  Uncertainty propagation software can have unknown, inadvertent biases
introduced by various means. This work is a case study in bias identification
and reduction in one such software package, the Microwave Uncertainty Framework
(MUF). 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 Combine's MC replicates is
analytically compared against its stated design goals. An alternative
construction is proposed for Combine's MC replicates and its performance is
compared, too, against Combine's 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 Combine's uncertainty results are unbiased and the extent of these
biases when these conditions are not met. For small MC sample sizes neither
construction, current or alternative, fully meets Combine's 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.
