Merna Nesigurnost
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Transcript of Merna Nesigurnost
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1
O OJ
,
Guide to Expression of Uncertainty in Measurement . , , . () . . . . 1.
19. 20. . , , . . . , , . , . , . , . , , , , 1978.
. 1980. . , 1993. , , 1. , . . , . . , , , , . . . , , . , dr hc (1897 1976), , : .
1 , , , , , .
1
-
2
: . . , , . .
2. ()
. .
3.1
, u (. Uncertainty), s, u = s. . , ,
, ( ), 68,2 % ( 4.1.3).
ux s sx
. . ,
ni xxxx ,...,...,, 21
= n ixnx 1s1
,
, uc, . , , , .
1
)( 2s
=
n
xxs
n
ii
. (1)
, ,
sx
sxs 2
, U, , k, , 3 3. , 99 %. , .
nss
sx= . (2)
, ( ) . . ix su = , u .
sxss=
. ( . ). , , (, .).
3.
, . ( ) , . , . , 1 C. , 20,0 C, 19,0 C 21,0 C. 20,1 C, 0,1 C.
. C10
, n . ,
ss
)1(2s = n
ss , (1.)
(1.) n. , ,
ss
=ns /s
8s
2 , , 1.3.
2
-
3
27 %. . 3.3
3.2 , . . . , P I U,
IUP = . , uI uU. uP . () r . .
, . , , . . . , , , .
, , , . , , , . , , . , , .
4.
. . , . , . .
. , , . , . , , . . . , . , . , , . , , .
, . n . n , . , , . . . . , , , + 200 V. ,
3
-
4
. , ( ). V. . . , (drift) . . , . . 1 N . N N + . , , () , , 4.1.1. 2 U = 1,000000 V. 30 V. 0,999970 V 1,000030 V. ) , ) ) . , .
4.1
: (), . .
4.1.1
.1. a.
x x ( -a, +a), . , 1.
, p(
. 1
1d)(p =
xx )x
2xx
-
5
, .2, , 65%. , .
.
, ( ).
( , , .) (xmin, xmax).
,2/)( maxmin xx += .minmax xxa ==
. 3 , .
4.1.2
4.1.3 ()
.2.
, .3, . . .
. . 2
p(x)
xx1 x2
3 (za = 99,7 %) P 2
2,58 (za = 99 %) P
ekvi val entpol u{ i r i nest andardnoodst upawe
sr edwavr ednost
P=68,2 %
1
p(x)
xx1 x2
a
pol u{ i r i nast andardnoodst upawe
sr edwavr ednost
a6
s=
P=65,0%
1a
.2 . a . . . .2 1, , a/1)(p = , .
(6) 2xx
x
22
12
1
,/)(p,/)(p
axxxaxx
==
)()(
xx
.3 () .
),,(,e2
1)(p
2
21
=
xx
x
(8) , . 2/1)(p = . , x , . , )3( 99,73%. ,
p(x) = 0, , , , (6) (4),
tt us =
5
6/tt aus == (7) 3 1.11
.
-
6
, . , , = 3 . 99% . = 2,56 . : 3=k
, .
56,2=k
1s = nn
sn
, . 68,2 %, ( .3) .1 .2. , , . .4
n
,
4 .
. , ,
( 10 == s ) . . 4 , .
.4 sn 20 40 . ,
minn20min n
%2,68P
40min n , . %99P
n
11 2,2
2N/m
, . .
P , .
, . 2 4.2.
4.2
, . . . - 5. , . 4.1. 1, . 1 N/m100,2( )1011 2. .
, . ( , .
11101,2 =,N/m10 2111=a
) .
5 , 1.13 4 . , 1.14
6
-
7
, (5), .N/m10577,03/ 211== au
) (7),
.N/m10408,06/ 211== au ) (, - .) . 99 %, , (1),
99,7 %, u
.N/m10388,058,2/ 211== au
03/ == a .N/m10333, 211 2 10 , , 1 g 2. 2 . 1 2 3 4 5 (kg)
1,002 0,995 1,000 1,008 1,005
. 6 7 8 9 10 (kg)
1,011 1,003 1,012 1,006 1,001
. . . (1), ( )
g3,1004s =m
g.2,5== su ,
g)29,03/5,0( = , 1 4 (5). . U . : g0,93 == uU ; T : g7,126 == uU ; g4,1358,2 == uU , ( %),99=P U . %)7,99(,g6, =P153 == u , a . U . %
.91s == nn%99=P
,99=P
sn
9.16 g25,3 == u73
g2,2109,4 == uU
100
. .
n
1 , . , , , , . . - 6 . . 1 , .
.
, (99 % 99,7 %) (2,58, 3).
( %99=P ) .
.
5.
, . , , . .
n . .
, . . .
6 , 1.15.
7
-
8
. ,
. .
ixix
1
..
(P = 100 %)
0,577 a 57,7 % a5,0
1,73
(P = 100 %)
0,408 a 65,0 % a1
2,45
P = 99 %
0,388 a
68,2 %
a03,1
2,58
P = 99,7 %
0,333 a
a20,1
3
5.1
,
, . , . , .
),...,...,( 21 ni xxxxfy =ix
7
= 2
2
ixi
y sxys (9)
.
(9),
ixs
,( 1xfixix ),...,...2 nxxy =
ix
= 2
2
ixi
y uxyu (10)
. (10)
. ,
ixu ix
ix
V , m
Vm /= . ( ), . , , . , .
,( 1 xxfy =
y
, 5.3.
5.2
.
),...,...,( 21 ni xxxxfy =y 8
= ii xxyy . (11)
),...,...2 ni xx ,
(11),
ix
= ixi uxyu (12)
( ) . (11) , yu
7 , 1.7. 8 , 1.7
8
-
9
u .
ix
x1
1x
21uxx
9 ,
),( 21 xxr11 r .
r . 1x 2x
1),( 21 =xxr bax += 2 , ( a ), . . , 5.3.
b
.0),( 1 xxr 2
, , , 1,(0
-
10
IRV nn =
ItRtV )()( = , nVn /)()( tVRtR = . ,
. ,
nR)t
1nV (V
)),(( n VtVr ,
.1=
i
e
RR
iR
0)
,
, ,
. (10) ,( ji RRr
. , , , .
18, 010R =R e = uu eR
%)99(,58,2 == Pk ,
, . 46= ,0eRu=e kU R )46,01000= (eR .
nF500=eCnF100=C
.nF1,0C =
eC
=Ce iC
1),( ji CCrCu
eC
nF5,05 C =U
C 5e =
Ce =UeC
nF)5,0500(e =C
)(tR nR
0/ nn RuR )(t
Vn =ItRt )()( =
IRn
I)(tR
.
nn /)()( VR
tVtR =
2nnn
/)()( VtVRV
tR = (12)
n2
n)(
nn)(
)(1VtVtR u
VtVu
VR =u . (14) 3,
. (14)
)(tR
. ( ) U . U .
n
VtVtR
Vu
tVu
tRu
n
)()()()( = (15)
, , . (15) .
nR )(tRVVtV uuu == n)(
)()()()(
tVu
tRu tVtR
-
11
V , ( ). , (10) ,
)(t nV
nn /)()( VtVRtR =
2
n
n
RuR
(tV
Vu
)
)
Ru
)(tR
C05,0 o
mW.
- . - 1 . 710- ( C.)123 o2
n
)(
)()( +
=Vu
ttRu VVtR (16) - < %.60
. V , ,
) n ( ), . , , , , . , , . , .
n
n(
( Ru
tRtR . (17)
(17) , .4, .
4 5.3.3. , , .5. .
6. E M
. . , , . , , .
- , . VR- ,
. 4321 ,,, RRRR- , . )(tI-
.
)(tT),( tTR
- , . Tu
, . 1% 5% . , .
( ,
T
T c
onst
.~ ~
Rn
R( )T V( )T
Vn
I
1.288453 V
vi sokoomskivol t met ar
et al onskiot por ni k
pl at i nskit er momet ar
stru
jni
gene
rato
r
t er most at
dvopol o` ajnipr eki da~
, ,
. , , . .
610
- 100 . .5 .4,
. - , , . - () . C23 o
, ).
- . , .
- 10
11
-
12
, , , .
, , ( , , , , , , ).
, , . , , . , , . .
. . , . , , , . .
6.
3 . 3 . , .
I1x
3
-
-
I 1 x1
II n, n>>1 (.6, )
nsu /A =
As ukx
( I)
III 1
Bu
Bs ukx ( I)
IV 1
BuC
Bukx Cs
() ( II
III)
V n -
CABu
CABs ukx
VI n (. 6 )
o, . .
CUu
CUukx s
- (, -)
12
-
13
13
: .
U
()
) )
)
ucBucAB
ucu k.
= k u cu.Uc
= =sxs uAsn
(xi s-x )2
n - 1=s
?
6 ) ; ) ; ) VI, 3.
-
. . . , , , .6 , ( 3.1). , , , .6 . 3, , . 1 2 4.
II
III
IV
V
V
VI
V
II III IV V
( ). , 5 5.3. , . , ( ) ( ). , 1 5.3. . 3 ( 6). . , , . ( ) . 6 . , , ,
Guide to Expression of Uncertainty i Measurement, BIPM, IEC, IFC, ISO, IUPAC, IUPAP, OIML, Geneva 1993. ., , , 1997. B.Taylor, C.Kuyatt Guidelines of Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297, Gaithersburg, 1994 Edition. K.Sommer, M.Kochsiek, Role of Measurement Uncertainty in Deciding Conformance in Legal Metrology,OIML Bulletin Vol.XLII, Number 2, April 2002. Expression of Uncertainty of Measurement in Calibration, EAL-R2, Edition 1, 1997. Abstract The aim of this contribution is to present in a short and concise manner the essence of the book Guide to the Expression of Uncertainty in Measurements that is today the international reference in the field of the Uncertainty of obtained experimental results. The majority of readers have not the necessary knowledge of random processes and basic error theory that is indispensable for practical use of the mentioned book. This contribution has to be the basis for future use as one of the textbook chapters for the undergraduate study. That is the reason why many rigid mathematical proofs are omitted. Many examples taken from the different subjects in electrical engineering have been supplied to make the better and easier understanding of the essence of related field.
14
14
n, n>>1 (??.6, ? ? ?)n (??. 6 ?)