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This paper discusses the maximum earth fault resistance which can be tolerated by a distance relay with Mho characteristic. This is defined as the boundary fault resistance the relay can discriminate between in-zone and out-of-zone faults. The robustness criterion is defined on the basis of the boundary fault resistance. In order to achieve this, the related equations are first derived and then the boundary fault resistance curve is presented. The simulation results for a typical transmission system shows the effectiveness of the proposed robustness criterion for distance relay settings.