Uncertainty Factors for Stage-Specific and Cumulative Results of Indirect Measurements

TL;DR

This paper analyzes how uncertainties propagate through cascade systems of indirect measurements, providing methods to predict stage-wise uncertainties and assess the reliability of the final results.

Contribution

It introduces a framework for predicting and analyzing uncertainties at each stage of cascade-SSRs in indirect measurements, enhancing the evaluation of measurement accuracy.

Findings

Stage-wise uncertainties can be predicted a priori.

Uncertainty propagation follows a linear combination of measurement uncertainties.

Non-uniform behavior is characteristic of data transformation scales.

Abstract

Evaluation of a variable Yd from certain measured variable(s) Xi(s), by making use of their system-specific-relationship (SSR), is generally referred as the indirect measurement. Naturally the SSR may stand for a simple data-translation process in a given case, but a set of equations, or even a cascade of different such processes, in some other case. Further, though the measurements are a priori ensured to be accurate, there is no definite method for examining whether the result obtained at the end of an SSR, specifically a cascade of SSRs, is really representative as the measured Xi-values. Of Course, it was recently shown that the uncertainty (ed) in the estimate (yd) of a specified Yd is given by a specified linear combination of corresponding measurement-uncertainties (uis). Here, further insight into this principle is provided by its application to the cases represented by cascade-SSRs. It is exemplified how the different stage-wise uncertainties (Ied, IIed, ... ed), that is to say the requirements for the evaluation to be successful, could even a priori be predicted. The theoretical tools (SSRs) have resemblance with the real world measuring devices (MDs), and hence are referred as also the data transformation scales (DTSs). However, non-uniform behavior appears to be the feature of the DTSs rather than of the MDs.