Experimentation, Validation, and Uncertainty Analysis for Engineers, 4th Edition

2COVERAGE AND CONFIDENCE INTERVALS FOR AN INDIVIDUAL MEASURED VARIABLE

We introduced the idea in Chapter 1 that generally the result of an experiment is not a directly measured variable but rather is determined from multiple measured variables combined in a data reduction equation, DRE. So it is necessary to consider errors and uncertainties for a single measured variable and then the propagation of those errors and uncertainties through the DRE into the result. Also in Chapter 1 we defined random and systematic standard uncertainties as the standard deviations of the populations from which the random (variable) errors and the systematic (invariant) errors originate, and we noted that the standard uncertainties have no percentage confidence or coverage associated with them. In this chapter we discuss the determination of coverage intervals and confidence intervals for the case in which a directly measured variable is the experimental result of interest, then in Chapter 3 we consider the determination of coverage intervals and confidence intervals for cases in which the experimental result is determined from a DRE that contains multiple measured variables.

An important point to note is that the 1993 GUM [1] TSM approach propagates standard uncertainties of individual variables to determine the standard uncertainty of the result, then an assumption is made about the form of the parent population of errors in the result to formulate an expanded uncertainty of the result with ...