Importance of probability levels for robustness analysis of geodetic networks

Robustness Analysis is a natural merger of reliability and strain and defined as the ability to resist deformations caused by the maximum undetectable errors. Internal reliability criterion describes maximum undetectable errors in observations, which would not be detected by Baarda's statistical testing method (data snooping) based on the chosen Type I and II error probabilities. The non-centrality parameter is a function of probability levels and it plays an important role in Robustness Analysis. In this paper, it is aimed to show the impact of non-centrality parameter on the displacements and the relationship between the selected confidence level for confidence regions and threshold values in a geodetic network. For a geodetic network example, a GPS network is chosen and computations of displacements and threshold values (derived from confidence regions) have been carried out for both in-context and out-of context approaches. According to our results, the non-centrality parameter controls the magnitudes of displacements without affecting their relative behaviours. Statistically, lower probability levels are desired. However, if error probabilities are decreased, the non-centrality parameter increases. Since, the non-centrality parameter scales the displacements, a balance between both types of decision error is needed to obtain displacement values that are smaller than threshold values in order to reach a totally robust network at the required level of probability.