Analytic standard uncertainty evaluation of polynomial in normal/uniform random variables

The standard uncertainty evaluation is very important in instrumentation and measurement industry because it is used to communicate, compare and combine uncertainty generated by various components in a system. The analytical evaluation of uncertainty has been recognized to be important and carries many advantages from theoretical perspective. Due to perceived complexity and feasibility of mathematical operation, the current practice of analytic uncertainty evaluation is confined to linear or linearized measurement equations, although the linearization is not always justifiable. A simple yet exact analytical method to evaluate standard uncertainty for polynomial nonlinearity was proposed by the authors, but the complexity of the method is high due to comprehensive and complete nature of the method. This paper presents a simplified procedure for normal and uniformly distributed random variables by taking advantage of the symmetry and simplicity of the functional forms. These two types of distributions are the most commonly used distributions in uncertainty analysis either through central limit theorem or maximal entropy principle. The effectiveness of the procedures is demonstrated using documented cases.