Fiducial inference applied to uncertainty estimation

doi:10.1088/0026-1394/46/6/008

Fiducial inference applied to uncertainty estimation when identical readings are obtained under low instrument resolution

R B Frenkel 2009 Metrologia 46 661-667 doi: 10.1088/0026-1394/46/6/008

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R B Frenkel
National Measurement Institute, Australia, Bradfield Road, West Lindfield, NSW 2070, Australia
E-mail: robert.frenkel@measurement.gov.au

Abstract. When identical readings are independently obtained under low instrument resolution d, so that a reading x implies an actual value between x − (d/2) and x + (d/2), the method of fiducial inference yields the result that the commonly assumed standard uncertainty $d/\sqrt{12} \approx 0.289d$ applies only to the case where the input standard deviation is known to be very low, 0.03d or less. The standard uncertainty $d/\sqrt{12}$ is the standard deviation of a rectangular distribution whose base is of length d. If there is little knowledge of the input standard deviation, the standard uncertainty is closer to $d/\sqrt{24} \approx 0.204d$ . The standard uncertainty $d/\sqrt{24}$ is the standard deviation of a symmetrical (isosceles) triangular distribution whose base is of length d. This latter standard uncertainty increases above $d/\sqrt{24}$ as the number of identical independent readings decreases.

Print publication: Issue 6 (December 2009)
Received 10 June 2009, in final form 24 August 2009
Published 26 October 2009

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Fiducial inference applied to uncertainty estimation when identical readings are obtained under low instrument resolution

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