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

APPENDIX C COMPARISON OF MODELS FOR CALCULATION OF UNCERTAINTY

In Appendix B we developed the equations that can be used to estimate the uncertainty of a determined result at any level of confidence. This methodology has been recommended by the International Organization for Standardization (ISO) in its guide [1] issued in 1993. Use of the ISO uncertainty methodology requires detailed knowledge of the variance and degrees of freedom for each uncertainty component; however, as shown in Appendix B, most engineering experiments can be analyzed satisfactorily by using the large-sample assumption for the uncertainty determination.

In this appendix we present the results of the Monte Carlo simulations that were performed to establish the validity of the large-sample model [2]. Six different data reduction equations were used in the simulations: mass balance, compressor efficiency, friction factor, mean of two temperatures, mean of five temperatures, and a single variable. For each equation the actual confidence levels attained were determined when the ISO models for 95% or 99% confidence were used and when the large-sample assumptions for these models were used.

C-1 MONTE CARLO SIMULATIONS

A Monte Carlo simulation technique was used to test the validity of the various uncertainty models for predicting the range around a result that contains the true result. For each example experiment, true values of the independent variables, X_i, were chosen and used to determine the true value ...