A number of recent studies have reported the phenomenon of "software aging", characterized by progressive performance degradation or a sudden hang/crash of a software system due to exhaustion of operating system resources, fragmentation and accumulation of errors. To counteract this phenomenon, a proactive technique called "software rejuvenation" has been proposed. This essentially involves stopping the running software, cleaning its internal state and then restarting it. Software rejuvenation, being preventive in nature, begs the question as to when to schedule it. Periodic rejuvenation, while straightforward to implement, may not yield the best results. A better approach is based on actual measurement of system resource usage and activity that detects and estimates resource exhaustion times. Estimating the resource exhaustion times makes it possible for software rejuvenation to be initiated or better planned so that the system availability is maximized in the face of time-varying workload and system behavior. In this paper, we propose a methodology based on time-series analysis to detect and estimate resource exhaustion times due to software aging in a web server while subjecting it to an artificial workload. We first collect and log data on several system resource usage and activity parameters on a web server. Time-series ARMA models are then constructed from the data to detect aging and estimate resource exhaustion times. The results are then compared with previous measurement-based models and found to be more efficient and computationally less intensive. These models can be used to develop proactive management techniques like software rejuvenation which are triggered by actual measurements.