Measured Quantity Value Estimator for Multiplicative Nonlinear Measurement Models

An estimate of a measurand using a nonlinear function of uncorrelated input quantities can be done by either applying the nonlinear function to the means of the input quantities (Method 1) or calculating the mean of a set of values obtained from propagating individual measurement values through the nonlinear function (Method 2). This paper proposes an improvement over the standard Method 2 procedures when the input quantities are assumed to be statistically independent and the nonlinear function has a general sum-of-product form, which covers many common measurement models. This paper shows that the proposed new approach (called Method 2S), if applicable, always produces a mean-squared error smaller than that of the conventional Method 2 procedures. The proposed approach improves the efficiency of Type-A evaluation as well as the Monte Carlo method. It also well complements the mainstream practices in the measurement uncertainty evaluation.