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Öğe Importance of probability levels for robustness analysis of geodetic networks(TAYLOR & FRANCIS LTD, 2014) Yetkin, M.; Berber, M.; Inal, C.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.Öğe Robustness analysis using the measure of external reliability for multiple outliers(TAYLOR & FRANCIS LTD, 2013) Yetkin, M.; Berber, M.Robustness analysis is a natural merger of reliability and strain and defined as the ability to resist deformations induced by the maximum undetectable errors as determined from internal reliability analysis. Thus far, robustness analysis has been carried out using reliability theory based on the assumption of a single outlier. However, in practice, there might be multiple outliers in a data set. Therefore, measures of reliability for multiple outliers ought to be used. This paper extends robustness analysis so that it can determine the deformation induced by multiple undetected errors through the evaluation of a strain matrix using the proper external reliability measure. In this study, the question of whether a network is robust against deformations induced by two or more undetected outliers is investigated. The results indicate that in the case of multiple outliers, robustness of geodetic networks decreases.
