An object of this paper is to discuss the logical development of the concept of uncertainty in measurement and the methods for its quantification from the classical error analysis to the modern approaches based on the Guide to the Expression of Uncertainty in Measurement (GUM). We review authoritative literature on error analysis and then discuss its limitations which motivated the experts from the International Committee for Weights and Measures (CIPM), the International Bureau of Weights and Measures (BIPM) and various national metrology institutes to develop specific recommendations which form the basis of the GUM. We discuss the new concepts introduced by the GUM and their merits and limitations. The limitations of the GUM led the BIPM Joint Committee on Guides in Metrology to develop an alternative approach—the draft Supplement 1 to the GUM (draft GUM-S1). We discuss the draft GUM-S1 and its merits and limitations. We hope this discussion will lead to a more effective use of the GUM and the draft GUM-S1 and stimulate investigations leading to further improvements in the methods to quantify uncertainty in measurement.
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