The on-line monitoring for illicit radioactive material with a minimum number of false detections is a critical need for homeland security; however, low signal-to-noise ratios make distinguishing between a transient radiation source and static natural background particularly difficult. The primary objectives of this work were to apply both Bayesian and classical statistical process control chart techniques to the on-line monitoring of radiological data and to then compare the Type I (false positive) and Type II (false negative) error incidence rates. The Shewhart (3-sigma) and cumulative sum (CUSUM) control charts were the classical procedures adopted, while the Bayesian technique employed was the Shiryayev-Roberts (S-R) control chart. Because on-line environmental monitoring does not allow for corrective action following an out-of-control signal, two versions of the CUSUM and S-R procedures known as total reset and alarm reset methods were developed that differ only in the manner in which test statistics are reset subsequent to an alarm. In addition, the S-R total reset method was modified to account for a delay in response before and after an out-of-control signal. The best method in terms of the minimization of Type I errors was the S-R total reset method followed by the 3-sigma and CUSUM total reset methods. In terms of Type II errors, the CUSUM alarm reset procedure more readily detected fleeting small changes and intermediate changes in the mean count rate, while the S-R alarm reset control scheme was better suited for detecting small sustained changes. At high count rates, the 3-sigma control chart resulted in the fewest number of false negative detects independent of the amount of time a source was present. Because of the inherent slow response time associated with the S-R method even at high count rates, it was difficult for these methods, as developed in this thesis, to minimize the number of Type II errors when the shift in the mean count rate was great enough for competing methods to detect.