Sharp JX-9400 Informations techniques télécharger pdf (Page 180)

Hence, we can state:

 ¼hxiI

ð7:65Þ

P is the probability that the conﬁdence interval contains the ‘true’ value. P is

chosen a priori, in practice between 0.9 and 0.99, depending on the degree of

conﬁdence needed. The higher the probability, the broader is the conﬁdence

interval ½I

; I

.

Note that the conﬁdence interval of the ‘true’ value stabilizes to a value

close to the standard deviation if more than seven measurements are performed.

Error analysis

What is the problem?

If several measurements are combined to obtain the needed results, the errors

should also be combined the proper way to get the resultant error. In other

words, the problem is the following.

Suppose that we nee d several results y

; y

; ...; y

, each of them

depending on measurements of several variables x

; x

; ...; x

¼ f

ðx

; x

; ...; x

Þð7:66Þ

Here, j ( j ¼ 1toM) enumerates the various results (for example, M diﬀerent

airﬂow rates) and i (i ¼ 1toN) enumerates the variables on which the results

depend (for example, the tracer gas concentrations and ﬂow rates or pressures

and conductances).

If the measurements, x

, each have an absolute error, x

, what are the

errors, y

, on the results, y

Most simple error analysis

The simplest rule, which is taught everywhere, is the following: the error y on

the result is estimated by replacing, in the total diﬀerential df of the function f,

234567891011121314151617181920

Confidence limit/standard deviation

Number of measurements

90%

50%

99%

P = 99.9%

Figure 7.5 Conﬁdence limit divided by standard deviation versus number

of measurements for various valu es of probability, P

Common Methods and Techniques 159

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