Evaluation of measurement uncertainty from a nonstationary process

Abstract

In metrology, when repeated measurements are autocorrelated, it is not appropriate to use the traditional approach to evaluate the uncertainty of the average of repeated measurements. In literature, methodologies were developed to evaluate the uncertainty of measurements from a stationary process, which demonstrated ‘statistical equilibrium’. In this paper, we discuss approaches to evaluate the measurement uncertainty when the data are from a nonstationary process. In particular, for some nonstationary processes with a time-dependent mean and a constant variance, we may be able to assess the uncertainty based on one realization. Specifically, after the effect of the time-dependent mean is removed, the residuals may show equilibrium behavior and thus can be treated as being from a stationary process. We propose approaches to evaluate the uncertainty of measurements based on one realization of such a process with practical examples presented for illustration.