Uncertainty Due to Finite Resolution Measurements

We investigate the influence of finite resolution on measurement uncertainty from the perspective of the Guide to the Expression of Uncertainty in Measurement (GUM). Finite resolution in a measurement that is perturbed by Gaussian noise yields a distribution of results that strongly depends on the location of the true value relative to the resolution increment. We show that there is no simple expression relating the standard deviation of the distribution of measurement results to the associated uncertainty at a specified level of confidence. There is, however, an analytic relation between the mean value and the standard deviation of the measurement distribution. We further investigate the conflict between the GUM and ISO 14253-2 regarding the method of evaluating the standard uncertainty due to finite resolution and show that, on average, the GUM method is superior, but still approximate.