Metrologia Enotita 8-12
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Transcript of Metrologia Enotita 8-12
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18
19
20
13
14
15
16
17
18
u
(
m
/
s
)
0.27 0.28 0.29 0.30 0.319
10
11
12
time series (sec)0.4
0.1
0.2
0.3
P
D
F
2009 2010 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 140.0
Velocity fluctuations (m/s)
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8
, ,
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, .
VIM (International vocabulary of basic and general terms inmetrology, 1993), :
, . , .
, ,
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, . : ,
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, (GUM)
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:
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( ()
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, . : :
( )
( )
, ,
=> =>
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, :
( , )
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, 1, 2 , 3 ,, i , , N1 2 3 i N f :
=f (1, 2 , 3 ,, N ) (6.1)
, ( ), , , , , , (.. ). , f . i
. , . , f
, , , , .
, ,
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i , .
1. . , , ,
. , , , .
2. , , .
, ,
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, y , (6.1) x1, x2,.., x 1, 2 , 3 ,, N . :
y=f(x1, x2,.., x ) (6.2)
, , , x1, x2,.., x :
xi
n , xi, (parent population).
, ,
-
(variance) , (variance) , (standard deviation),
.
(standard uncertainty of measurement) y y , u(y) .
xi, Xi, i i u(xi). .
, ,
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( (, , ), . . Q. n , Q , qj
q qj
(j=1, 2, ... , n)
1
1 nj
jq q
n
1jn
q :
, ,
-
(experimental variance) s2(q) , :
2 2
1
1( ) ( )1
n
jj
s q q qn
(experimental standard deviation). (experimentalq (experimentalstandard deviation of the mean), :
q
22 ( )( ) s qs q ( )s q
n
(experimental standard deviation of the mean). , :
( )u q q
( ) ( )u q s q
, ,
( ) ( )u q s q
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. . ,:
, .
, ,
. , , .
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I. Xi , , , , , , xi. u(xi), , . . ,
.
II. Xi , , , xi u(xi), .
, ,
-
III X III. Xi , , + , , (.. , ), X Xi ( ). :
1:
1 ( )2i
x :
2 21( ) ( )12i
u x
|+|=|-|=,:
2 21( )u x
, ,
( )3i
u x
-
IV IV. . , , , .: , , , + , , 100% + 100%. , , , . (+ + )/2
2 21( )6i
u x
V. xi, , , u(xi),
, ,
.
-
VI ' VI. , V. , 90, 95 99 % . , , . , , . , u(xi), xi . , , 1.64, 1.96 2.58.
, ,
-
: : :u
: u => 68%
+
: u 68% :u => 58% :u => 65%
+ +
, ,
-
(uncorrelated) f( ) y, y=f(x1, x2,.., x ), :
2 2( ) ( )N
iu y u y (6.3)1i
ui(y) (i=1, 2,..., ) y y xi
( ) ( )i i iu y c u x (6.4) ci xi, f Xi , xi: xi:
ii i
f fcx X (6.5)
, ,
,...,i i N Ni i X x X xx X
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ci, xi y. f (6.5), , y xi, +u(xi) -u(xi) ci y 2u(xi). y , , .. xi u(xi).
u(xi) , (6.4), u(y) , . , .
:
2( )u y u (6 6)( )c yu y u (6.6)
, ,
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, , , , , . n n . O . (6.1), . u(y) (RSS rootsum square) . . 6 1 6.1
( )
Xi xi u(xi) ci
ui (y)
X1 x1 u(x1) c1 u1 (y)X ( ) ( )X2 x2 u(x2) c2 u2(y): : : : :
XN xN u(xN) cN uN (y)
, ,
XN xN u(xN) cN uN (y)Y y u(y)
-
()
( ( ).
( )cU k u y (6.7)( )c y ( ) , k k=2. 95%. . . .. , , (3) , (3), , . , .
, ,
.
-
. k o u(y) y. , u(y) . . , , , . ', , veff , o ui(y).i
, ,
-
k :
() u(y) y.
() veff , u(y) W l h S tt th it Welch Satterthwaite:
4 ( )u yv (6 8)41
( )eff N ii i
vu y
v
(6.8)
ui(y) (i=1,2,,N), , y xi, , i, ui(y).
, ,
-
u(q) , i=n-1. . ,
. , , ,
, , - , , +, , , . , u(x ) u(xi) vi .
( ) k 5 2 () k 5.2. t .
:
Y = y U (6 9)
, ,
Y y U (6.9)
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5.2: kpv (kpv ,+ kpv),pv k 5. : kpv ( kpv , kpv), pv,k v (student)
pv,k
68.27 90 95 95.45 99 99.73 68.27 90 95 95.45 99 99.731 1.84 6.31 12.71 13.97 63.66 235.802 1.32 2.92 4.30 4.53 9.92 19.213 1.20 2.35 3.18 3.31 5.84 9.224 1.14 2.13 2.78 2.87 4.60 6.625 1.11 2.02 2.57 2.65 4.03 5.516 1.09 1.94 2.45 2.52 3.71 4.907 1.08 1.89 2.36 2.43 3.50 4.538 1.07 1.86 2.31 2.37 3.36 4.289 1.06 1.83 2.26 2.32 3.25 4.09
10 1 05 1 81 2 23 2 28 3 17 3 9610 1.05 1.81 2.23 2.28 3.17 3.9611 1.05 1.80 2.20 2.25 3.11 3.8512 1.04 1.78 2.18 2.23 3.05 3.7613 1.04 1.77 2.16 2.21 3.01 3.6914 1.04 1.76 2.14 2.20 2.98 3.6415 1 03 1 75 2 13 2 18 2 95 3 5915 1.03 1.75 2.13 2.18 2.95 3.5916 1.03 1.75 2.12 2.17 2.92 3.5417 1.03 1.74 2.11 2.16 2.90 3.5118 1.03 1.73 2.10 2.15 2.88 3.4819 1.03 1.73 2.09 2.14 2.86 3.4520 1 03 1 72 2 09 2 13 2 85 3 4220 1.03 1.72 2.09 2.13 2.85 3.4225 1.02 1.71 2.06 2.11 2.79 3.3330 1.02 1.70 2.04 2.09 2.75 3.2735 1.01 1.70 2.03 2.07 2.72 3.2340 1.01 1.68 2.02 2.06 2.70 3.2045 1 01 1 68 2 01 2 06 2 69 3 18
, ,
45 1.01 1.68 2.01 2.06 2.69 3.1850 1.01 1.68 2.01 2.05 2.68 3.16
100 1.005 1.660 1.984 2.025 2.626 3.077 1.000 1.645 1.960 2.000 2.576 3.000
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, . , , , , . . , . . , (6.3) . , (6.1) Xi . , :
( )Y f X X X X X X (6 10), ,
1 1 2 2( , ,..., )Y f X X X X X X (6.10)
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Taylor N . Taylor :
2 2 1 1
2 1
( ) ( )( ) ( ) ...1! 2! ( 1)!
n n
nn
df X d f X d f Xf X X f X RdX dX dX n
(6.11)
N (6.11)
1 2 1 21 2
( , ,..., , ) ( ... )Ndf df dfY f X X XdX dX dX
2 2 22 2 2
1 22 2 21 2
3
1 [ ( ) ( ) ... ( ) ] ...2!
1
NN
f f fX X XX X X
f
3 3
131
1 [ ( ) ...] ...3!
f XX (6.12)
, ,
-
. , , Y :
max
N
jfY Y Y X
X
(6.13)
1j
j jX , DC , :
P=I2R (6.14)
:
Pmax=2IR+I2R (6.15)
max( ) 2P I R
P I R (6.16)
, ,
P I R