The calculating formulae, and experimental methods in error propagation analysis

Error propagation is a basic problem in analysing uncertainty of reliable systems. The model of error propagation can be expressed as y=f(X+Z), where f is a system or propagation function, X is an input vector of the system, Z is an error vector of X, and y is a response or an output of the system. The error propagation analysis is conducted mainly to calculate or estimate the mean and variance of y given Z distributed s-normally with zero means. In this paper, we first assume that f(X) is calculable, and can be expressed in Taylor-series expansion; and we introduce the exact formulae and some approximate formulae for calculating the mean and variance of y given Z being s-independent or s-dependent. Second, we discuss the moment-methods of estimation for the mean and variance of y by experimental design. These methods can also be used when y=f(X) is a calculable function that may not be differentiable. Third, we give an example for comparing the different methods of error propagation, and discuss some results and comments according to many examples examined. Fourth, we discuss the robustness and usability on the methods of error propagation analysis. Finally, we give several conclusions.