Rapid static GPS positioning is an alternative to real time kinematic (RTK) GPS positioning or to static GPS positioning. With careful attention, one can obtain cm positioning using the method. Rapid static GPS has become popular through online rapid static GPS positioning services that emerged only recently. Then researchers have studied the accuracy of rapid static GPS from various software packages. However, thorough statistical evaluation of rapid static GPS results has been missing in the field. In this study, we analysed GPS data from SOPAC archives, targeting to provide a richer statistical description of BERNESE rapid static GPS solutions. We applied SEARCH ambiguity resolution in a single baseline mode over baseline lengths of shorter than 10 km. We investigated the distribution of the results, determined an appropriate outlier detection strategy using traditional and robust techniques as well as studying systematic behaviours in the data sets. The research results indicate that the number of successful solutions from the processing is decreased due to failures in ambiguity fixing if typical 1-15 min observing session durations is adopted. The failed ambiguity resolution results exist as outliers in the solution series. This degrades the efficiency of the method. At this stage, the robust outlier detection appears to be a fast, effective and objective method to clean these outliers. A fall at the outlier percentage is observed by extending the session duration for rapid static surveying from typical 1-15 to 30 min.