The Microwave Uncertainty Framework (MUF) is a software suite created, supported, and made publicly available by the Radio Frequency Division of the U.S. National Institute of Standards and Technology. The general purpose of the MUF is to provide automated multivariate statistical uncertainty propagation and analysis on a Monte Carlo (MC) basis. Combine is a key module in the MUF, responsible for merging data, raw or transformed, to accurately reflect the variability in the data and in its central tendency. In this work the performance of Combines MC replicates is analytically compared against its stated design goals. An alternative construction is proposed for Combines MC replicates and their performance is compared, too, against Combines design goals. These comparisons are made within an archetypal two-stage scenario in which received data are first transformed in conjunction with shared systematic error and then combined to produce summary information. These comparisons reveal the limited conditions under which Combines uncertainty results are unbiased and the extent of these biases when these conditions are dropped. For small MC sample sizes neither construction, current or alternative, fully meets Combines design goals, nor does either construction consistently outperform the other. However, for large MC sample sizes the bias in the proposed alternative construction is asymptotically zero, and this construction is recommended.
Monte-Carlo, Microwave Uncertainty Framework, uncertainty, statistics