Calibration of a gauge block of nominal length 50 mm
The calibration of the grade 0 gauge block (ISO 3650) of 50 mm nominal length is carried out by comparison using a comparator and a calibrated gauge block of the same nominal length and the same material as reference standard. The difference in central length is determined in vertical position of the two gauge blocks using two length indicators contacting the upper and lower measuring faces.The actual length of the gauge block to be calibrated is related to the actual length of the reference standard by the equation
l_{X}' = l_{S}' + δl
with δl being the measured length difference. l_{X} blocks under the measurement conditions, in particular at a temperature which on account of the uncertainty in the measurement of laboratory temperature may not be identical with the reference temperature for length measurements.
Model Equation:
l_{X} = l_{S} + δl_{D} + δl + δl_{C}  L * (α_{av} * δt + δα * Δt_{av} + u_{at})  δl_{V}

List of Quantities:
Quantity  Unit  Definition 

l_{X}  mm  length of the gauge block to be calibrated 
l_{S}  mm  length of the reference gauge block at the reference temperature of t_{0}=20 °C according to its calibration certificate 
δl_{D}  mm  Change of the length of the reference gauge block since its last calibration due to drift 
δl  mm  observed difference in length between the unknown and the reference gauge block 
δl_{C}  mm  correction for nonlinearity and offset of the comparator 
L  mm  nominal length of the gauge blocks under consideration 
α_{av}  K^{1}  average of the thermal expansion coefficients of the unknown and the reference gauge block 
δt  K  difference in temperature between the unknown the reference gauge block 
δα  K^{1}  difference in the thermal expansion coefficients between the unknown and the reference gauge block 
Δt_{av}  K  deviation of the average temperature of the unknown and the standard gauge block from the reference temperature 
u_{at}  coorection for second order terms of (δα * Δt_{av})  
δl_{V}  mm  correction for noncentral contacting of the measuring faces of the unknown gauge block 
l_{S}: 
Type B normal distribution Value: 50.000020 mm Expanded Uncertainty: 30·10^{6} mm Coverage Factor: 2.0 
δl_{D}: 
Type B triangular distribution Value: 0 mm Halfwidth of Limits: 30·10^{6} mm 
δl: 
Type A Method of observation: Direct Number of observation: 5
Arithmetic Mean: 94.00·10^{6} mm 
δl_{C}: 
Type B rectangular distribution Value: 0 mm Halfwidth of Limits: 32·10^{6} mm 
L: 
Constant Value: 50 mm 
α_{av}: 
Type B rectangular distribution Value: 11.5·10^{6} K^{1} Halfwidth of Limits: 1·10^{6} K^{1} 
δt: 
Type B rectangular distribution Value: 0 K Halfwidth of Limits: 0.05 K 
δα: 
Type B triangular distribution Value: 0.0 K^{1} Halfwidth of Limits: 2·10^{6} K^{1} 
Δt_{av}: 
Type B rectangular distribution Value: 0 K Halfwidth of Limits: 0.5 K 
u_{at}: 
Type B normal distribution Value: 0 Expanded Uncertainty: 0.236·10^{6} Coverage Factor: 1.0 
δl_{V}: 
Type B rectangular distribution Value: 0 mm Halfwidth of Limits: 6.7·10^{6} mm 
Uncertainty Budgets:
l_{X}: length of the gauge block to be calibratedQuantity  Value 
Standard Uncertainty 
Distribution 
Sensitivity Coefficient 
Uncertainty Contribution 
Index 

l_{S}  50.0000200 mm  15.0·10^{6} mm  normal  1.0  15·10^{6} mm  19.3 % 
δl_{D}  0.0 mm  12.2·10^{6} mm  triangular  1.0  12·10^{6} mm  12.8 % 
δl  94.00·10^{6} mm  4.75·10^{6} mm  normal  1.0  4.7·10^{6} mm  1.9 % 
δl_{C}  0.0 mm  18.5·10^{6} mm  rectangular  1.0  18·10^{6} mm  29.2 % 
L  50.0 mm  
α_{av}  11.500·10^{6} K^{1}  577·10^{9} K^{1}  rectangular  0.0  0.0 mm  0.0 % 
δt  0.0 K  0.0289 K  rectangular  580·10^{6}  17·10^{6} mm  23.6 % 
δα  0.0 K^{1}  816·10^{9} K^{1}  triangular  0.0  0.0 mm  0.0 % 
Δt_{av}  0.0 K  0.289 K  rectangular  0.0  0.0 mm  0.0 % 
u_{at}  0.0  236·10^{9}  normal  50  12·10^{6} mm  11.9 % 
δl_{V}  0.0 mm  3.87·10^{6} mm  rectangular  1.0  3.9·10^{6} mm  1.3 % 
l_{X}  49.9999260 mm  34.2·10^{6} mm 
Results:
Quantity  Value 
Expanded Uncertainty 
Coverage factor 
Coverage 

l_{X}  49.999926 mm  68·10^{6} mm  2.00  95% (ttable 95.45%) 