Estimating Bias Error Distributions

In this article we formulate a general methodology for estimating the bias error distribution of a device in a measurement domain from less accurate measurements when a minimal number of standard values (typically no more than two values) are available. A new perspective is that the bias error distribution can be found as a solution of an intrinsic functional equation in a domain. Based on this theory, the scaling- and translation-based methods for determining the bias error distribution are developed. These methods are applicable to virtually any device as long as the bias error distribution of the device can be sufficiently described by a power series (a polynomial) or a Fourier series in a domain. These methods were validated through computational simulations and laboratory calibration experiments for a number of different devices.