Calibration of a weight of nominal value 10 kg

The calibration of a weight of nominal value 10 kg of OIML class M1 is carried out by comparision to a reference standard (OIML class F2) of same nominal value using a mass comparator whose performance characteristics have previously been determined.

Model Equation:

mX = mS + δmD + δm + δmC + δB

List of Quantities:

Quantity Unit Definition
mX g conventional mass of the unknown
mS g conventional mass of the standard
δmD g change of value of the standard since its last calibration due to drift
δm g observed difference in mass between the unknown mass and the standard
δmC g correction for eccentricity and magnetic effects
δB g correction for air buoyancy

mS: Type B normal distribution
Value: 10000.005 g
Expanded Uncertainty: 45·10-3 g
Coverage Factor: 2
REFERENCE STANDARD: The calibration certificate for the reference standard gives a value of 10 000,005 g with an associated expanded uncertainty of 45 mg (coverage factor k=2)

δmD: Type B rectangular distribution
Value: 0 g
Halfwidth of Limits: 15·10-3 g
DRIFT OF THE VALUE OF THE STANDARD: The drift of conventional mass of the reference standard is estimated from previous calibrations to be zero within limits ±15 mg

δm: Type A
Method of observation: Indirect SUUS
Number of observation: 3
No. Hint Reading Observation
1 Standard 0.010 g  
  Unknown 0.020 g  
  Unknown 0.025 g  
  Standard 0.015 g 0.0100 g
2 Standard 0.025 g  
  Unknown 0.050 g  
  Unknown 0.055 g  
  Standard 0.020 g 0.0300 g
3 Standard 0.025 g  
  Unknown 0.045 g  
  Unknown 0.040 g  
  Standard 0.020 g 0.0200 g

Arithmetic Mean: 0.0200 g
Pooled Standard Deviation: 25·10-3 g
Standard Deviation of the Mean: 0.0142 g
Pooled Degrees of Freedom: 50

COMPARATOR / OBSERVATION: A previous evaluation of the repeatability of the mass difference between two weights of same nominal value gives a pooled estimate of standard deviation of 25 mg.

δmC: Type B rectangular distribution
Value: 0 g
Halfwidth of Limits: 10·10-3 g
COMPARATOR: No correction are applied for the comparator whereas the uncertainty due to eccentricity and magnetic effects is estimated to have rectangular limits of ±10 mg

δB: Type B rectangular distribution
Value: 0 g
Halfwidth of Limits: 10·10-3 g
AIR BUOYANCY: No correction is made for the effects of air boyancy, the limits of deviation are estimated to be ±1.0·10-6 of the nominal value

Uncertainty Budgets:

mX: conventional mass of the unknown
Quantity Value Standard
Uncertainty
Distribution Sensitivity
Coefficient
Uncertainty
Contribution
Index
mS 10000.0050 g 0.0225 g normal 1.0 0.022 g 59.6 %
δmD 0.0 g 8.66·10-3 g rectangular 1.0 8.7·10-3 g 8.8 %
δm 0.0200 g 0.0142 g normal 1.0 0.014 g 23.7 %
δmC 0.0 g 5.77·10-3 g rectangular 1.0 5.8·10-3 g 3.9 %
δB 0.0 g 5.77·10-3 g rectangular 1.0 5.8·10-3 g 3.9 %
mX 10000.0250 g 0.0291 g

Results:

Quantity Value Expanded
Uncertainty
Coverage
factor
Coverage
mX 10000.025 g 0.058 g 2.00 95% (t-table 95.45%)

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