**ERRORS IN WEIGHING SYSTEMS**

The first distinction is between **systematic errors** and **random errors**. While systematic errors are predictable, quantifiable and can be summed in an algebraic way, random errors are calculated in a statistical way. In order to minimize errors, it is necessary to establish the performances of the system defining two essential data:

**Error with constant room temperature**: it is the reference value for verification tests that must be established once the system has begun to work. It is calculated by adding systematic error to total random error. Zeroed errors related to system characteristics or operating conditions must be excluded from the calculation;**Error due to thermal drifts**: it is compensated by periodic calibrations and manifests itself in the long term; calibration frequency depends on user’s evaluations.

**SYSTEMATIC ERRORS**

As previously said, systematic errors can be summed in an algebraic way in absolute terms creating **total systematic error**. In measurement devices, errors are expressed as a percentage related to the specific full scale, therefore in systems with many cells, percentage values don’t change.

Among systematic values, there are:

**Cell rated output tolerance**: only related to systems with many cells, it depends on the shift of load barycentre; it can be compensated by the calibration of angles; without compensation, it can be calculated with the following equation:

Error= (rated output tolerance / 100) * (barycentre shift % / 100) * full scale capacity

**Cell linearity error**: it has to be considered in downward linearity, not only for downward measures;**Hysteresis error**: it has to be considered only when quantity changes during weighing process;**Drift under load**: it has to be considered only in systems in which measurement happens later than load application;**Measure resolution**: considered in all applications.

**RANDOM ERRORS**

Total random error is calculated through the square root extraction of the sum of the squares of each error. Due to their nature, random errors **must always be considered** in every application, because they **can’t be compensated**. The calculation refers to absolute values, and therefore it is related to total full scale.

Among random errors:

**Load cell repeatability error**: it is defined as standard deviation on 10 measures with a weight variation of approximately 50% of the rated capacity expressed in % with reference to weight variation; in the calculation of this error, the real weight variation that manifests itself in the system must be considered because it may not correspond to the full scale capacity;**Stability of cell output booster:**it is often an unavailable datum and should be divided into two parts to be considered separately: stability for variations of network supply voltage and stability over time;**Stability of A/D converter:**called “noise” by producers, it is standard deviation or peak value/peak; it is usually a negligible value because peak value/peak should be lower than indication resolution.

**ERRORS DUE TO THERMAL DRIFTS**

As systematic errors, also errors due to thermal drifts are calculated by the **algebraic sum of single errors**. Environmental operating conditions vary from system to system, therefore the error must be calculated for the **effective variation of temperature** in relation to the expected temperature for calibration.

In the long term, room temperature variations can be compensated with seasonal calibrations, reducing the values that have to be used for the calculation of the error due to thermal drifts. Moreover, errors due to thermal drifts produce:

**Zero errors**: they haven’t to be considered if the system is equipped with automatic zero setting before measurements;**Range errors**: they can’t be eliminated, therefore they must be considered in all applications.

**Devices** that can generate errors due to thermal drift are:

**Load cells****Cell signal booster****A/D converter****Cell power cables****Thermal expansions of the structure (they have to be considered only in very heavy or long structures or with high differential temperatures)****Cell supply voltage (in modern microprocessor systems the error is zero)**