Interval Computations and Interval-Related Statistical Techniques: Tools for Estimating Uncertainty of the Results of Data Processing and Indirect Measurements

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

12-2007

Comments

Technical Report: UTEP-CS-07-53b

Published in Franco Pavese and Alistair B. Forbes (eds), Data Modeling for Metrology Testing and Testing in Measurement Science, Birkhauser-Springer, Boston, 2009, pp. 117-145.

Abstract

In many practical situations, we only know the upper bound D on the (absolute value of the) measurement error d, i.e., we only know that the measurement error is located on the interval [-D,D]. The traditional engineering approach to such situations is to assume that d is uniformly distributed on [-D,D], and to use the corresponding statistical techniques. In some situations, however, this approach underestimates the error of indirect measurements. It is therefore desirable to directly process this interval uncertainty. Such "interval computations" methods have been developed since the 1950s. In this chapter, we provide a brief overview of related algorithms, results, and remaining open problems.