We investigate the dynamics of monitored memory resource utilizations in an operating system under stress using quantitative methods of fractal analysis. In the experiments, we recorded the time series representing various memory related parameters of the operating system. We observed that parameters demonstrate clear multifractal behavior. The degree of fractality of these time series tends to increase as the system workload increases. We conjecture that the H?older exponent that measures the local rate of fractality may be used as a quantitative measure of software aging. We propose a simple proactive computer crash avoidance strategy based on the online fractal analysis of system memory resource observations.