Comparison between different uncertainty propagation methods in multivariate analysis: An application in the bivariate case

Safety related systems performance optimization is classically based on quantifying the effects that testing and maintenance activities have on reliability and cost (R+C). However, R+C quantification is often incomplete in the sense that important uncertainties may not be considered. An important number of studies have been published in the last decade in the field of R+C based optimization considering uncertainties. They have demonstrated that inclusion of uncertainties in the optimization brings the decision maker insights concerning how uncertain the R+C results are and how this uncertainty does matter as it can result in differences in the outcome of the decision making process. Several methods of uncertainty propagation based on the theory of tolerance regions have been proposed in the literature depending on the particular characteristics of the variables in the output and their relations. In this context, the objective of this paper focuses on the application of non-parametric and parametric methods to analyze uncertainty propagation, which will be implemented on a multi-objective optimization problem where reliability and cost act as decision criteria and maintenance intervals act as decision variables. Finally, a comparison of results of these applications and the conclusions obtained are presented.