Monitoring and predicting human cognitive state and performance using physiological signals such as Electroencephalogram (EEG) have recently gained increasing attention in the fields of brain-computer interface and cognitive neuroscience. Most previous psychophysiological studies of cognitive changes have attempted to use the same model for all subjects. However, the relatively large individual variability in EEG dynamics relating to loss of alertness suggests that for many operators, group statistics cannot be used to accurately predict changes in cognitive states. Attempts have also been made to build a subject-dependent model for each individual based on his/her pilot data tb account for Individual variability. However, such methods assume the cross-session variability in EEG dynamics to be negligible, which could be problematic due to electrode displacements, environmental noises, and skin-electrode impedance. Here first we show that the EEG power in the alpha and theta bands are strongly correlated with changes in the subject's cognitive state reflected through his driving performance and hence his departure from alertness. Then under very mild and realistic assumptions we derive a model for the alert state of the person using EEG power in the alpha and theta bands. We demonstrate that deviations (computed by Mahalanobis distance) of the EEG power in the alpha and theta bands from the corresponding alert models are correlated to the changes in the driving performance. Finally, for detection of drowsiness we use a linear combination of deviations of the EEG power in the alpha band and theta band from the respective alert models that best correlates with subject's changing level of alertness, indexed by subject's behavioral response in the driving task. This approach could lead to a practical system for noninvasive monitoring of the cognitive state of human operators in attention-critical settings.