Modeling error propagation in a measurement system

We outline in this paper a hybrid method to propagate uncertainty in systems described by trees. Given a system described by a tree where nodes are basic operations and leafs are random variables described by their probability density functions (PDFs), one show that by a combination of exact computations with sampled versions of PDFs one can obtain the PDFs of output variables with great efficiency. This can be applied to a large variety of problems including uncertainty propagation in measurement systems, combination of PDFs in Fault trees or junction trees for expert systems. On top of that, this calculus is fast enough to cope with sensitivity studies, where one seeks to optimize one of the system parameter to achieve some requested features on the output PDFs. This paper focuses on the calculation of output random variables PDFs with sampled versions of the input PDFs.