Title: Measurement uncertainty contribution in the quantisation of measurement values : Expert Report DKD-E 13-1
Authors: Members of the Technical Committee Measurement Uncertainty of the DKD, Physikalisch-Technische Bundesanstalt (PTB), ISNI: 0000-0002-1140-5252
Contributors: HostingInstitution: Physikalisch-Technische Bundesanstalt (PTB), ISNI: 0000 0001 2186 1887
Resource Type: Text / Technical Requirement
Publisher: Physikalisch-Technische Bundesanstalt (PTB)
Rights: https://creativecommons.org/licenses/by-nc-nd/3.0/de/
CC by-nc-nd 3.0
Relationships: IsVariantFormOf: DOI 10.7795/550.20201012
Dates: Available: 2022-07-18
Created: 2020-10
File: Download File (application/pdf) 3.72 MB (3897986 Bytes)
MD5 Checksum: 08ae1edfb8c0c61b135757e7efd5e53e
SHA256 Checksum: 3055c4d1f9976675c864fede01a3a23de8ddbf89b3d242e45aabeb6cc394cdae
Keywords Expert report ; DKD ; PTB ; measurement device with digital indication ; readability ; last digit of a display value
Abstract: This report deals with the estimation of the measurement uncertainty contribution by way of quantisation for digitally indicating measuring instruments. Its aim is to describe quantisation processes in the best possible way based on the available information, and to make use of this information in practice. In addition to the usual consideration of the uncertainty influence of the readability of the last digit of a display value as a rectangular distribution within the limits of aR = ±0.5 Digit, this report is intended to provide information to better describe the quantisation process from a technical point of view.

The profound analysis of the measurement uncertainty of a digitally indicating measuring device shows that it makes sense to apply a triangular distribution density with a width 2aD of two quantisation steps (code jumps) for the entire measurement process. This yields a combined standard deviation (combined standard uncertainty) σD = uMU(dUKombD) = 2aD ∙ 0.41.

Assuming a normal distribution instead of a triangular distribution as an approximation, the estimated combined standard measurement uncertainty would be slightly too large. For this case, the standard deviation is σN = uMU(dUKombN) = 2aN ∙ 0.5 (with a coverage probability of 95 %), again with a width of distribution 2aN of two quantisation steps.

This report represents a kind of alternative approach or consideration to the methods used in practice when dealing with quantisation processes (or rounding). It is not so much to be understood as a binding procedure or replacement of previous estimates.
Citation: Expert report DKD-E 13-1 Measurement uncertainty contribution in the quantisation of measurement values, Edition 10/2020, Revision 0, Physikalisch-Technische Bundesanstalt, Braunschweig and Berlin. DOI: 10.7795/550.20220715