Sharp JX-9400 Technical Information PDF herunterladen (Seite 176)

domain. The statistical method allows one to obtain more information on the

reliability of the results.

Because of rando m reading errors and uncontrolled perturbations, the test

values will follow a given distribution. We can model such distributions by

treating x as a stochastic variable.

The probability density function, f ðXÞ , of the variable x is the probability to

ﬁnd x between X and X þ dx.

Its integral F(X) is the probability of hav ing x < X:

FðXÞ¼probðx < XÞ¼

1

fðxÞdx ð7:48Þ

The lower signiﬁcance limit is the value X

for which FðX

Þ¼p, where p is a

given probability. The upper signiﬁcance limit is the value X

for which

FðX

Þ¼1  p.

The conﬁdence interval [X

; X

] is the range between the lower and the upper

signiﬁcance limit (see Figure 7.2). The probability to ﬁnd x in this interval is

P ¼ 1  2p .

Average

If the same importance is given to all the results, an estimate of the average, ,

of the variable, x, based on N measurements is calculated by:

hxi¼

ﬃ  ð7:49Þ

where the sum runs over these N measurements (i ¼ 1; ...; N).

If we give more importance to some measurements than to the others, a

weight, w

, can be attributed to each value, x

, and the weighted average is

calculated by:

hxi¼

ð7:50Þ

0.1

0.2

0.3

0.4

0.5

-3 -2 -1 0 1 2 3

x-<x>

Confidence

interval

Figure 7.2 Signiﬁcance limits and conﬁdence interval

Common Methods and Techniques 155

1 2 ... 171 172 173 174 175 176 177 178 179 180 181 ... 210 211

Kommentare zu diesen Handbüchern

Keine Kommentare

Sharp JX-9400 Technical Information Seite 176

Kommentare zu diesen Handbüchern

Verwandte Produkte und Handbücher für Drucken & Scannen Sharp JX-9400