Measurement Uncertainty & Minimum Sample Weight for Balances

USP SECTION 41 (MEASUREMENT UNCERTAINTY): U.S. PHARMACOPEIA Section 41 Weights and Balances, details a formula to calculate the measurement uncertainty of a balance when the balance is used for Assay weighing. This same formula is referenced when determining the minimum sample weight of a balance.

USP Section 41 states that “when substances are to be ‘accurately weighed’ for Assay the weighing is to be performed with a weighing device whose measurement uncertainty (random plus systematic error) does not exceed 0.1% of the reading.” The formula for arriving at this measurement uncertainty value is three times the standard deviation, of at least ten replicate measurements, divided by the amount weighed. The resulting value shall not exceed 0.001.

We always want to remember that as we increase in weight, even though there may be a greater variance between the replicates with each increase, the measurement uncertainty value decreases. The heavier the weight applied, the greater the chances of that particular weight applied passing the test.

MINIMUM SAMPLE WEIGHT: The minimum sample weight, for Assay weighing, is calculated using the above mentioned test method. The minimum sample weight is determined by identifying the smallest mass value that passes the USP Uncertainty Test.

If a 10mg test load was desired on a 5-place analytical balance and the results of the test came to 0.16% of the applied weight. This particular balance, at that particular location, could not be used because its measurement uncertainty exceeds 0.1%. The unit would then need to be tested at 20mg or the balance would be needed to be upgraded to a 6-place micro balance. If the resulting value had been 0.14% instead of 0.16%, then the value could be rounded down to the same significant figures as the stated criteria (0.1%) and therefore would pass becaue it would be equal to the tolerance.

One of the more controversial aspects of this section is what in fact constitutes the “sample weight”. Is the sample to be measured alone considered the “sample weight”? Or is it the “sample weight” with a tare vessel? The “sample weight” in this case would be just the sample of product alone without the tare vessel. So a tare vessel can not be used to increase the weight and bring the sample into a desired range that will pass the USP Uncertainty Test.

As a general rule of thumb, the recommended minimum sample weight will is approximately 3000 to 5000 divisions (i.e. 30.00 mg or 50.00 mg on a 5-place analytical balance). In laboratory environments that are close to ideal (i.e. little to no vibration, air currents, people traffic etc.), then 2000 divisions (20mg) may also pass the Uncertainty Minimum Sample Weight Test. As stated earlier, when applying the USP Uncertainty Test, the heavier the weight applied, the greater the chance of the value coming within the 0.1% tolerance. In referencing the above example again, at a test load of 1000 divisions (10.00 mg), this balance would be required to produce 10 almost perfect replicates, leaving very little room for any deviations. At this mass, only 10 replicates with 1 deviation of 1 count would allow this 10mg to pass, which in real-world conditions, is not probable.

DEFINITIONS

Assay: A quantitative or qualitative analysis of the composition of a material.

Random Error: Errors due to the play of chance. Variability between successive measurements due fluctuating environmental conditions, different observers, etc. An error, which is in general, different each time a measurement, is made.

Systematic Error: Factors that consistently affect the variable being measured. An error that affects all measurements similarly, (mechanical problem with balance) and or can be eliminated by upgrading the system.

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