In order to predict the performance and the usefulness of the narrow-band underwater acoustic measurement system at design stage, whose error variance is not clearly described, in this study a boundary equation to estimate the measurement accuracy is proposed based on the confidency as SNR variation. The boundary is presented as a function of SNR and the number of samples. In this paper, the measurement performance for narrow-band signal is simulated by the proposed boundary equation and the results are reviewed in the biased noise condition and separately in the background noise rejected condition.