ABSTRACT
To begin with, this chapter provides a brief description of selected definitions and considerations underlying the theory and practice of measurements and the errors associated with them. After reviewing the main sources and features of errors, the current procedures for dealing with errors and uncertainties are presented for direct and for indirect measurements, to set the stage for a fundamental concept used for assessing the magnitude and effects of errors both in complex measurements and computations. The practical consequences of this fundamental concept are embodied in the “propagation of errors (moments)” equations. As will be shown in this chapter, the propagation of errors equations provides a systematic way of obtaining the uncertainties in results of measurements and computations, arising not only from uncertainties in the parameters that enter the respective computational model but also from numerical approximations. The “propagation of errors” equations combine systematically and consistently the parameter errors with the sensitivities of responses (i.e., results of measurements and/or computations) to the respective parameters, thus providing the symbiotic linchpin between the objectives of uncertainty analysis and those of sensitivity analysis. The efficient computation of sensitivities and, subsequently, uncertainties in results produced by various models (algebraic, differential, integrals, etc.) will then form the objectives of subsequent chapters in this book.
