Abstract
The Monte Carlo method is an established tool that is often used to evaluate the uncertainty of measurements. For computationally challenging problems, Monte Carlo uncertainty analyses are typically distributed across multiple processes on a multi-node cluster or supercomputer. Additionally, results from previous uncertainty analyses are often used in further analyses in a sequential manner. To accurately capture the uncertainty of the output quantity of interest, Monte Carlo sample distributions must be treated consistently, using reproducible replicates, throughout the entire analysis. We highlight the need for and importance of consistent Monte Carlo methods in distributed and sequential uncertainty analyses, recommend an implementation to achieve the needed consistency in these complicated analyses, and discuss methods to evaluate the accuracy of implementations.