After geodetic networks (e.g., horizontal control, leveling, GNSS etc.) are established, they are measured and point coordinates are estimated by the method of Least Squares. If one or more observations are burdened with errors, these contaminated observations affect the other good observations and may produce incorrect estimates of the parameters. Thus, these contaminated observations should be detected and corrected. Generally, in practice, they are removed and the network is readjusted. To detect the outliers among the observations statistical tests are performed. Yet, reliability measures should be accompanied to statistical tests to find out more about the ability of error detection and the effects of errors on the solutions. Now it is possible that reliability measures can be calculated for the cases of single or multiple outliers. In this paper, a GNSS network is analyzed using reliability measures in both cases. The results show that in the case of multiple outliers reliability measures worsen.