Propagating bias and precision errors using the perturbation method

Abstract

Calculations based on measured variables are subject to some uncertainty due to errors in measurements. These measurement errors, while unavoidable, can be quantified. The usual method for determining the uncertainty in a calculated variable, given the uncertainties (or expected errors) in the measured variables that define it, involves the use of the Taylor series method. With this method, the partial derivative of the result with respect to each of the measured variables must be determined. This can be tedious and time consuming. When results are calculated by computer, another method is available that does not require partial differentiation. This alternative is known as the perturbation method. This paper explains fow the perturbation method can be used in conjunction with the methodology for propagating measurement errors set forth in ANSI/ASME Performance Test Code 19.1-1985. The FORTRAN coding required to implement the perturbation method is also described. The program, which propagates the measurement uncertainties, is easily combined with the results calculation code and requires little or no maintenance. The code was developed to determine uncertainties associated with boiler performance calculations that were carried out as part of a test program for circulating fluidized bed combustion sponsored by the Electric Power Research Institute.