## 3.2.1 High Precision Mass Calibration

Carroll Croarkin

Statistical Engineering Division, ITL

Zeina Jabbour

Automated Production Technology Division, MEL

The purpose of this project is to re-design the weighing designs used for the highest precision mass measurements at NIST to take advantage of a newly acquired HK1000 balance.

Weighing designs are schemes for intercomparing reference standards with test weights in such a way that the least-squares values assigned to the test weights depend on known values of the reference standards. Mass calibrations at NIST start at the kilogram level with a 1,1,1,1 design that includes the two NIST reference kilograms, whose sum is the restraint for the system of equations, a test kilogram and a summation of weights totaling one kilogram.

Weights are calibrated in sets. A typical set consists of weights of 1kg, 500g, 200g, 200g, 100g, 50g, 20g, 20g, 10g, etc., in which case the summation in the first series is 500g+200g+200g+100g which becomes the restraint for the second series. The second design in the series consists of comparisons among 500g, 200g, 200g, 100g, 100g, and a summation of 50g+30g+20g weights and is referred to as a 5,2,2,1,1,1 design. The series of weighing designs continues in this manner down to the smallest weight.

The HK1000 balance is an enclosed automated weighing system with four pans which require equal loads. Therefore, a 5,2,2,1,1,1 design cannot be run on this balance. On the HK1000, all loads must be nominally equal, and we are restricted to four loads so that all designs are 1,1,1,1 designs.

The difficulty is to construct a series of designs for this balance that ties the values of all weights to the NIST kilograms at some desired level of uncertainty. The facing page shows a portion of a series for calibrating 200g and 100g weights from 2 sets of 5,2,2,1,1,1 weights where the value of the 200g+ 200g+ 200g+ 200g+ 100g+ 100g restraint comes from designs above this series.

A concern is that we may not achieve the level of precision that the HK1000 balance is capable of as we work through the entire series as: weights are placed on the pans; the balance is closed and allowed to come to thermal equilibrium; the system runs through the design at night; the balance is opened the next day; new weights are inserted; etc. It remains to be seen whether changes between weighings will significantly erode the inate capability of the balance.

```     OBS        2   2   2   2   1   1   1   1   1   1
Y(1)       +   -
Y(2)       +       -
Y(3)       +           -
Y(4)           +   -
Y(5)           +       -
Y(6)               +   -
Y(7)       +               -   -
Y(8)       +                       -   -
Y(9)       +                               -   -
Y(10)                      +   +   -   -
Y(11)                      +   +           -   -
Y(12)                              +   +   -   -
Y(13)          +           -   -
Y(14)          +                   -   -
Y(15)          +                           -   -
Y(16)                      +   +   -   -
Y(17)                      +   +           -   -
Y(18)                              +   +   -   -
Y(19)              +       -   -
Y(20)              +               -   -
Y(21)              +                       -   -
Y(22)                      +   +   -   -
Y(23)                      +   +           -   -
Y(24)                              +   +   -   -
Y(25)                  +   -   -
Y(26)                  +           -   -
Y(27)                  +                   -   -
Y(28)                      +   +   -   -
Y(29)                      +   +           -   -
Y(30)                              +   +   -   -
Y(31)                      +   -
Y(32)                      +       -
Y(33)                      +           -
Y(34)                          +   -
Y(35)                          +       -
Y(36)                              +   -
Y(37)                      +   -
Y(38)                      +               -
Y(39)                      +                   -
Y(40)                          +           -
Y(41)                          +               -
Y(42)                                      +   -
RESTRAINT       +   +   +   +   +   +
```

Date created: 7/20/2001
Last updated: 7/20/2001