Robustness analysis using the measure of external reliability for multiple outliers

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.