Need for Optimal Distributed Measurement of Cumulative Quantities Explains the Ubiquity of Absolute and Relative Error Components

Authors

Hector A. Reyes, The University of Texas at El PasoFollow
Aaron D. Brown, The University of Texas at El PasoFollow
Jeffrey Escamilla, The University of Texas at El PasoFollow
Ethan D. Kish, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

11-1-2022

Comments

Technical Report: UTEP-CS-22-111

Abstract

In many practical situations, we need to measure the value of a cumulative quantity, i.e., a quantity that is obtained by adding measurement results corresponding to different spatial locations. How can we select the measuring instruments so that the resulting cumulative quantity can be determined with known accuracy -- and, to avoid unnecessary expenses, not more accurately than needed? It turns out that the only case where such an optimal arrangement is possible is when the required accuracy means selecting the upper bounds on absolute and relative error components. This results provides a possible explanation for the ubiquity of such two-component accuracy requirements.