# Relative Standard Deviation of Repeatability

Repeatability describes the property that the **output signal** is the** same for all measurements of the same torque **when measured several times. During the measurements the **mounting position** of the torque transducer shall remain **unchanged** and the torque transducer shall not be mounted and

dismounted (repeat conditions). The standard deviation indicates the average deviation between all measurements of the same torque when measured several times.

The relative standard deviation of repeatability is a measure of the repeatability according to **DIN 1319**. It is defined as the standard deviation of repeatability according to DIN 1319 and is expressed as a percentage of the range of the signal span covered during the testing procedure. It is a statistic measure of

random measurement deviations. For this reason, **all those conditions are kept constant** that, if changed, might cause variations in **systematic measurement deviations** (repeat conditions to DIN 1319).

The determination of the relative standard deviation of repeatability is a **type test** carried out on a** static calibration system** as follows:

- The torque transducer is
**preloaded up to nominal torque**. The measurement signal*S*is taken at nominal torque_{1,100%} - The load is reduced to
**50 % of the nominal load**. The measurement signal*S*is taken at half the nominal torque_{1,50%} **Alternation**between 50 % and 100 % of nominal torque. The measurement signals*S*and_{i,50%}*S*are taken until 10 measured values each are available for each torque_{i,100%}- The
**equation**below is used to calculate the relative standard deviation (in mathematical terminology, the empirical standard deviation of a random sample) for each torque and relate it to the output signal span:

with

n=10 being the number of measurements for the respective torque applied (50 % or 100 %) and the arithmetic mean of the measurement signals according to

- The technical data specifies the inferior of the two values σ
and σ_{rel,50%}_{rel,100% }.

### Example:

HBM specifies the standard deviation of repeatability for its **T10F torque transducer** as *σ _{rel}* ≤ 0.03%. This value refers to the output signal span between the values of applied torque. Assuming a nominal torque of 1 kN·m, for example, this corresponds to a span of 500 N·m according to the test conditions specified above. Thus the standard deviation of repeatability in this case amounts to ≤ 0.15 N·m.

In the following example **repeatability** (quantitatively specified by the standard deviation of repeatability *σ _{rel}*)

**is of special importance to the user**. A

**test bench**for

**combustion engines**is used for measurements with the aim of comparing different settings of the engine’s control electronics.

**The**

**torque transducer’s**

**mounting and the ambient conditions remain unchanged**. The loading histories for the different measurement series are identical. In these measurements the differences between the torque values of the individual test series are more important than the absolute torque values. Under these circumstances, the contribution of the torque transducer to the uncertainty of these differences is given by its repeatability.