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The paper introduces a criterion for test generation based on minimising the expected magnitude of undetected errors. This criterion is used to develop a best strategy for testing, using the linear checks approach. The detailed analysis is carried out for single unidirectional and bidirectional errors and for multiple unidirectional errors. Specific results concerning the efficiency of the approach are given for basic arithmetical and logical instructions. This approach may be useful in the field testing of hardware which carries out data manipulation and in which small numerical errors can be tolerated; it may also be useful for testing digital transmission channels.