# Understanding Measurement Uncertainty In Weighing Scales & Instruments

It is easy to consider an industrial instrument to be a perfect machine that provides exact information. But every real-world system has limitations based on the machine itself, and the environment in which it is used. That is the case with voltmeters, flow meters, tachometers, thermometers, and weighing scales, where the weight sitting on the scale platform is measured.

## What Is Measurement Uncertainty Within Scales

When a load is placed on the scale platform, the weight indicator will display a numeric value. We know that this value cannot exactly match the true weight of the load to an infinite number of digits. But we are uncertain as to how much of a difference there is.

Every measurement has some level of doubt. This can be quantified by determining how high the level is, and how bad the doubt is. The level can be associated with the interval of measurement, while the doubt relates to how sure we are that the measurement is within the noted interval.

For example, if a scale has a weighing range of 5000 g with a resolution of 1 g, then the interval of measurement is +/- 1 g. The weighing instrument can show a weight of 3456 g or 3457 g, but it cannot show any value in between. For the reading of 3456 g, the actual weight should be between 3455 g and 3457 g.

There is still the issue of how much doubt do we have that the weight is within that range. Are we only 95% certain, or are we 99% certain? We can express the uncertainty of this example by stating that the weight is 3456 g +/- 1 g at a confidence level of 99%.

### Why Measurement Uncertainty Is Necessary For Weighing

As with any type of measurement, weight measurement always has some level of uncertainty. The weight of an item can be thought of as an analog measurement. Any analog value that is converted into a digital value must have some level of uncertainty.

The level of uncertainty can be minimized in a variety of ways. The example used of a scale with a capacity of 5000 g and resolution of 1 g can be compared with a scale with the same capacity of 5000 g, but with a better resolution of 0.1 g. In this case, the interval of measurement is +/- 0.1 g. If the confidence level remains the same, it is clear that the uncertainty will be only one-tenth as large.

Arlyn’s Ultra Precision scales are a real-life example of this reduced uncertainty. While typical high-quality industrial scales of that capacity will offer a resolution of 1 g, Arlyn’s Premium 5000 g SAW scale provides a resolution of 0.02 g. Therefore the uncertainty can be as low as only one-fiftieth of a standard scale.

All industrial scales provide a means of calibration. At the simplest level, the scale may have a screwdriver adjustment that can be used to match the reading on the display to the load that was applied. The suggested calibration load is generally about 50% of the capacity of the scale.

More advanced instruments, such as the platform scales from Arlyn Scales, will semi-automate the process. A menu-driven display will prompt the operator to enter the value of the calibration weight. When the weight is placed on the scale, it will automatically adjust itself for the best reading.

## Using Test Weights

The calibration process can only be as accurate as of the test weights that are used. Different accuracy class test weights are used for different requirements. A fairly typical classification, in the US, is NIST Class F, with specifications developed by the National Institute of Standards and Technology. They are suitable for many scales used in trade.

The American National Standards Institute, ANSI, Classes 4 through 6, are for more general-purpose scales and balances. Classes 0 through 3 are used for precision analytical work.

The materials used to fabricate the test weights are dependent on the class and the use. Heavier weights are usually made from cast iron. Higher precision, lighter weights are made from polished stainless steel.

## Process For Measuring Uncertainty

The most standard way to calculate uncertainty is by taking multiple measurements, such as 10 times. Make certain that the measurements are made under the exact same conditions. Calculate both the mean and the standard deviation of these measurements.

Standard uncertainty is calculated by identifying each source of uncertainty and taking the square of each value. Sum the results of the resultant calculations. The square root of this sum is the value of standard uncertainty.

## Relevant Factors

There are a limited number of specific error terms that apply to scales. They must often be determined independently. The quality of the scale, though, will be impacted by each term.

### Repeatability

One could expect identical results when placing the same load on the platform multiple times. But depending on the resolution of the scale, it is possible to obtain small variations. These differences define the repeatability of the scale.

### Eccentricity

An ideal scale would display the same weight independent of where the load was placed on the platform. In real life, though, there will be some variation, called eccentricity. This is caused by slight imperfections in the symmetry of the load cells.

### Nonlinearity

Graphing the weight on the platform compared to the result on the weight display should result in a perfectly straight line. The amount of the greatest deviation from this line defines the nonlinearity of the scale.

### Sensitivity

The smallest change in weight that can be seen on the weight display is considered to be the sensitivity of scale. As a rule of thumb, the better the sensitivity, the better the scale.

## Reduce Uncertainty By Using The Best Scales

While errors and uncertainty can never be fully eliminated, Arlyn’s high-quality scales and ultra-precision industrial scales reduce it to a minimum.

Reach out to the Arlyn Scales representatives today. Their knowledgeable staff will help guide you to the best solutions for your weighing requirements.