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This paper is devoted to the on-line testing methods based on the self-checking techniques. These methods are aimed to estimate the reliability of a result calculated at the output of the circuit during operations. Definitions of the totally self-checking circuit have fixed assumptions that limit development of the computing circuits in on-line testing within the framework of the exact data processing. The main part of the processed numbers belongs to the approximate data. The errors produced by the faults of the computing circuits are inessential for the reliability of approximated result in most cases. The on-line testing methods demonstrate a new property for rejecting the reliable results in case of inessential errors detection. This fact makes a problem of low reliability of result checking. The ways to increase reliability of on-line testing methods are offered