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

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-transformation process (Xi(s) Yd) in a given case, but a set of equations (fi({Yd}) = Xi, d, i = 1, 2, ..., N), or even a cascade of different such processes (“Xi(s) I Yd(s) II Yd(s) ... Yd(s)”, or “XJ I Yd II Yd ... Yd”, or so), 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-value(s). Of course, it was recently shown that the uncertainty ( d) in the estimate (yd) of a specified Yd, viz.: Xi’s Yd, is given by a specified linear combination of corresponding measurementuncertainties (ui’s). 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 ( I d, II d ... d), 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.