2.
Measurement Process Characterization
2.3. Calibration 2.3.4. Catalog of calibration designs


Tie to kilogram reference standards  Nearaccurate mass measurements require a sequence of designs that relate the masses of individual weights to a reference kilogram(s) standard ( Jaeger & Davis). Weights generally come in sets, and an entire set may require several series to calibrate all the weights in the set.  
Example of weight set 
A 5,3,2,1 weight set would have the following weights:
500g, 300g, 200g, 100g 50g, 30g 20g, 10g 5g, 3g, 2g, 1g 0.5g, 0.3g, 0.2g, 0.1g 

Depiction of a design with three series for calibrating a 5,3,2,1 weight set with weights between 1 kg and 10 g  
First series using 1,1,1,1 design 
The calibrations start with a comparison of the one kilogram test
weight with the reference kilograms (see the graphic above). The
1,1,1,1 design requires two kilogram
reference standards with known values, \( R_1^* \) and \( R_2^* \).
The fourth kilogram in this design is actually a summation of the
500, 300, 200 g weights which becomes the restraint in the next series.
The restraint for the first series is the known average mass of the reference kilograms, $$ R^* = \frac{R_1^* + R_2^*}{2} \, .$$ The design assigns values to all weights including the individual reference standards. For this design, the check standard is not an artifact standard but is defined as the difference between the values assigned to the reference kilograms by the design; namely, $$ C = \left( \widehat{R_1^*}  \widehat{R_2^*} \right) \, . $$ 

Second series using 5,3,2,1,1,1 design 
The second series is a 5,3,2,1,1,1 design
where the restraint over the 500g, 300g and 200g weights comes from
the value assigned to the summation in the first series; i.e.,
$$ R^* = \sum 1 = \widehat{X}_{500} + \widehat{X}_{300} + \widehat{X}_{200} \, .$$
The weights assigned values by this series are:


Other starting points  The calibration sequence can also start with a 1,1,1 design. This design has the disadvantage that it does not have provision for a check standard.  
Better choice of design  A better choice is a 1,1,1,1,1 design which allows for two reference kilograms and a kilogram check standard which occupies the 4th position among the weights. This is preferable to the 1,1,1,1 design but has the disadvantage of requiring the laboratory to maintain three kilogram standards.  
Important detail  The solutions are only applicable for the restraints as shown.  
Designs for decreasing weight sets 


Design for pound weights  
Designs for increasing weight sets 