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Weighing Uncertainty

Weighing Uncertainty

The main question in selecting a balance is whether it will meet the measurement uncertainty budget for the process under investigation.

by Ian Ciesniewski,Arthur Reichmuth
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A Risk-Based Approach to Selecting and Testing Lab Balances

Selecting, testing and verifying a laboratory balance for the modern laboratory is fraught with potential errors. The results generated by a typical analytical balance will influence the productivity of both the lab and the production units that depend upon it!

Balance selection

The process of accurate weighing begins with correct and appropriate selection of a balance. The main question is whether the balance chosen will meet the measurement uncertainty budget for the process under investigation.

It is not uncommon for a specifier to confuse readability with weighing accuracy. For example, a user may select an analytical balance with a capacity of 200 g and a readability of 0.1 mg because it is believed that this balance is “accurate to 0.1 mg.”

There are several properties quantified in the specifications of the weighing instrument that limit its performance. The most important are repeatability, eccentricity, nonlinearity and sensitivity. How do they influence the performance and hence the selection of a weighing instrument?

To answer this question, the term “weighing uncertainty” must first be discussed. The International Vocabulary of Metrology defines uncertainty as a parameter that expresses the dispersion of the values of a measurement.

The weighing uncertainty (i.e., the uncertainty when an object is weighed on a weighing instrument) can be estimated from the specifications of a weighing instrument (typically the case when performing a design qualification), from test measurements with the weighing instrument (typically the case when carrying out an operational or performance qualification) or from a combination of both. The essential influences can be combined according to statistical methods to obtain the weighing uncertainty:

Uncertainty can be expressed either as standard uncertainty u (corresponding to the standard deviation of a statistical process) or as expanded uncertainty U (also referred to as uncertainty interval). To obtain the expanded uncertainty, the standard uncertainty must be multiplied by the chosen expansion factor K=2 or K=3.

Equation for the expression of measurement uncertainty

Safety factor

Repeatability, as determined at the time of installation, will vary due to environmental conditions, lab location, differences in operators and other sources of uncertainty. It is therefore recommended to apply a safety factor that establishes a safety margin between the warning and the control limit for the process. For example, if the required minimum weight is 50 mg, then the balance is selected by its ability to reach, say, 25 mg, which will give a safety factor of 2, though the weighing system will be used for 50 mg or more. GWP® (Good Weighing Practice™)* recommends a safety factor of 2 by default to compensate for the variation in the determination of repeatability.


The recommended test frequency for any given balance will increase with higher accuracy requirements and increased severity of impact. By the same token, frequency will decrease with increased detectability of a malfunction. Sensitivity should be tested most often (due to its low-error, simple procedure), followed, with decreasing frequency, by repeatability and eccentricity.

GWP endeavors to eliminate the time-consuming and often confusing process of estimating tolerances for the standard weight tests, as well as provide unified procedures that can be assimilated into any standard operating procedure.

The test limits recommended by GWP are based on:

  • The weighing accuracy required by the application
  • The safety factor chosen by the user to establish a warning limit or the expansion factor chosen
  • The mass of the smallest sample to be weighed
  • The mass of the test weight used

Most likely the majority of all samples being weighed on laboratory weighing instruments, especially in laboratory applications, satisfy the condition of being “small samples” (i.e., samples with a mass considerably smaller than the capacity of the weighing instrument)—a few percent of capacity, say. When discussing the relative uncertainty versus sample mass, weighing uncertainty is governed by repeatability if a small sample is weighed.

Consequently, with the majority of weighings, repeatability is the most important contributor to uncertainty. This would be a good reason to recommend repeatability be tested most frequently. However, this test comprises weighing the same test weight multiple—typically 10—times. To perform this test properly, considerable effort and skill are required. On the other hand, the test of sensitivity can be carried out with one single weighing of a test weight, certainly less of an effort. What is more, the sensitivity test would reveal any serious problem either with the instrument or if the result were to drift; in short, it may be regarded as an elementary test of the functionality of the weighing instrument. Although sensitivity is not the most critical property of a weighing instrument by far, for the reasons cited it is proposed that the sensitivity test be carried out with the highest frequency, followed by repeatability with a lower frequency.

Eccentricity is tested when the weighing instrument is calibrated by authorized personnel. It is tested to a frequency that reflects the level of contribution to the measurement’s uncertainty.

Nonlinearity is not recommended for testing by the user at all, as its influence on weighing uncertainty is insignificant and hardly dominant with any model of weighing instrument; besides, it is taken care of when the weighing instrument is calibrated by authorized personnel.

GWP recommends test procedures for weighing instruments as follows:

1. Calibration by authorized personnel, including the determination of weighing uncertainty or minimum weight, if applicable; the aim is to assess the complete performance of the instrument by testing all its relevant weighing parameters.

2. Routine test of sensitivity, repeatability and eccentricity (but not nonlinearity) to be carried out by the user within defined intervals; the aim is to confirm its suitability for the application.

3. Automatic tests or adjustments, such as those for sensitivity, carried out automatically by the weighing instrument; the aim is to reduce the effort of manual testing.

Test frequencies

GWP recommends testing procedures and corresponding frequencies based on:
1. The required weighing accuracy of the application
2. The impact (e.g., for business, consumer or environment) in case the weighing instrument does not function properly
3. The detectability of a malfunction

The recommended frequencies for the test of all properties extend from daily for risky applications (user or automatic tests) to weekly, monthly, quarterly, biannually or annually (e.g., calibration by authorized personnel). It is assumed that the more stringent the weighing accuracy requirements, the higher the probability that the weighing result does not meet the accuracy requirements. In this case the test frequency is increased. Similarly, if the severity of the impact increases, the tests should be performed more frequently

If malfunction of the weighing instrument is easily detectable, the test frequency is decreased. Routine tests are based on the required weighing accuracy for an application. Simply speaking, the weighing accuracy must be better than or equal to the accuracy required. The required accuracy is referred to as control limit, meaning that if this limit is exceeded, immediate action must be taken. In its simplest fashion, the test limit is equal to the control limit and thus equal to the required weighing accuracy of the process.

Test weights

For the user tests, two test weights are recommended:

1. A large weight, preferably of a mass equal to the capacity of the weighing instrument. GWP recommends the next available single weight denomination according to the ASTM or OIML classification that is smaller than or equal to the nominal capacity of the weighing instrument.

2. A small weight, preferably of a mass equal to a few percent of the capacity of the weighing instrument. GWP recommends the next available single weight denomination according to the ASTM or OIML classification that is smaller than or equal to 5 percent of the nominal capacity of the weighing instrument.

In closing

In order to ensure that correct rules of metrology are obeyed, the following are observed:

1. Weights for testing the sensitivity of weighing instruments need to be calibrated and must be traceable (reference weight). Their maximum permissible error (mpe) must not be larger than one-third of the warning limit so that its influence compared with the warning limit may be ignored entirely. The lowest weight class that fulfills this condition is selected. Since the warning limit depends on the control limit and thus on the required weighing accuracy, so does the mpe of the test weight.

2. All other tests (i.e., tests of repeatability or eccentricity) may be performed with any weight, provided the weight does not change its mass during the test. Of course, it is always possible to use a calibrated test weight for these tests as well, but this is not required.

3. Testing for sensitivity with a test weight that is too small (compared with the capacity of the weighing instrument) runs the risk of the test measurement becoming “contaminated” by the influence of repeatability.

Test weights for sensitivity are typically of a higher accuracy class (ASTM 1 to 4/OIML F or E). However, even though in some cases an OIML class M weight would suffice for a test, GWP substitutes that class for an ASTM class 4 or OIML class F2 weight.

The reason is that the surface of class M weights is allowed to remain rough. This increases the chances for potential contamination, a feature that is not tolerated in laboratories. Test weights for sensitivity must be (re-)calibrated at regular intervals to provide traceability.

User tests

In short, using the premise that users need only two weights to test an individual balance, the following tests and weights are recommended:

1. Sensitivity, preferably with the large weight (100% of nominal capacity).
2. Repeatability, with the small weight (approximately 5%- 10% of nominal capacity).
3. Eccentricity, preferably with the large weight (100% of nominal capacity).
4. Linearity need NOT be tested by the user due to its insignificant contribution to measurement uncertainty across the whole weighing range.

is METTLER TOLEDO’s proprietary, risk-based approach for interpreting the regulations of specific industries and putting them into weighing practice. As part of the GWP program, lab weighing sales specialists can provide a GWP evaluation of any balance chosen for any application.