Physics – Data Analysis – Statistics and Probability
Scientific paper
2009-09-09
Physics
Data Analysis, Statistics and Probability
25 pages including 1 Appendix and 3 Tables
Scientific paper
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.
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