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A General Approach to Comparisons in the Presence of Drift

A general approach to comparisons in the presence of temporal drift is presented and comparison sequences are discussed for linear, quadratic and cubic drift. Circular comparison sequences of the form (ab..)n and (ab..)n a are proposed (where a, b,.. are different items, such as masses, and n is a repeat factor) with the best performance achieved when three to five items are involved in the comparison. A matrix least squares model is used to obtain information about the drift, the item differences and their uncertainties. The emphasis of the paper is on mass comparisons, where the dominant drift is in the balance zero, but the approach is applicable to comparisons generally and its application to gain drift is also presented.