What is the precision that I may expect from a weighing system?

The precision that we may expect from a weighing system is the highest value obtained between the two following calculations (a) and (b):

(a) Limit by minimum division of the load cell (related to repeatability): e_min(rep) = v_min * √ N -> (a)

Being,
e_min(rep): minimum error that can be obtained by the minimum division of the cell
v_min: the minimum load cell verification interval
N: number of load cells

(b) Limit by range of use of the cell (related to linearity):
e_min(lin) = Max / n_lc -> (b)

Being,
e_min(lin): minimum error that can be obtained by range of use of cell
Max: Net product weight
n_lc: number of load cell verification intervals

Result: e_min = el mayor de e_min(rep) o e_min(lin)

Recommendation: The precision is the error. The resolution or division of “display” is the fraction that is displayed. In certified scales, the resolution or division of display should not be finer than the error of the instrument itself. In certain industrial environments, an increased resolution is used, twice as fine than the real error or the precision of the system.

Example 1. Normal scale
Data of the weighing system:
Product Max= 600 kg
Dead Load DL = 120 kg
Total Load = 720 kg
Supports N = 3

Data of the Cells:
3 units Model 350i 500 kg
E_max = 500 kg
n_lc= 3000 divisions
v_min = E_max / Y = 500 / 10.000 = 0,05 kg

Calculations:
(a) Limit by minimum division of cell (related to repeatability): e_min(rep) = v_min * √ N = 0,05 * √ 3 = 0,086 kg
(b) Limit by range of use of cell (related to the linearity): e_min(lin) = Max / n_lc = 600 / 3000 = 0,2 kg

Result: e_min = 0,2 kg

For these scales we shall choose a display resolution of d = 0,2 kg

Example 2. Scale with quite a lot of dead load in respect to the weight of the product
Data of the Weighing System:
Product Max= 400 kg
Dead Load DL = 320 kg
Total Load = 720 kg
Supports N = 3

Data of the Cells:
Model 350i 500 kg
E_max = 500 kg
n_lc= 3000 divisions
v_min = E_max / Y = 500 / 10.000 = 0,05 kg

Calculations:

(a) Limit by minimum division of cell (related to the repeatability): e_min(rep) = v_min * √ N = 0,05 * √ 3 = 0,0865 kg
(b) Limit by range of use of cell (related to linearity): e_min(lin) = Max / n_lc = 400 / 3000 = 0,133 kg

Result: e_min = 0,133 kg
For this scale we shall choose a resolution of display of d = 0,2 kg in an environment of certified scales for commercial transactions or also the smaller d = 0,1 kg for an environment of industrial control.

Example 3. Scales with a great amount of dead load and very little product weight
Data of the Weighing System:
Product Max= 220 kg
Dead Load DL = 500 kg
Total Load = 720 kg
Supports N = 3

Data of the Cells:
Model 350i 500 kg
E_max = 500 kg
n_lc = 3000 divisions
v_min = E_max / Y = 500 / 10.000 = 0,05 kg

Calculations:

(a) Limit by minimum division of cell (related to the repeatability): e_min(rep) = v_min * √ N = 0,05 * √ 3 = 0,086 kg
(b) Limit by range of use of cell (related to the linearity): e_min(lin) = Max / n_lc = 220 / 3000 = 0,073 kg

Result: e_min = 0,086 kg
For these scales we shall choose a display resolution of d = 0,1 kg.