# Software

## The GUM Tree Calculator (GTC)

A tool for data processing with automatic calculation of measurement uncertainty is being developed at MSL, called the GUM Tree Calculator (GTC).

GTC simplifies measurement uncertainty calculations, by automating most  steps involved. It is a simple software tool that can be used as an interactive calculator, or to process script files.

GTC can be installed on Windows computers (XP, Vista or 7) and is integrated with the Windows file Explorer. A context-sensitive editor with on-line help is also provided.

A few design principles are being followed as we work on GTC. It should be:

1. Easy to use
2. Easy to install and operate
3. Interoperable with other software
4. Self-contained
5. Suitable for environments subject to formal quality control

As a result, we believe that GTC is suitable for a wide range of Test and Measurement applications. In particular, calibration laboratories following ISO 17025 guidelines may find that it can be used effectively for data processing.

### Uncertain Numbers

GTC employs an innovative method for simplifying uncertainty calculations called uncertain numbers. An uncertain number is a software entity that encapsulates information about a quantity that affects its uncertainty. GTC manipulates uncertain numbers as if they were ordinary numbers, but takes care of the additional uncertainty information automatically.

GTC supports uncertain number calculations involving real quantities and complex quantities.

Here is a simple example.

Suppose a flag is flying from a pole 15 metres from an observer (measured with an uncertainty of 3 cm). The angle from horizontal to the flag is 38 degrees (with an uncertainty of 2 degrees). What is the height of the flag pole?

The equation for this problem is

$h= d \times \sin(\theta) \;,$

where $d = 15 \pm 0.03 \mathrm{cm}$, $\theta = 38 \pm 2 \mathrm{deg}$ and $h$ is the height.

Using GTC as an interactive calculator we would do the following

>>> d = ureal(15,0.03)
>>> height = d * tan(theta)
>>> value(height)
11.719284397600761
>>> uncertainty(height)
0.843532951107579
>>> 

which obtains the height as $11.7 \pm 0.8 \mathrm{m}$. We might also be curious to know whether the base measurement or the angle measurement contributes more to the final measurement uncertainty. In that case we would continue as follows

>>> component(height,d)
0.023438568795201523
>>> component(height,theta)
0.8432072539400345

and clearly the component of uncertainty due to $\theta$ dominates in this case.

## Obtaining GTC

The GUM Tree Calculator is available for download at the Measurement Software Toolkit (MST). 1