1.5 Summary

The obtained model is :

$$T-55.52 = 2.69\times plastic+\left(4.31\times1.5mm^{2}-3.69\times2.5mm^{2}-4.69\times4mm^{2}\right)$$

$$+\left(-0.42\times welded+2.96\times screewed\right)+\left(-1.42\times silver+1.33\times brass\right)$$

$$+\left(2.81\times nylbloc-0.94\times overmoulding+0.56\times thermo\right)$$

The $\mathrm{VRF}_{exp}$ of this model is $13.6$ (i.e. its ability to forecast... backwards), and the associated standard discrepancy is around $1.6°C$. This remaining variability is due to both measurement uncertainties and non-linearity of the problem.

The $\mathrm{VRF}_{th}$ is $13.6*(16-12)/(16-1)\ \approx3.6$, taking also into account the difference between the obtained model and the best possible affine model affine, that would be based on a full factorial design.

Concerning the relative effects of the factors, we see that the choice of connecting wires is crucial (influence $9°C$), while the choice of the engine is the least influential ($2.7°C$). The other three have similar influence (around $5°C$).

According to the obtained model, the best choices are brass, crimped, silver, $4mm^{2},$ hypo4. The temperature predicted by the model is then $41.75°C$. This value has to be compared with the best experimental realization: brass, welded, CuNiSn, $4.0mm^{2}$, hypo4. For these choices, the prediction is $45.38°C$ and the experimental result $42°C$.

According to the objectives pursued, and in particular according to the requested reliability, some complementary tests can be useful.

Exercise 1.5.1   Determine all the choices (among all the 288 possible) for which the model provides a temperature below $45°C$.