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A statistical study of dc vacuum arc extinction in a vacuum interrupter (VI) with transverse axisymmetric magnetic field has been carried out at various external circuit parameters. The relationship between the maximum current that a VI can switch off and the magnetic field, the circuit inductance, and the VI shunt capacitance has been found. A statistical study has allowed us to define this maximum switched-off current with specified probability of failure. The possible causes of a VI failure are discussed.