Fault detection and isolation (FDI) techniques, which are called standard parity space approach (SPSA) and optimal parity vector approach (OPVA), have been presented in literature extensively for engineering sensor systems or sensor networks. This paper demonstrates the abilities of these approaches to detect and isolate outliers in geodetic networks. The ability to detect and isolate outliers has been measured by computing the mean success rate (MSR) for some given probability of significance levels. These approaches have been applied to a levelling network and a Global Navigation Satellite System (GNSS) network. Different matrix decomposition techniques have been used as an alternative way to the Potter algorithm, which is used in SPSA and OPVA. It has been proven that the abilities of FDI techniques, i.e. the MSRs of OPVA, increase with regard to the ones of SPSA in the levelling network and the GNSS network especially if the significance level a is chosen as 0.001 by using Monte-Carlo simulation.