A General Approach to Error Propagation

A computational approach to error propagation is explained. It is shown that the application of the first-order Taylor theory to a fairly general expression representing an inventory or inventory-difference quantity leads naturally to a data structure that is useful for structuring error-propagation calculations. This data structure incorporates six types of data entities: (1) the objects in the material balance, (2) numerical parameters that describe these objects, (3) groups or sets of objects, (4) the terms which make up the material-balance equation, (5) the errors or sources of variance and (6) the functions or subroutines that represent Taylor partial derivatives. A simple algorithm based on this data structure can be defined using formulas that are sums of squares of sums. The data structures and algorithms described above have been implemented as computer software in FORTRAN for IBM PC-type machines. A free-form data-entry format allows users to separate data as they wish into separate files and enter data using a text editor. The program has been applied to the computation of limits of error for inventory differences (LEIDs) within the DOE complex.