. (), . ( ) , , (.. ) .
, ε.
εi.
Ε=(1/N)Σεi
N . , ,
S=[Σ(εi-ε)2/(N-1)]1/2
, e ε,
ε=εSt(γ)/(N)1/2
(γ).
t(γ) γ N. 0,95-0,999.
, , .. ε.
10 0,95. , ε 4,7 5,5. ε Σε=50,3.
ε=50,3/10=5,03
S=(1,282/9)1/2=0,377
γ=0,95 N=9 t=2.26. ,
S/(10)1/2 =0,269.
ε=5,030,27
, 95% , ε
4,76≤ ε ≤ 5,30
Ui-Ucp | (Ui-Ucp)2 | ||||
27,2 | 0,3 | 0,3 | 3.04 | 9.25 | |
27,6 | 1,3 | 2.64 | 6,97 | ||
2,0 | 3,3 | 2.24 | 5,00 | ||
28,4 | 4,0 | 7,3 | 1.84 | 3,38 | |
28,8 | 8,5 | 15,8 | 1.44 | 2,07 | |
29,2 | 12,0 | 27,8 | 1.04 | 1,08 | |
29,6 | 14,5 | 42,3 | 0.64 | 0,41 | |
58,3 | 0.24 | 0,06 | |||
30,4 | 72,3 | 0.16 | 0,013 | ||
30,8 | 84,3 | 0.56 | 0,31 | ||
31,2 | 92,3 | 0.96 | 0,92 | ||
31,6 | 95,3 | 1.36 | 1,85 | ||
98,3 | 1.76 | 3,04 | |||
32,4 | 99,3 | 2.16 | 4,67 | ||
32,8 | 0,7 | 2.56 | 6,55 | ||
U=30,24 |
|
|
σ=0,676
k=2,24%
, n1 n2 , X0 s2.
S1 S2 . Xcp1 Xcp2,
s12/n1+s22/n2 = (n1 + n2)s2 /n1n2
S12 S22 s2 n1 -1 n2 -1, s2
S2 =[(n1 -1)S12 +(n2 -1)S22]/[(n1 -1)+(n2 -1)] =
= [S(X-Xcp)2 +S(X-Xcp)2]/(n1 +n2 -2)
t = [(X -Xcp1)2/S][n1n2 /(n1 +n2)]
t n1+n2 -2.
t=2,8, t=2,567 n=18 P=0,02. .. t, t . , .
. .
X'...Xn1 ' X"...Xn2 " Xcp1 Xcp2. S12 S22. , p , , s2.
F - ( ) - S12 S22 s, F=S12/S22. F , 0,05; 0,01 .
: . S12 .
- - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - -
. 4. . X1 =4,57 S12 =0,0295 n=19 (n=20). X2 =4,56 S22=0,0139 n=12
F=0,0295/0,0139=2,12. n=19 12 5% F=2,54. F , .
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
f=[(n -2)/n ]F, F- . 1, sr =+[(2n1 +n1 -2)/ n1(n2 -4)]1/2.
R=|f-1|/sr S12 S22.
R³3, .
R<3, .
, 4. n2. p f=1,77 sr =0,72 R=1,07. .
|
|
P(c2)
, F(X). -. , , , F(X), () F0(X). h. i , i. .
(c2) ,
c2 =S(Xh2/sh2) ( Xh =ni -n; n - ) , :
h
c2 =S(ni-npi)2/npi
i=1
i=ni/n h- ; Xh(h=1,n) - , , sh2 (h=1,n). n - .
m n - .
n=n-m. , c2 n n P(c2) , c2 .
, n=10 5% c2 =18,307. , , c2 10 18,307, 0.05. n>30 P(c2)
P(c2)=(1/2)[1-(x)],
(X) - .
n>30, (2c2)1/2 , (2n-1)1/2 , .
.
s2 , - S2. S2 c2 .
n X1,X2,...Xn , c2
c2 =S[(Xi -Xcp)2 /s ]
f=n-1 . c2 f:
f(c2)= 1/[2f/2 (f/2)] (c2)(f-2)/2 exp(-c2 /2), 0 < c < ¥.
f f 1-p .
Sx. ,
f.
c2 p/2 £c2 £c2 1-p/2
: c2 £ c21-p; c2 ³ c2p .
:
fS2x / c2 1-p/2 £ s2 £ fS2/c2
:
s2 £ fS2 /c2 s2 ³ fS2 /c21-
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
5. , X 17,2, 16,3, 15,5
.
S2 = S(X-X)2 /(3-2)=0,73
1-=0,9 f=2
c2 0,05 =6 c2 0,95 = 0,103
0,73 2/6 £ s2 £ 0,73 6/0,103
0,24 £ s2 £ 14,1
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
n>30 S s ss = sx /(2f)1/2 = Sx/(2f)1/2
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
6. s 31
S =0,85 1-p = 0,9.
:
c2 0,05 = 43,8 c2 0,95 =18,5
0,85.30/43,8 £ s2 £ 0,85.30/18,5; 0,48 £ s2 £ 1,13
Z
Z=f(X1,X2,...Xn). , . Sxi2 Sz2. , Z(X) m1,m2...mn, :
|
|
Z=f(m1, m2...mn) + (X1 -m1)df/dX1 + (X2 -m2)df/dX2 +...(Xn -mn)df/dXn
Sz ( )
n
Sz2 = S(df/dXi)Si2
i=1
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
7. v, G=3000 /, S =10 /, F=0,1 1 .
: v - v=G/F=3000/0,1=30000 /= =8,82 /. Sv =[(dv/dG)2 SG2 + (dv/dF)2 SF2 ]1/2 = [SG2/F2 + G2 SF2/F4]1/2 =
= [10000 + 900]1/2 = 100/3600 = 0,03 /c
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
( ).
m y1,y2,...yn
u
S2 =[S(y-ycp)]/(m-1)
u-1
( ) S = (S2)1/2
S2 = SS(yn -yi)/Smi -n
yn =Sym /mm.
(m1 =m2 =...=m), S2 =SSi2/n
n m
S2 = S S(yiu-yicp)2/n(m-1)
i-1 u-1
m1=mn=...=m,
n
G=S2max /SSi2
i=1