Uncertainty of primary standards 1.1.5



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1.1.5 Uncertainty of primary standards

Setting up and evaluating a primary standard usually entails a long and painstaking programme of experiments spread over several years before the necessary low level of uncertainty is achieved. A great effort is made to eliminate, or at least to identify and quantify, all possible contributions to the uncertainty of the standard. Statistical (random)^† contributions may be reduced arbitrarily, e.g. by increasing the number of measurements made, but there always remains the possibility that some unsuspected, non-statistical (systematic)^† source of uncertainty exists. The application of rules for the statement of uncertainty, as in section 6, is thus less straightforward in the case of primary standards work than it is in routine calibration work.

When the results of measurements are compared by those whose measurements are traceable to the same primary standard, they will be using identical units and any uncertainty in the primary standard may be neglected. Where traceability is to different primary standards, information about any difference in the sizes of the units may be obtained from the BIPM or from one of the national laboratories concerned.

In some scientific work it may be essential to consider the uncertainty in the primary standard when assessing the significance of the measurements. Much relevant information is published by the BIPM, particularly in reports on international comparisons of the units realized and maintained by the various national laboratories. It is always advisable to approach the appropriate expert at the NPL or other national laboratory in order to confirm the interpretation of such material, and to ascertain whether any more recent information is available.

For illustrative purposes only, the table below lists the 1-sigma uncertainties assigned to a number of NPL standards in 1991. Note that standards set up to provide calibrations of very large or very small values of quantities such as pressure, for example, will have much greater uncertainties than those of the base units.

Table of uncertainties

Quantiity	Unit	Uncertainty (one sigma)	Notes

Time interval	second	4 × 10⁻¹⁴
Length	metre	2.5 × 10⁻¹¹
Mass	kilogram	2.3 μg
Potential difference	volt	10⁻⁸
Electric resistance	ohm	10⁻⁸
Temperature	kelvin	0.000 1 K	At triple point of water
Luminous intensity	candela	3 × 10⁻⁴	For monochromatic radiation
Angle	arc second	10⁻²
Density	kgm⁻³	10⁻⁵	For solids
Force	newton	10⁻⁵	Up to 1.2 MN
Pressure:	pascal
atmospheric		3 × 10⁻⁶	At 100 kPa
high pressure		2 × 10⁻⁵	At 100 MPa
vacuum		10⁻²	At 1 μPa
Sound pressure level	dB re 10 μPa	0.04 dB	At 5 KHz in air
Acoustic pressure	pascal	1.5 × 10⁻²	At 5 MHz in water
Thermal conductivity	Wm⁻¹ K⁻¹	10⁻² to 2 × 10⁻²	Material-dependent
Electric power:	watt
supply frequency		5 × 10⁻⁵	At 50 Hz
microwave		10⁻³	At 10 GHz
Laser pulse energy	joule	1.5 × 10⁻²	0.4 μm to 1.06 μm
Optical power	watt	4 × 10⁻⁵
Colour	CIE LAB	0.25	For colour surface
Neutron emission rate	s⁻¹	2 × 10⁻³	For radionuclide neutron sources
Activity	becquerel	1.5 × 10⁻³ to 10⁻²	Depends on radionuclide
Absorbed dose	gray	3.5 × 10⁻³	In graphite
Amount of substance	mole	3 × 10⁻⁴	For gases, usually as gas mixtures, mole fraction

^†The BIPM suggests the use of ‘category A’ and ‘category B’ instead of ‘random’ and ‘systematic’.

O.C. Jones

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