Aggregating measurement data influenced by common effects

The requirement to aggregate measurement data, in the case where each measured value corresponds to nominally the same quantity, is important throughout metrology. Correlation associated with measured values is shown to arise in a number of measurement problems, with examples taken from the areas of interlaboratory comparisons, including key comparisons, the calibration of measuring systems and instruments, wireless sensor networks and prediction on the basis of different models. Consideration is given to the effect that correlation has on the determination of an aggregated estimate of the measured quantity, and on testing the consistency of measurement data. Approaches to quantifying the correlation associated with measured values are presented, and a formulation is given of the problem of determining the largest consistent subset of data having associated correlation. Results for three measurement problems are given, concerned with an interlaboratory comparison of noise in a coaxial line, the calibration of a thermometer and the analysis of data arising from a wireless sensor network.