts, thus producing a distribution of risk through time capable of capturing fundamentally different information than maximum risk. In addition to direct consideration of the time-dependent risks, measures for quantifying temporal variation in risk are explored: reliability, resilience, vulnerability, (RRV) and non-compliance projections (NCPs). The RRV measures serve to estimate the probability of an acceptable health risk, probability of system recovery, expected maximum health risk, and average exceedance of a prescribed health risk threshold. NCPs provide for visualization of unacceptable health risk as a function of time and population characteristics. The time-dependent chronic risk and accompanying measures are investigated in two systems: (1) two synthetic breakthrough curves of equal total mass but varying temporal distribution in concentration observed at the well and (2) a case study with uncertainty in hydraulic conductivity and variability in population characteristics. The results obtained for the synthetic curves demonstrate that episodic contamination events produce fundamentally different time-dependent risks than long-term events, even when both curves contain equal total mass arriving at the well: these differences are apparent in the risk versus time curve and can be captured via the RRV and NCP measures. The results from the case study highlight that assessment of time-dependent risks provides rich insight into the structure of the risk in time, space, and as a function of population variability. Overall, the results of this study demonstrate that further study of time-dependent risk from groundwater contamination, including application under different management scenarios, is well justified and promises to fundamentally enhance our ability to assess risk from a contaminated water supply. In particular, this work demonstrates that consideration of time-dependent risk provides a substantially broader set of tools for assessing potential chronic health risk from groundwater contamination than is available from the classic, maximum risk methodology.