The ability of a critical dimension scanning electron microscope (CD-SEM) to resolve differences in the widths of two lines depends on the instrument's measurement repeatability and any sample-dependent biases. The dependence of repeatability and bias on eight different parameters is studied using the MONSEL Monte Carlo electron simulator. For each of 14,400 different combinations of values of eight parameters, three describing the sample and five describing characteristics of the instrument or measurement condition, an image is simulated, noise is added, and the edge positions are "measured" as would be done in a CD-SEM. From 100 repetitions of noise, the repeatability of such CD determinations is ascertained. Biases (i.e., average errors) are also determined. Noise amplitude, edge detection algorithm, and beam size are shown to be significant factors in measurement repeatability. The CD-SEM's measurement repeatability may be an order of magnitude better than its spatial resolution. For standard edge detection methods, the bias depends on the sample. This means that in a manufacturing environment in which the sample shape varies, there will be a random component of error that is not measured by the industry's usual same-sample tests of instrument precision.