Estimating measurement uncertainties

After having dealt with the uncertainty of the reference, we will now estimate the uncertainty associated with the measurements and the luxmeter.

The illumination ELU measured with the luxmeter that is to be calibrated can be modelled by:

where

Table 7
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The series of five measurements in similar conditions gave the following results:

Table 8
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Deduce the values of and of the estimated standard deviation

Knowing that the luxmeter's resolution is of 0.5 lux for a read value of 100 lux, deduce the corresponding standard uncertainty urés.

From all the previous questions, deduce the value of the combined uncertainty uc(ELU).

The model for the measurement is . Even if the corrections are null, the associated uncertainties are not. We thus have:

that is to say

Express the measurement result of the illumination under standardized form, justifying in particular the choice of the value for the coverage constant.

We consider that the standard uncertainties uréf. and urés are exactly known, thus they are not associated with any degrees of freedom νi In such conditions, the number of degrees of freedom associated with uc(ELU) is ν=5–1=4 which corresponds to a factor t=2,78 (cf. tableau 5) (cf. table 5) of level of confidence hence :