The within-device precision for quantitative assays is the square root of the total variance, which is defined as the sum of the between-day, between-run, and within-run variances under a two-stage nested random-effects model. Currently, methods for point and interval estimations have been proposed. However, the literature on sample size determination for within-device precision is scarce. We propose an approach for the determination of sample size for within-device precision. Our approach is based on the probability for which the 100(1-α)% upper confidence bound for the within-device precision smaller than the pre-specified claim is greater than 1-β. We derive the asymptotic distribution of the confidence upper bound based on the modified large-sample method for sample size determination and allocation. Our study reveals that the dominant term for sample size determination is the between-day variance. Results of simulation studies are reported. An example with real data is used to illustrate the proposed method.