At present, in-beam positron emission tomography (PET) is the only method for in vivo and in situ range verification in ion therapy. At the GSI Helmholtzzentrum für Schwerionenforschung GmbH (GSI) Darmstadt, Germany, a unique in-beam PET installation has been operated from 1997 until the shut down of the carbon ion therapy facility in 2008. Therapeutic irradiation by means of (12)C ion beams of more than 400 patients have been monitored. In this paper a first quantitative study on the accuracy of the in-beam PET method to detect range deviations between planned and applied treatment in clinically relevant situations using simulations based on clinical data is presented. Patient treatment plans were used for performing simulations of positron emitter distributions. For each patient a range difference of + or - 6 mm in water was applied and compared to simulations without any changes. The comparisons were performed manually by six experienced evaluators for data of 81 patients. The number of patients required for the study was calculated using the outcome of a pilot study. The results indicate a sensitivity of (91 + or - 3)% and a specificity of (96 + or - 2)% for detecting an overrange, a reduced range is recognized with a sensitivity of (92 + or - 3)% and a specificity of (96 + or - 2)%. The positive and the negative predictive value of this method are 94% and 87%, respectively. The interobserver coefficient of variation is between 3 and 8%. The in-beam PET method demonstrated a high sensitivity and specificity for the detection of range deviations. As the range is a most indicative factor of deviations in the dose delivery, the promising results shown in this paper confirm the in-beam PET method as an appropriate tool for monitoring ion therapy.