Propagation of uncertainty: Expressions of second and third order uncertainty with third and fourth moments

The propagation of uncertainty in higher orders with corresponding mean values is frequently required to track, for example, non-linearities in systems. This propagation is modelled by the higher order terms. Higher order uncertainty analysis can reveal effects of physical phenomena in the instance of multiple variables composing the measurement. Higher order moments may exhibit many desirable properties, among which are the detection and characterization of non-linearities and probable sources of errors. In this paper, complete expressions of second and third order average and uncertainty of measurements have been derived for one and two variable systems. An example is given to illustrate the magnitude of these orders and results are compared with other methods.