The evaluation of standard uncertainty in the presence of limited resolution of indicating devices

Abstract

Since the type A evaluation of standard uncertainty according to the rules given in the ISO Guide to the Expression of Uncertainty in Measurement does not take into account the uncertainty that arises from the limited resolution of indicating devices, we show in this design note that the treatment of this problem calls for a quantity about which no statistical information is available; therefore, its uncertainty has to be derived from a type B evaluation.

Interval estimation of the mean of a normal distribution based on quantized observations

“…Moreover, the joint fiducial distribution (19) gives more detailed information about the unknown parameters µ and σ, which could be used for more complex statistical inferences. We would like to stress the possibility to construct the simultaneous regions for the parameters (µ, σ), here denoted as the joint (1 − α) × 100% likelihood region, which could serve as an approximate simultaneous (1 − α) × 100%-confidence region for the parameters (µ, σ).…”

“…However, as we now explain, the simple two-sided (1 − α) × 100% interval estimator, based on the fiducial distribution (19), derived with sampling mechanism V (·) that is uniformly distributed over the polygon Q(x, z), could be inadequate, especially in cases when the number of distinct observed results is equal either to 1 or 2, see Figure 1 and Figure 2.…”

“…A version of the algorithm is also available at http://www.mathworks.com/matlabcentral/ fileexchange/ (look for the file DigitFD). Now, we will discuss possibilities how to construct the appropriate interval estimates which could serve as an approximate (1−α)×100%-confidence intervals for the parameter µ, based on a sample from fiducial distribution (19).…”

“…Without loss of generality we have considered designs with resolution δ = 1, only. (1 − α), which was calculated from an independent sample of size M = 10000 from the fiducial distribution given by (19). Fortunately, because of the discrete nature of the random vector (X 1 , X 2 , .…”

“…For recent studies see e.g. [19], [6], [15], [16], [10], [24], [23], [18], [3], [22], [25] and [14]. It has been observed in many instances that the effect of quantization diminishes and the standard statistical inference (i.e.…”