Decade Designs for Weighings of Non-uniform Variance

Morris, E C

doi:10.1088/0026-1394/29/6/001

Cited by 11 publications

(6 citation statements)

References 5 publications

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“…The advantage of the former is the orthogonality of the scheme (orthogonality is advantageous only when all the weighings in the design have the same variance [4]). …”

Section: Analysis Of Variances For Multiplication Methodsmentioning

confidence: 99%

Subdivision or Multiplication? The Choice of Calibration Design for Multiples of Kilogram

Vâlcu¹,

Boiciuc²

2008

Measurement Science Review

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The realization, maintenance and dissemination of the SI base unit, the kilogram, is one of the tasks of the NMI's mass laboratory and is assured by means of reference standards which are traceable to the International Kilogram Prototype through the mass of the National Prototypes. This paper describes the dissemination of mass scale from 1 kg reference standard to weights of E 1 class between (1...10) kg, using one of the two methods of calibration: subdivision or multiplication. The paper compares the variance of each weight obtained by both methods. The presented subdivision method deals with a link of standards following the example of MihailovRomanowski where the measurements start downwards from 10 kg to 1 kg. The multiplication method is the one usually used in many calibration laboratories and starts from 1 kg to 10 kg. The paper also presents an example of calibration and uncertainty calculations.

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“…The advantage of the former is the orthogonality of the scheme (orthogonality is advantageous only when all the weighings in the design have the same variance [4]). …”

Section: Analysis Of Variances For Multiplication Methodsmentioning

confidence: 99%

Subdivision or Multiplication? The Choice of Calibration Design for Multiples of Kilogram

Vâlcu¹,

Boiciuc²

2008

Measurement Science Review

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“…Efficiency is especially useful when comparing the designs involving the same masses and balances, even if the number of mass comparisons is different. It is desirable for the efficiency of a design to be large, as this will indicate that the variances are small [9]. For an efficient scheme, it is advantageous that each mass is used approximately the same number of times and as often as possible.…”

Section: Det Nomentioning

confidence: 99%

Metrology and Measurement Systems

Vâlcu

2021

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The paper proposes an alternative approach to the dissemination of the mass unit in the context of the new definition of the kilogram. Considering the fact that redefinition allows mass to be directly realized at any value, the paper presents a model of the dissemination of mass which can be used for different series in grams, where the measurements are performed in the downward direction, but using 1 g as the reference standard (whose mass value is assumed to be determined after the redefinition using the capacitive or electrostatic techniques). The subdivision method presented (suitable for 𝐸 1 weights) has as its starting point the approach used by Mihailov-Romanowski for the calibration of series in kilograms which uses an orthogonal system of equations. Thus, according to this method, a solution for obtaining the orthogonality of a system can be the use as defining standard of the ratio between the mass having the highest nominal value in the set and the standard (unit). The results obtained for a set of weights from 10 to 1 g using the subdivision method, in accordance with the Mihailov-Romanowski principle, are validated with those obtained with the multiplication method, where the measurements start from 1 to 10 g, as in the case of the kilogram series. The mass values obtained with both methods are equal, while the estimated uncertainties are slightly different, yet insignificant. The results obtained previously for the same sequence of weights using the traditional dissemination method, where the 1 kg standard is used as reference, are also presented in the paper. The results show that only three weights out of six have a mass value insignificantly different by 1 × 10 −4 mg compared to those obtained with the methods presented in this article, but, in terms of uncertainty, there are some differences.The way of disseminating the mass unit presented in this article can be extended to other different sequences of nominal values such as: (5 . . . 1) g, (20 . . . 1) g, (50 . . . 1) g or (500 . . . 100) g if the reference standard is 100 g.

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“…Uncertainty. The evaluation of the uncertainty of mass comparisons is described, for example, in Croarkin (1989), Morris (1992), Chapman (1995), Bich et al (1993/94), EA-4/02 (1999), Jones and Schoonover (2002), OIML (2004) and Schwartz et al (2007). For the following short summary of the main input quantities and their contributions, the terminology of the 'Guide to the Expression of Uncertainty in Measurement' (GUM 1995) and the International Recommendation OIML R 111 ( 2004) is used.…”

Section: Electrostatic and Magnetic Fieldsmentioning

confidence: 99%

Precision mass measurements

Gläser¹,

Borys²

2009

Rep. Prog. Phys.

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Mass as a physical quantity and its measurement are described. After some historical remarks, a short summary of the concept of mass in classical and modern physics is given. Principles and methods of mass measurements, for example as energy measurement or as measurement of weight forces and forces caused by acceleration, are discussed. Precision mass measurement by comparing mass standards using balances is described in detail. Measurement of atomic masses related to 12 C is briefly reviewed as well as experiments and recent discussions for a future new definition of the kilogram, the SI unit of mass.

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Decade Designs for Weighings of Non-uniform Variance

Cited by 11 publications

References 5 publications

Subdivision or Multiplication? The Choice of Calibration Design for Multiples of Kilogram

Subdivision or Multiplication? The Choice of Calibration Design for Multiples of Kilogram

Metrology and Measurement Systems

Precision mass measurements

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