**GMP 14**

**Good Measurement Practice**

**for the**

**Selection and Use of Sensitivity Weights in Weighing Procedures**

1.  Introduction

> Mass calibration procedures are based on comparing the unknown mass,
> *X*, to a standard mass, *S*, utilizing the balance as a comparator.
> This comparison relies on the accuracy of balance indications. Most
> balance indications are not accurate enough for precision mass
> calibrations, and they tend to drift with time. Drift can often be
> assumed to be linear over a short period. Concerns over balance
> inaccuracy and drift result in two possible causes of errors in mass
> determination procedures. Inaccuracy of the balance indications can be
> corrected by incorporating a sensitivity weight in the procedure that
> calibrates the range of use of the optical scale (mechanical balances)
> or of the digital indications (electronic balances). Errors due to
> drift can be minimized by using the correct comparison method,
> selecting a suitable sensitivity weight, and by consistent timing
> within the procedure. The proper selection of procedures (GMP 12), the
> adherence to those procedures, and equal time intervals between
> weighing operations will allow the measured difference between *X* and
> *S* to be corrected for inaccuracy of the balance indications and for
> balance drift.

1.  Purpose

> The following practice will guide you through the process of selecting
> and using a correct sensitivity weight for mass determination
> procedures.

2.  Prerequisites

    1.  Verify that valid calibration certificates are available for the
        masses to be used as standards, sensitivity weights, and tare
        weights.

    2.  Verify that weight-handling equipment is available and in good
        operational condition.

    3.  Verify that the operator is familiar with the design and the
        operation of the balances and familiar with weighing procedures.

3.  Safety

    1.  Handling of large or small weights can represent a hazard to
        either the weights or personnel if the weights are dropped.

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2.  Methodology

    1.  Summary

A sensitivity weight is selected to calibrate the balance over the range
to be used in the measurement procedure. Minimizing the difference in
mass values between *X* and *S* is critical when choosing an appropriate
sensitivity weight. Therefore, tare weights may be necessary whenever
the difference in mass values is significant. Minimizing the difference
between *X* and *S* works to our benefit since the range of the
measurements is minimized and reduces potential errors that can be
introduced by nonlinearity of the balance.

2.  Apparatus

2.2.1. Sensitivity weights with accurate and traceable calibration
values.

2.2.2. Tare weights with accurate and traceable calibration values.

3.  Clean forceps to handle the weights, or gloves to be worn if the
    weights are to be moved by hand.

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3.  Procedure for selection

    1.  Conduct preliminary measurements to determine the approximate
        mass value for the difference between the standard and the
        unknown (*X -- S*).

    2.  Define the range of use for the balance to be used:

        1.  Equal arm -- number of scale divisions

        2.  Mechanical -- optical scale

        3.  Combination -- digital indications

        4.  Fully electronic -- capacity

        5.  Comparators -- digital indications

    3.  Determine the need for tare weights if the difference between
        *X* and *S* exceeds the values shown in Table 1.

**Table 1. Maximum allowed difference between *X* and *S***

  -------------------------------------- --------------------------------
  **Balance**                            ***(X -- S)***

  Equal arm                              balance each other within one
                                         division on the scale

  Mechanical                             1/10 optical scale

  Combination                            1/10 digital range

  Fully electronic                       0.05 % capacity

  Comparator                             1/10 digital range
  -------------------------------------- --------------------------------

4.  Select tare weights, if necessary, making sure that the difference
    between *X* and *S*, with the appropriate tare weights, do not
    exceed the values shown in Table 1.

5.  Select a sensitivity weight according to Table 2.

**Table 2. Selection of Sensitivity Weight**

+----------------+------------------------+---------------------------+
| **Balance**    | **Procedure**          | **Sensitivity Weight**    |
+----------------+------------------------+---------------------------+
| Equal Arm      | SOP 3, 5, 6, 7, 8, 28  | change turning points by  |
|                |                        | 20 %                      |
+----------------+------------------------+---------------------------+
| Mechanical     | SOP 4, 5, 7, 28        | ≥4 times (*X -- S*); ½    |
|                |                        | optical scale             |
|                | SOP 8                  |                           |
|                |                        | ¼ optical scale           |
+----------------+------------------------+---------------------------+
| Combination    | SOP 4, 5, 7, 8, 28     | ≥4 times (*X -- S*); ½    |
|                |                        | digital Range             |
| Elec           |                        |                           |
| tro-mechanical |                        |                           |
+----------------+------------------------+---------------------------+
| Fully          | SOP 4, 5, 7, 28        | 1 % capacity              |
| Electronic     |                        |                           |
|                | SOP 8                  | 2 times the applicable    |
|                |                        | tolerance                 |
+----------------+------------------------+---------------------------+
| Comparator\*   | SOP 4, 5, 7, 8, 28     | ≥4 times (*X -- S*); \< ½ |
|                |                        | digital range             |
+----------------+------------------------+---------------------------+

\*A sensitivity weight is not required if the electronic mass comparator
that is used has been tested (with supporting data available) to
determine that the balance has sufficient accuracy, resolution,
repeatability, and stability so that no advantage is gained using a
sensitivity weight. For example, any possible errors must be less than
the last digit retained in the expanded uncertainty. When a mass
comparator is used without a sensitivity weight, the sensitivity must be
periodically verified and documented (e.g., prior to each use).

4.  Use of sensitivity weight

> The sensitivity weight is used to ensure that the mass differences
> determined with the optical scale, or electronic range, have valid
> accuracy and traceability. The sensitivity weight calibrates the range
> of use of the balance used for making the mass determinations. Using a
> sensitivity weight provides us with a sensitivity value in terms of
> mass units per division.

$$\text{sensitivity}\text{  } = \text{  }\frac{\text{mass}\text{  }\text{units}}{\text{divisions}}\text{  } = \text{  }\frac{M_{\text{sw}}}{\text{deflection}}$$

Where *M~sw~* represents the mass of the sensitivity weight.

2.  Calculations

No special calculations are associated with this practice. See each mass
SOP for calculation of sensitivity within the procedure.

3.  Uncertainty

No uncertainty calculations are associated with this practice. See the
appropriate SOP for the calculations of uncertainty. (The uncertainty of
the sensitivity weight does not need to be included in calculations of
uncertainty since the uncertainty value is distributed across the range
of use. However, it does no harm to incorporate it in uncertainty
calculations when spreadsheets are set up to handle all of the data.)