Гефан Ширяева Основы теории эксперимента 2017

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2017
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27.04.02 «
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519.2
22.171
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, 2017
2
................................................................................................... 5
1.
1.1.
1.2.
1.3.
1.4.
.
....................................................................
....................................................................
…………… ................
……………………...............
6
6
6
8
...................................................................................... 9
1.5.
.................................................................. 12
1.6.
.............................................................. 13
1.7.
...............................................
.......................................................
.........................................................
:
,
..............................................................................
1.8.
1.9.
14
15
16
18
2.
...................................... 21
.
…. ............ 21
………………………………………….. ............. 23
…………………………… ............. 25
……………………………….. .............. 28
:
2.1.
2.2.
2.3.
2.4.
.................................................................... 30
.
....................... 33
3.
3.1.
3.2.
3.3.
3.4.
.
3.5.
4.
4.1.
...............................................................
.........................................
.
...................
.
...........................................................
..........................................
:
........................................................
.............................................................
33
34
36
39
40
44
50
.
........................................................................................ 50
3
4.2.
4.3.
4.4.
4.5.
4.6.
4.7.
5.
5.1.
5.2.
5.3.
5.4.
5.5.
5.6.
5.7.
6.
6.1.
6.2.
6.3.
6.4.
6.5.
6.6.
6.7.
6.8.
6.9.
6.10.
7.
7.1.
7.2.
7.3.
7.4.
...................................
.......................
...................................................................
.............................................................
..........
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.............................................................................................
:
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...................................................
..........
.......................................
.......
53
55
58
59
60
61
65
68
68
70
72
..................................................... 74
......................................................................... 75
.......................................... 76
... 78
:
...................................................... 79
...................................................... 83
............................................................................ 83
......................................... 85
................ 86
.
............ 88
..................................................................................... 90
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............................................... 95
............ 96
.
........................... 99
........................... 100
:
........................................................................................... 106
......................................... 110
................................................. 110
............... 112
..................... 119
................................................................ 121
:
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……………………………………………….. . 126
…………………………………………………. ....................... 127
4
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(2.9)
a2
( zcr )
)/2.
(1
H 1 : a1
.
a2
a2 ,
H 1 : a1
z cr ,
( zcr )
( z cr )
1
2
.
2.4.
,
x2
,
:
10
x1 22, 34, 52, 62, 30, 40, 64, 84, 56, 59 ;
52, 71, 76, 54, 67, 83, 66, 90, 77, 84 .
0.05
,
.
:
-
(
):
22 30 34 40 52 52 54 56 59 62 64 66 67 71 76 77 83 84
84 90
1 2 3 4 5.5 5,5 7 8 9 10 11 12 13 14 15 16 17 18.5 18,5 20
,
.
–
(
-
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:
W 1 2 3 4 5.5 8 9 10 11 18.5; W
72.
. 6.
0.05
,
wcr (
.) 82 , wcr (
H 1 : a1
,
.) 128 .
W
a2 ,
wcr (
.) .
,
,
,
.
(2.6)
M (W )
,
(2.7)
10 21
105 , (W )
2
( zcr )
,
27
10 10 21
13.23.
12
1
0.05 0.45 , z cr
2
1.64 .
.
-
W M (W )
W
33;
M (W )
W
zcr
W
zcr
21.7 ;
H1 .
,
,
x1
. 2.2.
50.3
x2
,
s 2 ( x1 ) 315.6 ,
2
72
2
:
( x2 )
s 2 ( x2 ) 141.6 .
Z
Z (2.3):
50 .3 72
315 .6 141 .6
10
10
( zcr )
,
Z
( x1 )
3.2 .
1
2
0.05 0.45 , zcr 1.64.
H1 .
zcr
,
:
,
-
.
2.4.
2
).
,
,
-
.
x1i , i 1, n1 ,
,
x2 j , j 1, n2
.
,
u-
, n1u
n 2 u , u 1, k , k –
.
:
1
2
…
u
…
l
1
n11
n12
…
n1u
…
n1l
n1
2
n21
n22
…
n2u
…
n2 l
n2
28
m1
m2
…
mu
…
ml
n
2
k
2
u
nu
,
.
(nu nu ) 2
,
n
1
u
u-
(2.10)
,
,
,
nu
-
.
-
(
)
2
k
n1n2
u
2
cr (
k 1
1
1 n1u
n2 n
n2
2
.
(2.11)
,
-
, k 1)
2
. 5).
n2 u
n1u
n1
2
cr (
(
, k 1) ,
–
).
,
,
,
n 50 .
2.5.
,
.
(
6
38 10 7
62 10 7
2
)
,
:
1
1
9
13
17
8
2
50
1 (38–42)
2 (42–46)
3 (46–50)
4 (50–54)
5 (54–58)
6 (58–62)
2
2
7
18
15
6
2
50
3
16
31
32
14
4
100
,
0.05
.
2
(2.11)
2
cr ( 0.05, 5)
11.07
. 5.
1.8 .
-
.
.
29
:
1.
n1
8
10 :
n2
19.68, 15.17, 20.54, 10.12, 22.69, 18.07, 22.65, 18.27 ;
23.22, 23.04, 22.44, 20.64, 17.67, 19.47, 19.27, 15.29, 16.4, 17.45 .
x1
x2
(
0.05 )
,
:
.
.
x1
1.
2
( x1 ) 4
x2 ,
2
( x2 ) 3 ,
-
Z (2.3) c
z cr .
.
2.
2
2
,
( x1 )
,
( x2 )
2
s ( x1 )
3.
-
2
,
s ( x2 )
. 1.
,
(
(
-
. 6).
).
4.
,
,
W (2.6), (2.7)
-
.
1
x1
1.
x2
Excel
,
ABS.
z cr
( zcr ) (1
(
. 2)
.
)/2,
s 2 ( x1 )
2.
s 2 ( x2 )
-
Excel
.
3.
:
–
(1
2),
(
.
–
«
»)
( -
30
).
n1 n 2
1
–
,
18).
)
(
,
),
(1-
,
–
,
-
1(
),
–
(3-
).
M (W ) (2.6)
4.
(2.9).
(W ) (2.7)
,
z cr
. 1.
?
2.
2
( n1
50
55 ):
n2
x2 :
x1 :
28.3
35.1
28.0
25.9
26.4
27.8
27.0
33.1
32.0
29.9 27.4
33.9 31.6
29.0
30.1
29.3
32.9
29.5
30.6
32.8
31.7
27.9
26.7
25.9
33.8
31.5
34.8
34.1
24.1
33.4
24.4
29.9
30.4
31.6
33.4
27.0
27.6
29.1
29.0
34.7
33.8
28.6
32.7
30.5
28.2
30.0
26.9
31.1
24.0
24.8
25.8
25
28.3
34.0 35.1
25.8 24.5
26.8 29.8
27.9
28.9
32.1
28.7
31.9
29.4
31.8
28.5
35.9
30.6
25.5
29.6
32.5
28.0
28.4
32.7
29.3
32.9
29.3
24.5
30.9
29.6
28.5
28.2
30.5
30.4
24.3
32.6
30.6
30.6
27.1
26.7
30.4
29.4
30.3
31.8
25.9
32.4
28.4
31.4
34.5
28.2
29.3
29.0
31.2
29.0
0.05
-
.
2
2
.
-
k
n
k 1 3.332lg n.
50
7
.
24.0 35.9,
60,
,
R
x max
7,
(
-
x min
1.7.
,
: 24.0 25.7, 25.7 27.4, 27.4 29.1, 29.1 30.8,
30.8 32.5, 32.5 34.2, 34.2 35.9.
.
:
31
)
(
).
,
.
.
F2
),
CTRL+SHIFT+ENTER.
,
.
2
2
cr (
-
, k 1) ,
.
.
,
. 2.2.
0,40
0,35
0,30
0,25
0,20
0,15
0,10
0,05
0,00
1
2
3
4
5
6
7
. 2.2.
1.
?
2.
3.
?
?
4.
5.
6.
7.
.
?
?
?
32
3.
.
.
.
-
.
3.1.
(
2.1).
,
-
,
(
)
0
.
H0 :
2
: H1 :
2
0
( x1 )
.
H1 :
2
2
2
0,
( x1 )
x1
2
0.
( x1 )
-
,
,
–
2
,
.
(n 1) s 2 ( x1 )
2
0
H1 :
2
.
(3.1)
2
0
( x1 )
–
2
cr (
2
, n 1) .
).
.
2
cr
,
-
H0
-
H0 .
H1 :
2
2
0
( x1 )
2
cr (1
–
2
, n 1) .
).
2
cr
.
,
(
H0
-
H0 .
3.1.
17
s 2 ( x1 )
0.24 ,
2
0
,
0.18 .
0.05
H0 :
2
( x1)
2
0,
H1 :
,
(3.1)
).
33
2
( x1 )
2
0.
16 0.24
21.33 .
0.18
2
(
H0 .
2
cr
. 4)
(0.05; 16)
2
26.5 . . .
2
cr
,
-
.
3.2.
,
,
2
,
,
,
,
.
(
)
(
,
).
,
(
)
-
.
.
,
-
,
,
(
)
,
(
.
,
,
)
,
-
(
).
.
:
2
1
H0 :
2
2.
x1
x2
n1
-
n2
s 2 ( x1 )
.
s 2 ( x2 ) .
,
2
2
s ( x1 ) > s ( x2 ) .
F
s 2 ( x1 )
s 2 ( x2 )
.
(3.2)
,
k2
F,
k1
n1
n2 1 .
(
. 7),
k1 k 2 .
H1 :
34
2
1
2
2
,
H1 :
2
1
2
2 .
1
P( F Fcr )
.
Fcr ( , k1 , k 2 ) .
,
-
P( F Fcr )
,
Fcr (
2
2,
, k1, k2 ) .
,
,
,
,
.
,
H0 :
2
1
2
2
.
H1 :
2
1
2
2
.
Fcr ( , k1 , k 2 )
;
2
1
H1 :
-
F Fcr
H0
.
2
2
Fcr (
2
, k1, k2 ) .
F
;
-
Fcr
H0
.
3.2.
.
2= 0.01
: 8.1, 7.8, 8.0, 8.2, 8.1, 8.1, 7.9, 7.8.
8.3, 8.5, 8.0.
,
2,
1- ?
,
,
,
,
.
1: 7.9, 7.7,
:
2
s ( x2 ) 0.023,
:
s 2 ( x1 ) 0.102 ,
Fcr (0.01, 4, 7) 7.85 .
F
4.4.
F
Fcr ,
.
:
,
!
.(
.
,
,
).
,
,
-
.
«
0.05
Fcr ( 0.05, 4, 7)
4.12 ,
,
,
.
35
».
( n 12 ),
3.9 .
3.3.
2
2
s ( x2 ) 5.7, s ( x1 )
,
0.02
2
1
H0 :
2
2
H1 :
2
1
2
2 .
,
Fcr (
2
, k1, k2 ) Fcr (0.01, 11, 11) 4.46,
1.46.
F
Fcr ,
.
-
.
3.3.
.
,
-
,
-
.
.
.
m
.
,
c
-
.
,
,
(
,
!)
,
,
,
,
,
. .
,
. 2.2.
.
.
,
,
,
,
m
,
.
,
(
C52
)
!)
10
-
.
,
-
.
.
,
,
).
(
.
36
k
1, 2, ..., m –
«
(
-
»); nk –
m
k; n
nk –
; x ki –
,
k 1
i
k
.
-
k
:
1
nk
xk
nk
x ki .
(3.3)
i 1
:
1 m nk
x ki
n k 1i 1
x
1 m
nk x k .
nk 1
(3.4)
.
SS
Sumof Squares
).
m nk
( xki
SST
x )2 ,
2
1
SST
n
( x)
k 1i 1
(
,
.
)
m
SSA
(3.5)
( xk
x ) 2 nk ,
,
2
A
k 1
1
SSA
n
(3.6)
-
.
,
, . .
-
.
.
m nk
( xki
SSR
x k )2 ,
2
R
k 1i 1
1
SSR
n
(3.7)
«
.
,
(
)
.
.
(
)
37
:
»
2
1
nk
( xk )
nk
x k )2 ;
( xki
2
R
i 1
(
1 m
nk 1
)
2
( xk )nk .
(3.8)
:
2
A
1 m 2
( x k nk
nk 1
2
R
m
k 1
2x
n
2 x k xnk x nk )
nk
m
2
x k nk
2
x
1 m nk 2
( xki
n k 1i 1
2
2
2
x2
xk
k 1
m
xki
i 1
2 xki x k
2
x k nk
x2
k 1
n
2
xk )
n
x
2
2
.
,
2
.
2
A
2
R,
SST
SSA SSR .
(
(3.9)
)
.
,
.
,
-
,
.
2
0
SSA
1
SST
(3.10)
,
-
.
3.4.
. 3.1
20
( ),
(
4
-
5
).
.
3.1
1
)
1
2
3
4
2
»
1.8
2.1
1.8
1.9
3
»
»
2.1
2.3
2.4
2.6
. 3.2.
38
4
1.8
1.6
1.9
2.1
5
»
1.6
1.8
1.3
1.5
»
1.9
2.4
2.2
2.3
3.2
xk
2
( xk )
1
1.9
2
2.35
3
1.85
(k)
4
1.55
5
2.2
0.015
0.0325
0.0325
0.0325
0.035
2
x = 1.97.
2
2
R
2
A
2
R
2
A
0.1081 ,
0.0295 .
:
0.0786 ,
-
2
,
0.727 .
72.7 %
,
27.3 %
.
.
,
.
-
,
.
.
,
3.4
2.33 (
Fcr ( 0.05, 3, 3)
).
9.28 ,
.
3.4.
.
.
,
3.4,
,
.
«
,
»
«
»,
«
1.5
,
,
.
»
.
,
,
-
,
.
(
–
)
.
.
(3.2).
.
.
n 1
(3.5)
(Mean Square)
MST
SST
n 1
39
-
,
s2 ( x)
n
n 1
2
( x) .
(3.11)
m 1
(3.6)
, ,
-
:
MSA
SSA
m 1
2
A.
m 1
(3.7)
,
,
n
s 2A
(3.12)
n m
,
:
MSR
SSR
n m
n
s R2
«
»
2
R.
n m
(3.13)
,
«
,
»
:
n 1 m 1 (n m) .
(3.14)
-
A
,
:
MSA
.
MSR
F
F
(3.15)
Fcr ( , m 1, n
,
.
Fcr
A
3.4 (
m) .
,
).
20
20 5
20
2
2
0.393 , sR
A
5 1
Fcr ( 0.05, 4, 15) 3.06 . F Fcr ,
s 2A
2
R
0.03933,
F
s 2A s R2
9.99 ,
.
.
3.5.
x
B.
,
,
.
.
Ak ( k 1, m ),
Bi ( i 1, l ),
N,
.
–
n mlN
40
-
,
A
n
B.
ml .
-
:
A
…
…
…
…
…
…
A1
x11
…
x1i
…
x1l
B1
…
Bi
…
Bl
…
Ak
xk1
…
x ki
…
x kl
…
…
…
…
…
Am
x m1
…
xmi
…
x ml
,
.
1.
(
Ak Bi
).
n
xki ,
ml .
:
xk
1 l
xki ,
li 1
x
xi
1 m
xki .
mk 1
(3.16)
1 m l
xki .
n k 1i 1
(3.17)
:
–
(
,
m
l
)
( xki
x )2 ;
(3.18)
( xk
x )2 ;
(3.19)
x)2 ;
(3.20)
SST
k 1i 1
–
A
m
SSA l
k 1
–
B
l
SSB m
( xi
i 1
–
(
41
)
m
l
SSR
( xki
xk
x )2 .
xi
(3.21)
k 1i 1
SST SSA SSB SSR ,
(3.22)
ml 1 (m 1) (l 1) (m 1)(l 1) .
(3.23)
-
:
MSA
–
–
1
m 1
SSA ; MSB
A
B
1
l 1
SSB ; MSR
(3.24)
:
MSA MSR Fcr ( , m 1, ( m 1)(l 1)) ;
MSB MSR Fcr ( , l 1, (m 1)( l 1)) .
(« Ak Bi
,
,
2.
»
1
SSR .
(m 1)(l 1)
).
x (ki1) , x (ki2 ) , … x (kiN ) ,
N
n mlN .
:
x ki
1
N
N
xki( j ) .
(3.25)
j 1
:
xk
1 l
x ki ,
li 1
x
xi
1 m
x ki .
mk 1
(3.26)
1 m l
x ki .
n k 1i 1
(3.27)
:
–
(
,
N m l
SST
j 1 k 1i 1
–
( x (kij )
)
x) 2 ;
(3.28)
A
m
SSA lN
( xk
k 1
42
x)2 ;
(3.29)
–
B
l
SSB mN
x )2 ;
( xi
(3.30)
i 1
–
m
A
B
xk
xi
l
SSAB N
( x ki
x )2 ,
(3.31)
k 1i 1
–
(
N m
l
)
( xki( j ) x ki )2 .
SSR
(3.32)
j 1k 1i 1
SST
SSA SSB SSAB SSR ,
(3.33)
:
Nml 1 (m 1) (l 1) (m 1)(l 1) ml( N 1) .
(3.34)
-
:
MSA
1
m 1
SSA ; MSB
1
l 1
SSB ;
(3.35)
MSAB
1
SSAB ; MSR
(m 1)(l 1)
1
SSR .
ml ( N 1)
:
–
A
MSA MSR
–
B
,
Fcr ( , m 1, ml ( N 1)) ;
,
MSB MSR Fcr ( , l 1, ml ( N 1)) ;
–
MSAB MSR
,
Fcr ( , ( m 1)( l 1), ml ( N 1)) .
-
.
43
:
1.
,
,
-
.
,
.
-
.
,
,
,
.
,
,
.
.
– A1 , A2 , A3 , A4 .
,
(
.
),
:
A1
A2
A3
A4
18.5
24.0
17.2
19.9
18.0
26.3
25.3
24.0
21.2
24.5
20.6
25.2
20.8
24.7
22.9
25.4
19.9
22.6
17.5
20.4
1
Excel
.
,
,
.
1.
(3.3)
(3.4).
.
2.
SST
,
,
.
2
( x)
(
.
-
)
n 20 .
3.
nk
SSA (3.6).
5
,
xk .
44
4.
SSR (3.7)
(
,
-
SST n 1 19 ,
SSA
-
),
.
5.
:
m 1 3,
SSR n m 16 .
MST, MSA, MSR (3.11–3.13).
MSA
.
MSR
F
6.
7.
Fcr ( 0.05, 3, 16)
.7
8.
F
.
,
«
»
-
,
(3.10).
.
,
.
,
-
. 3.1).
. 3.1.
(
45
)
,
. 3.2.
. 3.2.
(
.
«
»
)
,
. 3.2 –
,
(
Excel
«
»
).
,
. 1–8.
,
(3.46 3.23) ,
«
.
»
(3.10)
2
SSA 63.2855
0.394
SST 160.7895
,
39.4 %.
,
60.6 %
.
46
2.
.
.
,
,
.
,
1-
,
,
,
,
?
,
?
,
,
,
.
1,
21-
,
,
,
:
A1
A2
A3
A4
20.6
18.0
19.0
21.3
13.2
22.6
24.6
19.6
23.8
27.1
27.7
18.6
20.8
25.1
17.7
21.5
20.0
21.1
23.9
16.0
2
,
«
2
».
4
B
– 5
, m 4, l
.
A
).
2 , N 5, n
40 .
,
,
1:
1.
x ki (3.25)
.
2.
3.
4.
5.
(3.26)
(3.27).
SST (3.28).
SSA (3.19) SSB(3.20).
SSAB (3.31).
1,
.
SSR (3.32)
6.
,
,
,
5
,
.
47
SST n 1 39 ,
SSA
SSAB (m 1)(l 1) 3 ,
SSR ml( N 1) 32 .
7.
:
m 1 3,
SSB l 1 1 ,
MST, MSA, MSB, MSAB, MSR (3.35).
FA
8.
MSA
, FB
MSR
MSB
, FAB
MSR
MSAB
MSR
FAcr ( 0.05, 3, 32) FBcr ( 0.05, 1, 32) FABcr ( 0.05, 3, 32 ) .
,
.
,
.
,
-
(
)
(
. 3.3).
,
. 3.4.
.
(
,
(
)
).
,
.
,
-
,
–
)
(
(
).
. 3.3.
(
48
)
. 3.4.
(
)
(0.05),
:
,
.
FAB
,
. 3.4,
F = 0.01 < 2.90,
. 3.4,
F)
,
FAcr
F.
,
.
.
49
,
).
,
-
A
,
.
FA
,
5.20
2.90 ,
FAcr
-
,
,
FB
B–
,
.
0.81 FBcr
,
,
4.15 .
,
,
.
1.
.
2.
,
-
?
3.
?
4.
5.
6.
?
.
-
(
).
4.
.
.
.
.
-
.
4.1.
.
(
,
)
.
,
,
,
,
v0 ,
H
v02 / 2 g ,
,
g = 9.81 /c2 –
.
,
,
.
,
.
,
.
-
,
,
.
,
.
.
-
50
.
,
v0 (
-
,
)
H.
x
y
,
x
y,
y
-
,
f (x) .
,
,
,
.
X
Y,
.
4.1.
.
,
,
(
,
,
.),
-
.
,
.
,
.
.
(
-
,
)
-
. .
).
-
.
.
y j , j 1, m .
-
,
,
,
X
Y
.
xi , i 1, k ,
: pij
,
p( xi , y j ) .
P( X
xi )
pij ; P(Y
j
yj)
pij
i
51
P( X
xi Y
yj)
pij / P(Y
y j );
P(Y
yj X
xi ) pij / P( X
xi ).
–
,
( xi ):
(Y)
(X)
M (Y X
xi )
y j P (Y
xi ) .
yj X
(4.1)
j
M (Y X
x)
(x)
( x) ,
Y
X.
.
,
.(
!
-
,
X
Y).
(
)
,
,
,
. .
,
.
«
»
-
,
X
Y.
, . .
)
X
Y
:
( X ,Y ) M [ X
M ( X )][Y
M (Y )]
( X ,Y ) M ( XY ) M ( X ) M (Y ),
(
)
.
.
( X ,Y ) 0 ,
(
).
,
.
r( X ,Y )
( X ,Y )
( X ) (Y )
M ( XY ) M ( X ) M (Y )
.
( X ) (Y )
(4.2)
!),
(
52
.
-
r( X ,Y ) 1 .
4.2.
(X, Y).
(X,Y)
f ( x, y )
lim
x
y
f1 ( x )
P( x
f ( x, y )dy;
x)
x, y Y
x y
x
0
0
Y
M (Y X
X
f 2 ( y)
y)
y
.
f ( x, y )dx .
f ( x, y )
f1 ( x ) f 2 ( y ) .
( y x)
f ( x, y ) / f1 ( x ).
X
y ( y x )dy,
(4.3)
(X ,Y),
f ( x, y )
exp {
1
2
1 r
2
1 2
f ( x, y )
1
2 (1 r
2
x
(
[
)
a1 2
1
)
5
2r(
x a1
1
)(
y a2
: a1 , a 2 ,
,
2
1,
) (
2,
,
y a2 2
r.
,
f ( x, y )dxdy 1;
( x a1 ) 2
1
f 1 ( x)
2
2
1
e
;
f 2 ( y)
1
M [( X
a1 )(Y
1 2
r
0
f1 ( x ) f 2 ( y )
f ( x, y ) .
,
:
53
a2 )]
( y a2 ) 2
1
2
r.
e
2
2
2
;,
2
)
]} .
-
f ( x, y )
X
;
Y–
,
M (X )
a1 ,
M (Y )
a2 ,
(X )
1,
2;
(Y )
r
;
(
).
,
( a1 , a2 ),
«
-
»
1
2.
:
2
x a1
2r
x a1
1
y a2
1
y a2
2
2
const .
2
( r 0 ),
.
-
1=
2,
.
. 4.1
.
. 4.1,
:
8
f(x, y)
0,15
0,1
0,05
0
a1
6
0
4
-
3; a2
5;
1
1;
2; r
2
0.7.
Y
-
4
2
.
,
6
2
X
X
Y(
!).
. 4.1,
)
:
a1
11
0,04
f(x, y)
0,02
3; a2
2;
(
5
2
Y)
Y
2; r
X,
:
1
-3
3
Y
1
0.
-
7
0
5;
M (Y X
x) a2
r
9
-1
y
( x a1 );
x
X
)
. 4.1
M (X Y
y ) a1 r
x
y
54
( y a2 ).
X
r
1
.
-
,
:
y
a2
(
x )( x
y
a1 )
x
a1 (
y )( y
x
a2 ) .
4.3.
.
,
-
X
.
Y.
)
,
X
Y,
-
XOY.
(
)
,
nij ).
(
X
,
Y
X
.
-
xi , i
k
1, k ; Y
m
nij
y j , j 1, m .
n
i 1j 1
(
).
:
m
k
nxi
nij , n yj
nij .
j 1
x
(4.4)
i 1
1 k
nxi xi ,
ni 1
1
n
y
m
n yj y j ,
(4.5)
j 1
Y
y( xi )
1
nxi
X:
m
nij y j , i 1, ..., k .
(4.6)
j 1
)
,
(4.1)
(4.3).
y ( xi ), i 1, ..., k ,
.
rxy
xy
xy
x
55
y
,
(4.7)
x,
y–
,
(4.2).
,
xy
,
1 k m
xi y j nij ;
ni 1j 1
:
1 k
( xi
ni 1
2
x
x)2 nxi ;
1 m
(yj
nj 1
2
y
y)2 n yj .
(4.2),
1
1.
( . .
0,
1.
rxy
),
rxy
,
,
-
r( X ,Y )
,
rxy .
X
rxy
-
,
-
,
Y
rxy
0,
.
X
Tr
rxy
.
-
0.
rxy
H 0 : r( X ,Y )
Y,
0; H 1 : r ( X , Y )
0.
-
n 2
,
1 rxy2
(4.8)
.
t 2.cr ( , k ) ,
.
(
Tr
-
t 2.cr ( , k ) ,
);
k = n – 2,
. 5).
(
(
H0
).
(
,
(4.7)
2
x
,
-
).
,
x
-
:
1 n
1 n
xi ; y
yi ;
ni 1
ni 1
2
1 n 2
2
xi
x ;
y
ni 1
56
xy
1 n
xi yi ;
ni 1
1 n 2
yi
ni 1
2
y .
,
X
,
Y
-
.
4.2.
(
30
-
. 4.1).
4.1
X Y
1
2
3
4
5
6
26
57
36
87
44
35
X Y
77
34
59
25
56
72
7
8
9
10
11
12
19
26
48
33
87
57
X Y
68
67
58
79
16
55
13
14
15
16
17
18
X,
64
98
12
45
5
48
X Y
32
34
78
78
89
35
19
20
21
22
23
24
72
30
18
25
23
78
X Y
42
78
67
57
68
31
25
26
27
28
29
30
25
44
38
52
25
37
68
76
57
38
65
73
0–20, 20–40, 40–
. 4.2.
Y
60, 60–80, 80–100,
.
4.2
X
Y
10
30
50
70
90
30
–
–
3
9
–
50
–
3
3
2
–
70
–
2
1
–
–
90
1
2
–
–
–
nx
4
12
8
3
3
n 30
y ( xi )
75
65
47.5
36. 67
23.33
–
(4.4) (4.6)
x
ny
10
–
–
–
3
1
1
7
7
14
1
ny ,
nx
42.67 , y 54.67
,
y ( xi ) .
,
-
,
.
:
xy 1980;
:
x 43.13; y
57.73; xy
2
x
2
y
519.56;
2120.5;
2
x
57
364.89; rxy
,
531.05;
2
y
0.809.
360.93; rxy
0.844.
4.4.
,
,
(X, Y)
(
. 4.2,
(
).
!)
-
.
,
,
.
:
Y
?
(
X,
3).
–
-
,
,
,
X ( xi , i
X
.
,
2
y
2
y
( yi
y ( xi ) –
(3.5)
1
n
Y
-
1, 2, ..., k ).
Y
m
y )2 n yj
(4.9)
y ) 2 n xi ,
(4.10)
(yj
j 1
1 k
( yi
ni 1
).
(3.6).
Y,
X.
Y
-
(3.10):
2
yx
2
y
2
y
.
(4.11)
(
.
yx
=0
0
,
Y
X.
rxy
yx
=1
yx
1(
rxy ,
).
58
2
yx
yx
)
1,
-
4.1.
2
y
2
yx
364 .89
0.664 ,
2
y
(4.10), (4.11)
y x
242 .11 ,
0 .815 .
,
,
,
.
4.5.
Y
-
X 1 , X 2 , ..., X k ,
A
r11
r12
... r1k r1 y
r21
r22
... r2 k r2 y
...
ry1
...
ry 2
... ... ...
... ryk ryy
,
(4.12)
rij
riy
A
rxi , y .
,
-
rij r ji , riy
1.
X 1 , X 2 , ..., X k
R
D det A ,
rx i , x j ,
D yy
1
ryi .
,
Y
D
,
D yy
(4.13)
,
.
4.3.
:
X1
X2
X3
Y
X1
X2
X3
Y
1
0.3
0.7
0.3
1
0.4
0.5
0.4
0.7
0.5
1
0.2
0.1
59
0.2
0.1
1
.
D det A 0.162 ,
(4.13) R 0.757 .
,
D yy
0.38 .
-
,
,
-
4.6.
.
(
,
,
. .),
,
-
.
(
.
,
,
. .).
:
.
,
.
,
,
«
i
»).
1, n .
xi .
,
,
(
»).
(4.7).
«
y
yi .
,
i.
xi
i 1, n
.
.
yi
xi ,
-
,
.
(4.8).
4.4.
11
,
-
:
xi
1 2 3 4 5 6 7
8
9 10 11
yi
1 2 3 5 4 9 8 11 6
7
10
.
-
?
0.01.
60
rxy
:
Tr
0.818 ,
4.27 ,
Tr
t 2. cr ( 0.01, 9 )
t2. cr ,
,
3.25 .
-
.
,
-
,
,
yi :
xi
n
6
rxy
i 1
1
(4.14)
4.3
6(1 1 9 1 9 9
11 120
1
.
n( n 2 1)
,
rxy
yi ) 2
( xi
9 1)
4.7.
1
240
11 120
9
11
0.818 .
.
(
)
,
(
)
-
.
.
»
«
-
».
X (t )
t
,
.
.
,
,
.
.
.
.
,
,
,
-
.
.
,
,
,
. .
,
.
,
,
,
.
.
,
.
,
,
,
61
-
,
.
.
,
.
(
x
,
.
-
),
,
.
«
»,
.
«
»
»
«
.
t
,
: X (t
t)
X (t ) .
–
–
.
-
.
x(t )
– xi , i
,
n
1, n ,
,
, . .
ti
(
,
const .
)
.
ti
1
.
,
-
–
.
,
,
:
x1
x2
x
…
-
x
1
x1
…
x
x2
2
…
…
(4.7).
2
:
–
xn
,
,
x
xn
,
-
,
x1 ,
-
x1 , x2 , ..., xn ,
,
-
x
xn –
».
x 2 ,…,
«
1
xn .
,
,
r.
(4.7)
,
1
r
n
n
xi
x 1,n
x
i 1
i
x
1, n
(4.15)
x 1, n
x
62
1, n
n
1
xi x
n
r
x
i
1,n
x 1,n
i 1
.
x 1,n
(4.16)
1,n
x
,
x
x
-
.
1, n .
,
2
x
,
2
x2
x ,
(4.16)
n
1
xi x
n
r
i
x
2
i 1
x
2
x
(
.
2
(4.17)
,
-
)
0.
n/3
n/4.
(4.15)–(4.17)
,
r0
. .
.
,
,
1,
-
–
,
,
,
.
:
1.
2.
«
»
.
r
,
,
(
1)
r0
r1 .
-
r.
,
3.
(
,
,
,
r ,
)
.
4.
,
,
4.5.
.
,
,
F10 .7 ,
.
11-
. 4.2
(
F10 .7 ,
10)
).
63
53
( 1948
2000
.
2500
F10.7
10
2000
1500
1000
500
2000
1996
1992
1988
1984
1980
1976
1972
1968
1964
1960
1956
1952
1948
0
. 4.2.
1948–2000
.
. 4.3
:
(4.17) –
(4.16) –
(2).
,
. 4.2)
(1),
(
.
,
,
.
,
r
1
0,8
2
0,6
1
0,4
0,2
0
-0,2
1
2
3
4
5
6
7
8
9
-0,4
-0,6
-0,8
-1
. 4.3.
64
10
11
12
13
14
15
16
:
1.
. 4.4.
Excel
4.2,
-
1
.
nx , n y
.
,
(4.5)
.
(4.6).
Y,
,
(4.9) (4.10)
(4.11)
-
(
-
.
xy
rxy
).
,
?
(
-
).
3.
»
,
10
70
70
70
90
30
50
50
50
70
70
70
70
70
70
70
70
70
50
30
30
30
50
50
50
70
70
:
:
70
30
30
50
90
10
30
30
X,
;
Y
,
,
nij .
,
,
,
3.
.
,
.
65
-
2.
30
X Y
1
2
3
4
5
6
7
8
9
10
26
57
36
87
44
35
19
26
48
33
77
34
59
25
56
72
68
67
58
79
:
X Y
11
12
13
14
15
16
17
18
19
20
87
57
64
98
12
45
5
48
72
30
16
55
32
34
78
78
89
35
42
78
X Y
21
22
23
24
25
26
27
28
29
30
18
25
23
78
25
44
38
52
25
37
67
57
68
31
68
76
57
38
65
73
X: 0–2, 2–4, 4–6, 6–8, 8–10;
22, 22–28, 28–34, 34–40;
.
,
1.
?
Y: 10–16, 16–
-
?
3.
-
Y
X1 , X 2 , X 3 :
X1
X2
X3
Y
4.9
5.3
4.6
5.3
4.8
5.3
4.7
5.3
5.3
5.3
5.3
5.3
4.9
5.5
4.9
5.3
5.4
5.3
5.0
5.0
3.0
3.1
3.4
2.9
3.0
3.1
3.5
2.9
2.8
3.2
3.4
3.3
3.5
2.8
2.9
2.7
2.8
3.0
3.2
2.6
1.5
2.5
0.9
2.2
1.5
2.7
1.1
2.8
2.9
2.0
2.2
1.6
1.4
2.4
2.2
2.5
2.9
2.3
2.1
2.5
9.2
8.6
10.4
8.0
8.5
8.6
10.2
7.9
7.2
9.6
9.7
9.8
10.5
8.2
7.9
7.7
7.8
8.1
8.9
6.8
66
,
-
.
3
(
).
-
(4.13).
.
(
).
4.
Excel
4.3
:
(4.14).
5.
1948–2000 . (
F10.7
1744
1778
1282
1189
854
739
702
950
1846
2327
2317
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1
4.4):
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
F10.7
2097
1621
1054
904
812
726
764
1021
1432
1493
1512
F10.7
1562
1185
1208
934
865
761
734
869
1436
1920
1985
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
F10.7
2026
1753
1196
1011
747
741
852
1409
2137
1896
2082
1992
1993
1994
1995
1996
1997
1998
1999
2000
F10.7
1507
1099
852
772
720
810
1179
1537
1798
16.
5
.
,
1778
B2
C3
. .
1744,
= B2
,
B3 –
B.
C
1 537.
.
,
B2
.
1-
(0.7785) –
.
67
-
.
. 4.2
. 4.3,
1).
1.
?
-
2.
?
3.
?
4.
?
5.
6.
«
».
-
?
5.
.
.
.
-
.
5.1.
,
,
(
).
-
,
:
x
y f (x)
x0
y0
x1
y1
…
…
x2
y2
x
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+1
+1
+1
y1
2
+1
+1
–1
–1
+1
+1
y2
3
+1
–1
+1
–1
+1
+1
4
+1
+1
+1
+1
+1
+1
y3
y4
92
1 2
5
x12
x0,
+1.
(
.
.
-
)
,
,
,
.
,
.
,
,
,
,
0.
2k
.
.
,
, . .
,
,
2, . .
n.
,
k
2k
,
,
-
.
,
,
,
.
k
2
,
n,
,
,
n.
2
3
n = 3.
.
.
n = 23 = 8
,
.
2
2
2
. 6.4.
3
,
,
,
.
,
,
,
.
,
.
,
,
,
,
.
93
,
-
6.4
-
–1
y1
y11
y2
y12
y3
y13
+1
+1
y21
y12
y23
+1
–1
+1
y31
y32
y33
+1
–1
–1
–1
y41
y42
y43
+1
+1
–1
–1
+1
y51
y52
y53
–1
+1
–1
+1
–1
–1
y61
y62
y63
–1
+1
+1
–1
–1
+1
–1
y71
y72
y73
+1
+1
+1
+1
+1
+1
+1
y81
y82
y83
0
1
2
3
1 2
1 3
2 3
1
+1
–1
–1
–1
+1
+1
+1
2
+1
+1
–1
–1
–1
–1
3
+1
–1
+1
–1
–1
4
+1
+1
+1
–1
5
+1
–1
–1
6
+1
+1
7
+1
8
+1
1 2 3
y
y1
y2
y3
y4
y5
y6
y7
y8
j(
-
)
m
.
yj1, yj2, …, yjm
,
1 m
y ji .
mi 1
yj
(6.9)
,
,
. .
–
.
.
,
2
3
-
3
6
:
2
5
1
7
4
8
4
1
8
5
3
2
7
6
,
3,
–
6
. .
1
(j = 1,…, n)
-
4,
–
. .
j.
,
j-
(
94
. 6.4).
6.7.
m
m
2
s yj
i 1
y ji
yj
m 1
2
(6.10)
.
.
2
s yj
max
, . .
Gp
s2 y j
n
max
,
(6.11)
2
j 1
s yj
,
.
Gp
1/n ,
(
n –
).
G
(
. 8),
f1
-
f2 (
): f1 = m – 1; f2 = n.
f1
),
(
f2
)
.
Gp < G ,
(
1– )
.
j
-
.
,
(
,
,
-
.).
,
s 2y ,
.
( . .
95
-
s 2y
)
-
:
n
s 2y
n m
1
n m 1
n–
m–
yji –
yj –
y ji
j 1i 1
j 1
2
yj
s2 y j
,
n
(6.12)
(
);
(
)
;
i
j
;
j
,
-
(6.9).
6.8.
,
-
,
.
,
(6.6)
.
,
:
y
b0
b1 x1
b2 x2 .
n
yj
2
yj
min .
b
i
j 1
n
b1
2
yj
b0
b1
1j
b2
2j
1j
0;
yj
b0
b1
1j
b2
2j
2j
0;
j 1
n
b2
2
j 1
n
b0
2
yj
b0
b1
1j
b2
0.
2j
j 1
,
n
n
yj
j 1
1j
b0
n
1j
j 1
n
2
1j
b1
x
j 1
96
b2
1j
j 1
2j
0;
n
n
yj
n
b0
2j
j 1
n
b1
2j
1j
j 1
2j
j 1
n
yj
0;
j 1
n
n
b0 n b1
j 1
2
2j
b2
b2
1j
j 1
2j
0.
j 1
:
–(
k
)
–(
k
)
0;
xij
j 1
x 2 ij
n;
j 1
k
–(
)
x ji x
0.
i
i 1
n
yj
1j
b1n
0;
yj
2j
b2 n
0;
j 1
n
j 1
n
j 1
yj
0.
b0n
:
yj
yj
1j
j 1
b1
n
n
n
b2
;
n
yj
2j
j 1
b0
;
n
j 1
n
.
,
(6.6)
y
.
,
-
,
(6.7)
(
b0
br , p
1
n
,
)
. .:
bi
1
n
n
j 1
1
n
x0 j y j ,
n
j 1
xij y j , i =1, … ,k;
(6.13)
n
x rj x pj y j , r
p, r 1,..., k , p 1, ..., k
. .,
j 1
.
b0
,
,
x0 ,
+1.
97
-
,
,
)
,
(6.13)
-
.
(
)
.
-
,
.
,
–
,
-
.
,
.
,
,
-
,
,
.
(
),
-
.
,
.
,
.
6.1.
2
2, . .
y1 = 6, y2 = 3, y3 = 4, y4 = 7.
22 :
0
1
2
+1
+1
+1
+1
–1
+1
–1
+1
–1
–1
+1
+1
,
1 2
~
y
y
+1
–1
–1
+1
-
6
3
4
7
y
4,5
4,5
5,5
5,5
y y
6
3
4
7
0
0
0
0
,
-
x0 ,
.
~
y
b0
b1
(6.13)
b1 x1 b2 x2 :
b0
1
6 3 4 7 5;
4
1
6 3 4 7 0;
4
98
b2
~
y
~
y
1
4
6 3 4 7
0,5 .
0,5 x2 .
5 0 x1
.
~
y,
y
,
.
,
y
b0
b1 x1 b2 x2
b12 x1 x2 .
.
(6.13):
b12
1
6 3 4 7 1,5.
4
y 5 0 x1 0,5 x2 1,5 x1 x2 .
b12
y ).
,
)
(
,
,
,
.
(
,
.
,
,
,
.
6.9.
.
,
(6.13).
-
.
t
:
.
(
)
-
.
(
)
-
.
tk
-
bk
s
:
tk
bk
s
99
.
t cr ,
tk
,
bk
.
bk
,
tcr
s
-
bk
t cr s
.
-
b = t cr s
.
tcr
. 5).
n–
(
n(m – 1),
, bk
.
-
(n = 2k)…, m –
b ),
bk
.
tk
t cr (
;
tk
.
t cr ,
,
-
bk
,
s
s 2y (6.12)
s 2y
s
m n
.
(6.14)
,
.
-
.
6.10.
:
F
.
<F
,
–
,
F
s2
,
s 2y
F
s 2y –
s2
,
–
,
(6.15)
(6.12),
-
:
100
s
m
n
n r
j 1
2
n–
m–
r–
yj–
2
yj
yj ,
(6.16)
;
;
;
,
j-
;
yj–
(
j-
-
(6.9)).
F
. 7)
(
k1= n – r
k2 = n(m – 1).
k1
(6.15) –
s2 ,
k2 –
s 2y .
(6.15) –
,
.
,
;
-
–
.
,
,
,
.
,
,
.
.
-
,
.
,
.
,
).
.
,
«
»
,
,
»–
zi
.
xi
101
-
(6.5).
-
,
.
,
,
,
,
.
6.2.
3
2,
y
.
),
2
); z2 –
,
2
: z1 –
( ); z3 –
2
(
).
. 6.5.
6.5
2
z1
)
0,04
0,02
0,06
0,02
z2 )
z3
180
120
300
60
2
)
5
3
8
2
,
-
,
.
:
(6.5):
1.
xi
zi0
zi
,
i
zi0 –
(
x1
),
z1 0,04
,
0,02
x2
i
–
z2 180
,
120
.
x3
z3 5
.
3
2.
.
. 6.6.
102
(6.9)
-
6.6
y1
y2
y3
y4
y5
–1
9,38
8,78
9,38
8,79
9,41 9,148
–1
–1
11,69
11,83
11,97
11,41
11,81 11,742
–1
+1
–1
10,44
10,19
10,59
10,28
10,34 10,368
+1
+1
+1
–1
13,35
13,02
13,34
13,05
13,11 13,174
5
+1
–1
–1
+1
11,12
11,01
10,89
11,22
11,19 11,086
6
+1
+1
–1
+1
14,57
13,93
14,35
14,50
14,46 14,362
7
+1
–1
+1
+1
12,66
12,66
12,57
12,73
12,50 12,624
8
+1
+1
+1
+1
15,69
15,97
16,09
15,75
15,50 15,800
0
1
2
3
1
+1
–1
–1
2
+1
+1
3
+1
4
3.
y
(6.10)
:
s2(y1) = [(9,38 – 9,148)2 + (8,78 – 9,148)2 + (9,38 – 9,148)2 +
+ (8,79 – 9,148)2 + (9,41 – 9,148)2]/4 = 0,1100;
s2(y2) = [(11,69 – 11,742)2 + (11,83 – 11,742)2 + (11,97 – 11,742)2 +
+ (11,41 – 11,742)2 + (11,81 – 11,742)2]/4 = 0,0443.
s2(y3) = 0,0237; s2(y4) = 0,0254; s2(y5) = 0,0185;s2(y6) = 0,0647;
s2(y7) = 0,0080; s2(y8) = 0,0544.
(6.11),
:
Gp = 0,11/(0,1100 + 0,0443 + 0,0237 + 0,0254 + 0,0185 + 0,0647 + 0,0080 + 0,0544);
Gp = 0,3151.
(
. 8)
f1 = 5 – 1 = 4; f2 = 8,
= 0,05
= 0,3910; G > Gp, . .
, . .
.
(6.12)
-
s 2y
8.
103
0,043628 .
4.
y (
. 6.7).
6.7
y
y
-
0
1
2
3
1
+1
–1
–1
2
+1
+1
3
+1
4
1 2 3
y
y
1 2
1 3
2 3
–1
+1
+1
+1
–1
9,148
9,0545
–1
–1
–1
–1
+1
+1
11,742
11,7545
–1
+1
–1
–1
+1
–1
+1
10,368
10,4615
+1
+1
+1
–1
+1
–1
–1
–1
13,174
13,1615
5
+1
–1
–1
+1
+1
–1
–1
+1
11,086
11,1515
6
+1
+1
–1
+1
–1
+1
–1
–1
14,362
14,3775
7
+1
–1
+1
+1
–1
–1
+1
–1
12,624
12,5585
8
+1
+1
+1
+1
+1
+1
+1
+1
15,800
15,7845
5.
(6.13):
b0 = (+1·9,148 + 1·11,742 + 1·10,368 + 1·13,174 + 1·11,086 + 1·14,362 +
+ 1·12,624 + 1·15,8)/8;
b0 = 12,288;
b1 = (–1·9,148 + 1·11,742 – 1·10,368 + 1·13,174 – 1·11,086 + 1·14,362 –
– 1·12,624 + 1·15,8)/8;
b1 = 1,4815;
b2 = (–1·9,148 – 1·11,742 + 1·10,368 + 1·13,174 –1·11,086 – 1·14,362 +
+ 1·12,624 + 1·15,8)/8;
b2 = 0,7035.
b3 = 1,18; b12 = 0,014; b13 = 0,1315; b23 = 0,0405; b123 = –0,039.
6.
.
S
(6.14).
S y2
S
0,043628
8 5
m n
0,033026.
= 0,05
(
f
n m 1
8 4
. 5)
32
104
-
tcr
2,04 .
,
2,04 0,033026 0,067372.
b t cr S
-
,
b23
b123
,
0,067372.
,
b12,
,
,
.
,
y 12,288 1,4815 x1 0,7035 x2 1,18 x3 0,1315 x1 x3 .
7.
.
,
S
F
(6.16).
yj,
2
-
j,
. 6.7.
y1 12,288 1,4815
y2
0,7035
12,288 1,4815 1 0,7035
y3
y4
1
12,288 1,4815
13,1615 ; y5
1
1
1
1,18
1,18
1
0,7035 1 1,18
11,1515 ; y6
1
14,3775 ; y7
0,1315 1 9,0545 ;
0,1315
1
11,7545 ;
0,1315 1 10,4615 .
1
12,5585 ; y8 15,7845.
:
S
2
m
n
n r
j 1
2
yj
yj
5
(8 5)
[(9,0545 – 9,148)2 + (11,7545 – 11,742)2 +
+(10,4615 – 10,368)2 + (13,1615 – 13,174)2 + (11,1515 – 11,086)2 + (14,3775 –
–14,362)2 + (12,5585 – 12,624)2 + (15,7845 – 15,8)2] = 0,044763.
F
F
0,05
f2 = n(m – 1) = 8 4 = 32 : F
s2
s 2y
0,044763
1,026 .
0,043628
F
(
. 7)
f1 = n – r = 8 – 5 = 3
(0,05; 3; 32) = 2, 901.
105
F
.
= 1,026<F
= 2, 901,
-
8.
:
y 12,288 1,4815 x1 0,7035 x2 1,18 x3 0,1315 x1 x3 .
,
1
–
,
.
(
)
2
3
–
–
(
1 3
:
.
-
)
–
.
,
,
(
)
.
9.
,
(6.5)
-
zi :
xi
y 12,288 1,4815x1 0,7035x2 1,18x3 0,1315x1x3 12,288
1,4815
z1 0,04
z 180
z 5
z 0,04 z3 5
.
0,1315 1
1,18 3
0,7035 2
0,02
3
3
120
0,02
,
-
:
y
6,7414 63,1167 z1 0,0059 z2
0,3057 z3 1,8858 z1 z3 .
:
1.
6.2.
SExcel.
1
(
Excel
A2:F9
. 6.3).
(
F2:F9).
106
. 6.3.
,
,
G2:G9.
,
.
. 8 (
G13).
G14,
, . . 8.
G10
Excel
. 6.7 (
y (
. 6.4,
J17:K24
).
(6.13)
A27:H27.
-
A17:I24),
-
,
-
G29
S
(6.14),
.
(
tcr
. 5)
-
2,04
b tcr S
.
G31.
b
,
107
b
A34:H34).
. 6.4.
.
-
yj.
J17:J24
,
(
js2
A34:H34)
( A17:H17
A24:H24).
(6.16)
,
-
,
,
,
,
(
K17:K24).
.
F
J29,
F
K25.
(6.15)
.7(
-
J32).
F = 1,026 < F
.
2.
(U –
= 2, 901,
-
(z1), I –
108
(z2), T –
(z3))
.
-
: U = 30 , I = 18 , T = 220 °C.
2
3
.
. 6.8.
6.8
z1 = U,
z2 = I,
30
2
32
28
z3 = T,
220
20
240
200
18
1
19
17
5
. 9.
, yi –
,
.
:
1.
2.
.
.
3.
4.
5.
.
6.
.
.
.
,
,
.
,
.
7.
8.
.
.
S Excel
2
1.
1.
?
.
2.
3.
4.
5.
6.
?
.
.
?
?
?
109
-
7.
?
8.
?
?
9.
-
10.
-
?
?
11.
12.
?
,
yi
,
,
,
?
13.
-
?
F
?
14.
?
7.
.
-
.
.
7.1.
,
(n > 6),
.
2
-
n
7
7
2 = 128
,
.
.
,
-
(
,
7
N
1 C72
C73 C74
C75 C76 1 128 .
b0
b2 x2
)
,
y
b1 x1
,
bk xk ,
1+7 = 8
;
1 + 7 + 21 =
29.
,
2
n
.
,
,
«
»
110
-
,
-
.
.
,
(
-
).
,
-
,
.
.
,
.
,
,
-
.
(6.13)
,
.
23,
2, 3, 5, 8,
. 7.1,
:
.
7.1
x1
–1
+1
–1
+1
1
2
3
4
x2
–1
–1
+1
+1
x3
–1
–1
–1
–1
x1
–1
+1
–1
+1
5
6
7
8
x2
–1
–1
+1
+1
x3
+1
+1
+1
+1
,
x2
x1
,
2
-1
-
2
=2 .
x3
x3
x1 x 2 ,
(7.1)
x3
x1 x 2 .
(7.2)
–
.
(
2
2 (
. 7.2),
x3
,
,
)
,
x1x2.
111
-
7. 2
x1
1 (2)
2 (3)
3 (5)
4 (8)
x2
x3
+1
–1
–1
+1
x1
–1
+1
–1
+1
–1
–1
+1
+1
1
2
3
4
x2
+1
–1
–1
+1
,
x3
–1
+1
–1
+1
. 7.1.
22
,
x1x2
–1
–1
+1
+1
-
x3.
.
(7.1)
(7.2)
-
,
.
,
,
,
-
.
2k-p,
p–
.
k
2.
,
p=1
,
(1/2-
)
26-1 n = 26-1 = 32,
-
.
p=1
6-2
6-2
2 n = 2 = 16
).
p = 2
(1/47.2.
,
,
.
,
.
,
-
,
,
.
,
.
2k-p
:
1.
.
2.
l=k–p
2l
, . .
1, 2, …, l.
3.
2k-p.
112
2l ,
l+1,
l+2,
…,
k,
p = k – l.
,
,
.
.
:
1.
y
. .
k=3
b0
b1 x1
b2 x2
b3 x3
b12 x1 x2
k=3
b13 x1 x3
8
:
b23 x 2 x3
.
p = 1, . .
2.
1
22 (
)(
b123 x1 x 2 x3 ,
n = 23-1 = 4
.
2, . . l = k – p = 2.
-
. 7.3).
7.3
1
2
3
4
3.
x3 = x1x2. . .
1
2
–1
+1
–1
+1
–1
–1
+1
+1
x3 = x1x2
+1
–1
–1
+1
,
3
1 2.
,
. 7.3
(
,
-
. 7.4).
7.4
1
2
3
4
0
1
2
3
+1
+1
+1
+1
–1
+1
–1
+1
–1
–1
+1
+1
+1
–1
–1
+1
8,
,
7,
2–
1 2
1 3
2 3
1 2 3
+1
–1
–1
+1
–1
–1
+1
+1
–1
+1
–1
+1
+1
+1
+1
+1
1
3–
6,
4–
5.
,
.
-
,
.
113
,
b0 , b1 , b2 , b3 ,
,
:
y
b0
b3 x3 ,
b1 x1 b2 x2
i,
(
).
,
(8)
(4).
-
,
-
.
«
.
»
,
.
:
23,
2–
13,
3–
b0 =
0+
12,
123,
0–
b1 =
123 (
1+
1
.
23 ,
. 7.4).
b2 =
2+
13,
b3 =
3+
12,
–
.
,
bi
1
n
,
-
n
j 1
xij y j .
,
,
.
,
x4
24-1
,
, . . x4
x1 x 2 x3 .
,
x1 x 2 , x4
,
x1 x 3 , x 4
.
,
(
x2 x 3
,
-
).
7.1. (
[5])
-
.
25-2
114
.
-
,
.
5:
4
.
: z1 –
3
,
,
3
(
. 7.1.
3
,
3
; z3 –
; z4 –
,%
,
; z2 –
; z5 –
. 7.1).
(z1, ..., z5)
(y)
. 7.5.
7.5
z1,
(
)
3
z2,
5250
4000
6500
1250
3
3
z3,
3900
3100
4700
800
3
z4,
2650
1750
3500
900
z5, %
1100
700
1500
400
74
50
98
24
(6.5):
zi0
zi
xi
,
(7.3)
i
zi0 –
x1
z1 5250
, x2
1250
–
zi 2650
, x4
900
(
z2 3900
, x3
800
),
:
z i 74
.
24
i
zi 1100
, x5
400
zi
,
,
i
= –1.
115
i
= +1,
-
25 = 32
, . .
1/4-
.
25-2,
-
2
x4 = x1x2, x5 = x1x2x3.
3
2 = 8.
,
»
.
,
(
.
. 7.6
)
-
23,
–
-
(
).
7.6
3
2
1
0
1
2
3
4
5
+1
+1
+1
+1
+1
+1
+1
+1
+1
–1
+1
–1
+1
–1
+1
–1
+1
+1
–1
–1
+1
+1
–1
–1
+1
+1
+1
+1
–1
–1
–1
–1
+1
–1
–1
+1
+1
–1
–1
+1
+1
–1
–1
+1
–1
+1
+1
–1
2
yi
y1
y2
yi
–0,6
0,1
0,6
–0,1
0,6
–0,2
0,1
0,3
–0,5
0,5
0,4
0,2
0,2
–0,2
0,2
0,3
–0,55
0,30
0,50
0,05
0,40
–0,20
0,15
0,30
–0,3750
0,2625
0,5375
–0,1250
0,2250
–0,1625
0,1125
0,4750
,
-
6:
1.
:
yj
y j1
y j 2 ...
yjm
m
m=2–
.
y1
( 0,6) ( 0,5)
2
,
,
0,55.
(
2.
(
m
( y ji
2
s yj
y j )2
i 1
m 1
;
2
s y1
)
.
. 7.6).
:
( 0,6 ( 0,55))2 ( 0,5 ( 0,55))2
2 1
116
0,005.
,
s 2 y 2 = 0,08;
s 2 y5 = 0,08;
s 2 y3 = 0,02;
s 2 y6 = 0;
s 2 y7 = 0,005;
(
8
s 2 y 4 = 0,045;
)
s 2 y8 = 0.
:
s 2 y j = 0,005 + 0,08 + 0,02 + 0,045 + 0,08 + 0,005 = 0,235.
j 1
3.
:
Gp
s 2 yi
n
max
s 2 yi
0,08
0,235
0,34 .
i 1
.8
G ( ; f1; f2).
G (0,05; 1; 8) = 0,6798.
f2 = n = 8
= 0,05, f1 = m –1;
Gp < G ,
-
.
4.
:
n
j 1
b0
y j x0 j
n
0,55 0,3 0,5 0,05 0,4 0,2 0,15 0,3
8
0,11875;
0,55 0,3 0,5 0,05 0,4 0,2 0,15 0,3
8
0,00625;
n
j 1
b1
y j x1 j
n
n
b2
j 1
y j x2 j
n
0,55 0,3 0,5 0,05 0,4 0,2 0,15 0,3
8
0,13125;
0,55 0,3 0,5 0,05 0,4 0,2 0,15 0,3
8
0,04375;
0,55 0,3 0,5 0,05 0,4 0,2 0,15 0,3
8
0,06875;
n
b3
j 1
y j x3 j
n
n
b4
j 1
y j x4 j
n
n
b5
j 1
y j x5 j
n
5.
0,55 0,3 0,5 0,05 0,4 0,2 0,15 0,3
0,256.25 .
8
.
(
):
117
n
1
n m 1
s 2y
n
m
j 1i 1
y ji
yj
j 1
2
s2 y j
0,235
0,02938.
8
n
:
S 2y
S
0,02938
2 8
m n
0,04285.
tcr
n(m –1) = 8·1 = 8
-
= 0,05
.
tcr (0,05;8)=2,31.
-
:
bj
b3 = 0,044 < 0,099
,
,
2,31 0,04285 0,099 .
t cr S
bj
b1 = 0,006 < 0,099;
,
b4 = 0,069 < 0,099.
.
y = 0,119 – 0,131x2 – 0,256x5.
. 7.6.
yi
6.
.
:
s
m
n
n r
j 1
2
2
~
yj
yj .
r –
.
m = 2; n = 8; r = 3
s2
2
( 0,55 0,375) 2
8 3
(0,4 0,225)2
(0,3 0,2625) 2 (0,5 0,5375) 2 (0,05 0,125) 2
( 0,2 0,1625)2
(0,15 0,1125) 2
F
118
(0,3 0,475) 2 ] 0,0512.
S2
s 2y
F
0,0512
1,7427 .
0,02938
F
= 0,05
k2 = n(m – 1) = 8·1 = 8.
k1 = m(n – r) = 2(8 – 3) = 10
k1
s 2y .
s ,
k2 –
F
(0,05; 10; 8) = 3,07.
.
F
< F
,
(7.3).
z2 3900
zi 74
,
x5
800
24
y = 0,119 – 0,131x2 – 0,256x5:
x2
y 0,119 0,131
z2 3900
800
zi 74
.
24
0,256
ó 1,547 0,00016z2 0,0107z5 .
7.3.
,
-
.
?
-
.
. 7.4.
.
1 2.
3
,
,
.
.
.
.
,
,
.
1 2,
3
3
2
3
3,
12
1 2 1.
,
-
1 2 3.
1 2.
xi 2
,
,
1 2 3
119
1.
1,
.
1,
2
1 2 3
1
2 3,
1 2,
3
0
. .
2 3.
1
1,
1 3,
2
3,
2,
1
2 3
,
1 2 3.
0
:
b0 =
0+
123,
b1 =
1+
23,
b2 =
2+
13,
b3 =
,
3+
12.
,
.
,
,
4-1
.
2
4
1 2 3 4
4
1 ),
4.
(
,
1,
1 2 4
1 2
1 2 3
-
3.
.
-
.
1 2 3,
4
,
,
4
–
. 7.7).
1 2
7.7
1
2
3
4
5
6
7
8
0
1
2
3
+1
+1
+1
+1
+1
+1
+1
+1
–1
+1
–1
+1
–1
+1
–1
+1
–1
–1
+1
+1
–1
–1
+1
+1
–1
–1
–1
–1
+1
+1
+1
+1
4=
2 3
–1
+1
+1
–1
+1
–1
–1
+1
2
4
:
1
2 3 4
b1
1
+
234;
2
1 3 4
b2
2
+
134;
120
1
x5 = 1
+1
–1
–1
+1
+1
–1
–1
+1
1 2 3 4
1.
2
3
1 2 4
b3
3
+
124;
4
1 2 3
b4
4
+
123;
1 2.
4
2
4
,
1.
1 2 4
1 2 4
:
1
2 4
b1
1
+
24;
2
1 4
b2
2
+
14;
b3
1 2 3 4
3
b4
1 2
4
3
4
+
+
1234;
12.
.
,
.
,
.
,
4=
1
2 3.
.
4
-
,
1 2
,
.
,
, . .
-
,
.
,
.
7.4.
,
,
(
-
).
,
,
.
,
,
:
1
1 2 4
5-2
1
4
1 2
2
5
1 2 3
1 2 3 5.
;
,
,
121
-
2
1=
,
1
2
1
2
3 4 5
3 4 5.
=
:
1 2 4 ,1
1 2 4=
1
1
1 2 3 5
1 2 3
:
5=
3 4 5
.
3 4 5.
:
x1:
1
2 4
=
2 3 5= 1 3 4 5;
x2:
2
1 4
=
1 3 5=
x3:
3
1 2 3 4=
x4:
4
1 2
x5:
5
1 2 4 5=
=
2 3 4 5;
1 2 5=
1 2 3 4 5=
1 2 3=
4 5
;
3 5;
3 4.
b1
1
24
+
235+
1345;
b2
2
14
+
135+
2345;
b3
3
1234
b4
4
12
b5
5
1245
+
+
+
125+
45;
12345+
35;
123+
34.
,
.
,
.
.
,
-
1/4.
7
.
1/427-2,
.
(
1/47
,
2,
128
29
32
– 1,
–7
– 21).
,
,
.
x1, x2, x3, x4, x5
.
,
,
:
x6 = x1x2x3x4;
122
-
x7 = x1x2x3x4x5.
,
1 = x1x2x3x4x5x7
:
1 = x1x2x3x4 x6 .
,
1 = x1x2x3x4x5x7 = x1x2x3x4 x6 = x5x6x7.
: 1 = x5x6x7, . .
:
x1:
1=
2 3 4 5 7
x2:
2
1 3
4 5
7=
1 3
x3:
3
1 2
4 5
7=
1 2 4 6
x4:
4
1 2 3 5
7=
1 2 3 6=
4 5 6 7
2 3 4 6=
1 5
6 7;
4 6=
2 5 6 7;
=
3 5 6 7;
. .
b1
1 + 23457
+
2346+
1567;
b2
2
13457
+
1346+
2567;
b3
3
12457
+
1246+
3567;
b4
4
12357
+
1236+
4567
. .
,
,
,
.
,
,
:
x1x2 = x3x4x5x7 = x3x4 x6 = x1 x2x5x6x7.
27-2
,
,
7
2 .
,
(6.7).
k
2.
k=5
1/4-
k = 2, 3 4
1/2-
k=6
.
2k- 1,
-
k = 7, k = 8
2k- 2 .
1/4-
,
,
,
-
,
.
,
,
,
,
123
-
,
.
:
1.
2
,
6
.
:
V
5-2
t,
2 .
,
6.
,
z1, z2, z3
-
(U –
(z1), I –
(z2), T –
(z4) t –
.
. 7.8.
(z3), V –
-
(z5))
5-2
2 .
7.8
z1 = U,
z2 = I,
30
2
32
28
. 7.9.
z3 = T,
220
20
240
200
18
1
19
17
x4
z4 = V,
z5 = t,
10
3
13
7
80
15
95
65
x5
.
7.9
0
1
2
3
1
+1
–1
–1
2
+1 +1
3
+1
y1
y2
y3
4
5
–1
–
–
7,87
7,41
8,12
–1
–1
–
–
16,23
15,42
15,64
–1
+1
–1
–
–
6,55
5,89
6,26
4
+1 +1
+1
–1
–
–
8,49
9,21
8,79
5
+1
–1
–1
+1
–
–
20,16
19,84
20,59
6
+1 +1
–1
+1
–
–
28,34
27,59
28,16
7
+1
–1
+1
+1
–
–
8,85
8,20
9,64
8
+1 +1
+1
+1
–
–
24,19
23,56
23,04
: y –
.
,
124
-
:
1.
.
x4
x5
.
2.
.
3.
4.
5.
6.
.
7.
.
.
.
.
S Excel
.
S Excel
1.
1
6.
,
?
2.
?
3.
,
?
4.
?
5.
?
6.
7.
8.
9.
?
.
2 -l?
.
125
1.
.
.
/ . .
, 2014. – 344 .
. .
.–
:
. .
,
:
2.
. .
3.
:
:
4.
. .
/ . .
,
.
.
,
.
.
.–
:
.
/
, 2011. – 72 .
,
.
, 2013. – 132 .
/ .
.
,
.
.–
.
:
.–
:
.
6.
7.
[
, .
. .
:
.
.–
. .
.
] / . .
, 2014. – 77 .
.–
.
.:
/
.
,
.
.
.
:
,
. – 2-
.,
, 2014. – 495 .
:
» /
2010. – 90 .
8.
. .
:
2012. – 185 .
-
, 2003. – 208 .
5.
.
. .
-
/
.
.
,
126
.
.
.
.
«
. –
. –
:
,
:
,
1
(z)
z
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
0.32
0.34
0.36
0.38
0.40
0.42
0.44
0.46
0.48
0.50
0.52
0.54
0.56
0.58
0.60
0.62
0.64
0.66
0.68
0.70
0.72
0.74
0.76
0.78
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
(z )
0.39894
0.39886
0.39862
0.39822
0.39767
0.39695
0.39608
0.39505
0.39387
0.39253
0.39104
0.38940
0.38762
0.38568
0.38361
0.38139
0.37903
0.37654
0.37391
0.37115
0.36827
0.36526
0.36213
0.35889
0.35553
0.35207
0.34849
0.34482
0.34105
0.33718
0.33322
0.32918
0.32506
0.32086
0.31659
0.31225
0.30785
0.30339
0.29887
0.29431
0.28969
0.28504
0.28034
0.27562
0.27086
0.26609
0.26129
0.25647
0.25164
0.24681
1
e
2
z
1.00
1.02
1.04
1.06
1.08
1.10
1.12
1.14
1.16
1.18
1.20
1.22
1.24
1.26
1.28
1.30
1.32
1.34
1.36
1.38
1.40
1.42
1.44
1.46
1.48
1.50
1.52
1.54
1.56
1.58
1.60
1.62
1.64
1.66
1.68
1.70
1.72
1.74
1.76
1.78
1.80
1.82
1.84
1.86
1.88
1.90
1.92
1.94
1.96
1.98
z2
2
(z )
0.24197
0.23713
0.23230
0.22747
0.22265
0.21785
0.21307
0.20831
0.20357
0.19886
0.19419
0.18954
0.18494
0.18037
0.17585
0.17137
0.16694
0.16256
0.15822
0.15395
0.14973
0.14556
0.14146
0.13742
0.13344
0.12952
0.12566
0.12188
0.11816
0.11450
0.11092
0.10741
0.10396
0.10059
0.09728
0.09405
0.09089
0.08780
0.08478
0.08183
0.07895
0.07614
0.07341
0.07074
0.06814
0.06562
0.06316
0.06077
0.05844
0.05618
127
z
2.00
2.02
2.04
2.06
2.08
2.10
2.12
2.14
2.16
2.18
2.20
2.22
2.24
2.26
2.28
2.30
2.32
2.34
2.36
2.38
2.40
2.42
2.44
2.46
2.48
2.53
2.58
2.63
2.68
2.73
2.78
2.83
2.88
2.93
2.98
3.03
3.08
3.13
3.18
3.23
3.28
3.38
3.48
3.58
3.68
3.78
3.88
3.98
4.20
5.00
(z )
0.05399
0.05186
0.04980
0.04780
0.04586
0.04398
0.04217
0.04041
0.03871
0.03706
0.03547
0.03394
0.03246
0.03103
0.02965
0.02833
0.02705
0.02582
0.02463
0.02349
0.02239
0.02134
0.02033
0.01936
0.01842
0.01625
0.01431
0.01256
0.01100
0.00961
0.00837
0.00727
0.00631
0.00545
0.00470
0.00405
0.00348
0.00298
0.00254
0.00216
0.00184
0.00132
0.00094
0.00066
0.00046
0.00031
0.00021
0.00014
0.00006
0.00000
2
1
2
( x)
x
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
0.32
0.34
0.36
0.38
0.40
0.42
0.44
0.46
0.48
0.50
0.52
0.54
0.56
0.58
0.60
0.62
0.64
0.66
0.68
0.70
0.72
0.74
0.76
(x )
0.00798
0.01595
0.02392
0.03188
0.03983
0.04776
0.05567
0.06356
0.07142
0.07926
0.08706
0.09483
0.10257
0.11026
0.11791
0.12552
0.13307
0.14058
0.14803
0.15542
0.16276
0.17003
0.17724
0.18439
0.19146
0.19847
0.20540
0.21226
0.21904
0.22575
0.23237
0.23891
0.24537
0.25175
0.25804
0.26424
0.27035
0.27637
x
0.78
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12
1.14
1.16
1.18
1.20
1.22
1.24
1.26
1.28
1.30
1.32
1.34
1.36
1.38
1.40
1.42
1.44
1.46
1.48
1.50
1.52
(x )
0.28230
0.28814
0.29389
0.29955
0.30511
0.31057
0.31594
0.32121
0.32639
0.33147
0.33646
0.34134
0.34614
0.35083
0.35543
0.35993
0.36433
0.36864
0.37286
0.37698
0.38100
0.38493
0.38877
0.39251
0.39617
0.39973
0.40320
0.40658
0.40988
0.41308
0.41621
0.41924
0.42220
0.42507
0.42785
0.43056
0.43319
0.43574
128
x
e
z2
2
dz
0
x
1.54
1.56
1.58
1.60
1.62
1.64
1.66
1.68
1.70
1.72
1.74
1.76
1.78
1.80
1.82
1.84
1.86
1.88
1.90
1.92
1.94
1.96
1.98
2.00
2.02
2.04
2.06
2.08
2.10
2.12
2.14
2.16
2.18
2.20
2.22
2.24
2.26
2.28
(x )
0.43822
0.44062
0.44295
0.44520
0.44738
0.44950
0.45154
0.45352
0.45543
0.45728
0.45907
0.46080
0.46246
0.46407
0.46562
0.46712
0.46856
0.46995
0.47128
0.47257
0.47381
0.47500
0.47615
0.47725
0.47831
0.47932
0.48030
0.48124
0.48214
0.48300
0.48382
0.48461
0.48537
0.48610
0.48679
0.48745
0.48809
0.48870
x
2.30
2.32
2.34
2.36
2.38
2.40
2.42
2.44
2.46
2.48
2.50
2.55
2.60
2.65
2.70
2.75
2.80
2.85
2.90
2.95
3.00
3.05
3.10
3.15
3.20
3.25
3.30
3.40
3.50
3.60
3.70
3.80
3.90
4.00
4.20
4.40
4.70
5.00
(x )
0.48928
0.48983
0.49036
0.49086
0.49134
0.49180
0.49224
0.49266
0.49305
0.49343
0.49379
0.49461
0.49534
0.49598
0.49653
0.49702
0.49744
0.49781
0.49813
0.49841
0.49865
0.49886
0.49903
0.49918
0.49931
0.49942
0.49952
0.49966
0.49977
0.49984
0.49989
0.49993
0.49995
0.49997
0.49999
0.49999
0.49999
0.50000
3
t ( , n)
n
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
35
40
45
50
60
70
80
90
100
120
0,95
0,99
0,999
2.78
2.57
2.45
2.37
2.31
2.26
2.23
2.20
2.18
2.16
2.15
2.13
2.12
2.11
2.10
2.09
2.06
2.05
2.03
2.02
2.02
2.01
2.00
2.00
1.99
1.99
1.98
1.98
1.96
4.60
4.03
3.71
3.50
3.36
3.25
3.17
3.11
3.06
3.01
2.98
2.95
2.92
2.90
2.88
2.86
2.80
2.76
2.72
2.71
2.69
2.68
2.66
2.65
2.64
2.63
2.63
2.62
2.58
8.61
6.86
5.96
5.41
5.04
4.78
4.59
4.44
4.32
4.22
4.14
4.07
4.02
3.97
3.92
3.88
3.75
3.66
3.60
3.56
3.53
3.50
3.46
3.44
3.42
3.40
3.39
3.37
3.29
129
4
2
s
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
0.05
0.01
0.001
3.84
5.99
7.81
9.49
11.07
12.59
14.07
15.51
16.92
18.31
19.68
21.03
22.36
23.68
25.00
26.30
27.59
28.87
30.14
31.41
32.67
33.92
35.17
36.42
37.65
38.89
40.11
41.34
42.56
43.77
6.63
9.21
11.34
13.28
15.09
16.81
18.48
20.09
21.67
23.21
24.73
26.22
27.69
29.14
30.58
32.00
33.41
34.81
36.19
37.57
38.93
40.29
41.64
42.98
44.31
45.64
46.96
48.28
49.59
50.89
10.83
13.82
16.27
18.47
20.52
22.46
24.32
26.13
27.88
29.59
31.26
32.91
34.53
36.12
37.70
39.25
40.79
42.31
43.82
45.32
46.80
48.27
49.73
51.18
52.62
54.05
55.48
56.89
58.30
59.70
130
5
(
k
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
40
60
120
)
0.10
6.31
2.92
2.35
2.13
2.01
1.94
1.89
1.86
1.83
1.81
1.80
1.78
1.77
1.76
1.75
1.75
1.74
1.73
1.73
1.73
1.71
1.70
1.68
1.67
1.66
1.64
0.05
12.70
4.30
3.18
2.78
2.57
2.45
2.36
2.31
2.26
2.23
2.20
2.18
2.16
2.14
2.13
2.12
2.11
2.10
2.09
2.09
2.06
2.04
2.02
2.00
1.98
1.96
0.02
31.82
6.97
4.54
3.75
3.37
3.14
3.00
2.90
2.82
2.76
2.72
2.68
2.65
2.62
2.60
2.58
2.57
2.55
2.54
2.53
2.49
2.46
2.42
2.39
2.36
2.33
0.01
63.70
9.92
5.84
4.60
4.03
3.71
3.50
3.36
3.25
3.17
3.11
3.05
3.01
2.98
2.95
2.92
2.90
2.88
2.86
2.85
2.79
2.75
2.70
2.66
2.62
2.58
0.002
318.30
22.33
10.22
7.17
5.89
5.21
4.79
4.50
4.30
4.14
4.03
3.93
3.85
3.79
3.73
3.69
3.65
3.61
3.58
3.55
3.45
3.39
3.31
3.23
3.17
3.09
0.001
631.00
31.60
12.90
8.61
6.86
5.96
5.40
5.04
4.78
4.59
4.44
4.32
4.22
4.17
4.07
4.01
3.96
3.92
3.88
3.85
3.72
3.65
3.55
3.46
3.37
3.29
0.05
0.025
0.01
0.005
0.001
0.0005
(
131
)
6
W
132
7
Fcr ( , k x , k y )
= 0.01
ky\kx
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1
2
3
4
5
6
7
8
9
4052
98.49
34.12
21.20
16.26
13.74
12.25
11.26
10.56
10.04
9.86
9.33
9.07
8.86
8.68
8.53
8.40
4999
99.01
30.81
18.00
13.27
10.92
9.55
8.65
8.02
7.56
7.20
6.92
6.70
6.51
6.36
6.23
6.11
5403
90.17
29.46
16.69
12.06
9.78
8.45
7.59
6.99
6.55
6.22
5.95
5.74
5.56
5.42
5.29
5.18
5625
99.25
28.71
15.98
11.39
9.15
7.85
7.01
6.42
5.99
5.67
5.41
5.20
5.03
4.89
4.77
4.67
5764
99.33
28.24
15.52
10.97
8.75
7.46
6.63
6.06
5.64
5.32
5.06
4.86
4.69
4.56
4.44
4.34
5889
99.30
27.91
15.21
10.67
8.47
7.19
6.37
5.80
5.39
5.07
4.82
4.62
4.46
4.32
4.20
4.10
5928
99.34
27.67
14.98
10.45
8.26
7.00
6.19
5.62
5.21
4.88
4.65
4.44
4.28
4.14
4.03
3.93
5981
99.36
27.49
14.80
10.27
8.10
6.84
6.03
5.47
5.06
4.74
4.50
4.30
4.14
4.00
3.89
3.79
6022
99.36
27.34
14.66
10.15
7.98
6.71
5.91
5.35
4.95
4.63
4.39
4.19
4.03
3.89
3.78
3.68
10
11
6056 6082
99.40 99.41
27.23 27.13
14.54 14.45
10.05 9.96
7.87 7.79
6.62 6.54
5.82 5.74
5.26 5.18
4.85 4.78
4.54 4.46
4.30 4.22
4.10 4.02
3.94 3.86
3.80 3.73
3.69 3.61
3.59 3.52
= 0.05
ky \ kx
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1
2
3
4
5
6
161 200 216 225 230 234
18.51 19.00 19.16 19.25 19.30 19.33
10.13 9.55 9.28 9.12 9.01 8.94
7.71 6.94 6.59 6.39 6.26 6.16
6.61 5.79 5.41 5.19 5.05 4.95
5.99 5.14 4.76 4.53 4.39 4.28
5.59 4.74 4.35 4.12 3.97 3.87
5.32 4.46 4.07 3.84 3.69 3.58
5.12 4.26 3.86 3.63 3.48 3.37
4.96 4.10 3.71 3.48 3.33 3.22
4.84 3.98 3.59 3.36 3.20 3.09
4.75 3.88 3.49 3.26 3.11 3.00
4.67 3.80 3.41 3.18 3.02 2.92
4.60 3.74 3.34 3.11 2.96 2.85
4.54 3.68 3.29 3.06 2.90 2.79
4.49 3.63 3.24 3.01 2.85 2.74
4.45 3.59 3.20 2.96 2.81 2.70
133
7
8
237
239
19.36 19.37
8.88 8.84
6.09 6.04
4.88 4.82
4.21 4.15
3.79 3.73
3.50 3.44
3.29 3.23
3.14 3.07
3.01 2.95
2.92 2.85
2.84 2.77
2.77 2.70
2.70 2.64
2.66 2.59
2.62 2.55
9
241
19.38
8.81
6.00
4.78
4.10
3.68
3.39
3.18
3.02
2.90
2.80
2.72
2.65
2.59
2.54
2.50
10
11
242
243
19.39 19.40
8.78 8.76
5.96 5.93
4.74 4.70
4.06 4.03
3.63 3.60
3.34 3.31
3.13 3.10
2.97 2.94
2.86 2.82
2.76 2.72
2.67 2.63
2.60 2.56
2.55 2.51
2.49 2.45
2.45 2.41
8
G
n
= 0,05
f = m –1
1
2
3
4
5
6
2
0,9985
0,9750
0,9392
0,9057
0,8772
0,8534
3
0,9669
0,8709
0,7977
0,7457
0,7071
0,6771
4
0,9065
0,7679
0,6841
0,6287
0,5859
0,5598
5
0,8412
0,6338
0,5991
0,5441
0,5065
0,4783
6
0,7608
0,6161
0,5321
0,4803
0,4447
0,4184
7
0,7271
0,5612
0,4800
0,4307
0,3974
0,3726
8
0,6798
0,5157
0,4377
0,3910
0,3595
0,3362
9
0,6385
0,4770
0,4027
0,3584
0,3286
0,3067
10
0,6020
0,4450
0,3733
0,3311
0,3029
0,2823
12
0,5410
0,3924
0,3264
0,2880
0,2624
0,2439
16
0,4709
0,3346
0,2758
0,2419
0,2195
0,2034
20
0,3894
0,2705
0,2205
0,1921
0,1935
0,1602
134
9
7
1
3, 31
5, 52
3, 50
7, 99
4, 97
9, 23
6, 03
14, 80
2
3,51 3,05
6,47 6,14
4,61 4,93
9,15 9,66
5,28 5,47
13,41 13,81
8,64 8,71
25,75 25,63
3
2,24 2,50
3,82 3,94
2,05 2,52
4,07 4,42
3,07 3,89
5,81 5,48
3,48 3,01
6,83 6,20
4
2,88 2,97
4,91 4,65
3,01 3,31
5,09 5,53
3,73 3,30
6,18 6,52
4,63 4,96
9,38 9,53
5
3,72 3,28
5,93 5,59
3,32 3,55
7,94 7,26
4,40 4,04
9, 63 9,17
6,36 6,96
14,76 14,68
3, 04
5, 93
3, 27
7, 41
4, 84
9, 35
6, 71
14, 72
3, 35
5, 77
3, 36
7, 11
4, 88
9, 66
6, 43
14, 95
3, 39 3,21
5, 09 5, 51
3, 98 3,89
7, 38 7,07
4, 30 4, 29
9, 34 9, 17
6, 39 6, 37
14,68 14,67
6
4, 92 4, 85
8, 85 8, 90
5, 81 5, 86
13, 49 13,32
7, 89 7, 68
20, 52 20,71
11, 82 11,69
66,71 66,13
7
4,07 4,84
8,87 8,96
5,32 5,73
13, 29 13,04
7,79 7,15
20,55 20,78
11,26 11,38
66,99 66,05
8
3,83 3,05
6,55 6, 64
4,75 4,90
9,04 9,30
5,55 5,89
13,40 13,11
8,38 8,31
25,86 25,44
9
3,54 3,32
5,47 5,70
3,26 3,95
7,17 7,21
4,01 4,82
9,50 9,19
6,90 6,83
14,77 14,70
10
2,49 2,37
4,18 4,64
3,36 3,20
5,45 5,45
3,25 3,12
6,21 6,14
4,51 4,89
9,35 9,93
3,53 3,92 3,27
6,35 6,62 6,81
4,16 4,92 4,01
9,34 9,52 9,28
5,42 5,05 5,86
13,51 13,89 13,63
8,38 8,65 8,66
25,11 25,78 25,34
2,39
3,68
2,55
4,76
3,96
5,23
3,14
6,32
2,10
3,74
2,74
4,17
3,19
5,92
3,51
6,58
2,57
3,72
2,73
4,55
3,37
5,73
3,19
6,69
2,42
4,52
3,02
5,48
3,80
6,60
5,01
9,02
2,37
4,29
3,99
5,11
3,89
6,09
4,52
9,46
2,39
4,38
3,48
5,45
3,52
6,43
5,07
9,77
3,80 3,49 3,69
5,63 5,20 5,68
3,93 3,15 3,39
7,49 7,02 7,58
4,68 4,98 4,24
9,60 9,33 9,91
6,69 6,05 6,57
14,25 14,22 14,41
135
4, 33
8,44
5, 47
13, 57
7, 39
20,27
11, 93
66,62
4,24
8, 21
5,90
13, 42
7, 19
20, 58
11, 49
66,85
4, 77
8,39
5,69
13, 56
7, 42
20,31
11,54
66,20
4,28
8,30
5,86
13,28
7,45
20,04
11,71
66,88
4,16
8,89
5,43
13,40
7,68
20,79
11,34
66,55
4,66
8,04
5,62
13,12
7,38
20,61
11,73
66,62
3,23 3,23 3,87
6,23 6,59 6,11
4,76 4,98 4,44
9,24 9,57 9,30
5,27 5,81 5,63
13,45 13,61 13,36
8,03 8,19 8,10
25,78 25,62 25,56
3,024 3,46 3,19
5,78 5,90 5,77
3,37 3,31 3,15
7,01 7,30 7,91
4,90 4,18 4,19
9,15 9, 62 9,36
6,84 6,78 6,78
14,18 14,90 14,93
2,63
4,55
3, 02
5,49
3,90
6,41
4,55
9,05
2,64
4,26
3,12
5,72
3,82
6,04
4,41
9,11
2,69
4,51
3,07
5,55
3,81
6,22
4,81
9,26
16
8,46
12,52
10,05
15,82
11,51
17,31
14,06
22,74
11
2,64
3,47
2,39
4,81
3,86
5,82
3,50
6,55
2,65
3,38
2,68
4,51
3,84
5, 28
3,32
6,70
2,45
3,22
2,51
4,96
3,81
5,17
3,08
6,75
2,50
3,18
2,48
4,76
3,22
5,06
3,35
6,72
2,63
3,58
2,70
4,69
3,68
5,78
3,01
6,07
8,39
10,23
9,01
12,16
10,08
13,10
11,95
14,20
12
1,83
3,04
2,35
3,67
2,88
4,91
3,85
5,83
1,51
3,24
2,15
3,94
2,23
4,67
3,10
5,79
1,69
2,84
2,28
3,84
2,15
4,92
3,15
5,63
1,81
2,83
2,94
3,83
2,77
4,43
3,24
5,70
1,35
3,07
2,38
3,03
2,73
4,60
3,75
5,77
7,39
12,65
9,92
15,47
11,27
19,69
14,45
26,77
13
2,32
3,73
2,08
4,77
3,075
5,83
3,78
6,98
2,67
4,48
3,34
5,58
3,78
6,13
4,98
9,78
3,73
5,91
3,84
7,52
4,43
9,78
6,04
14,70
2,14
3,24
2,645
4,54
3,74
5,76
3,28
6,08
14
2,87
4,13
3,59
5,85
3,08
6,22
4,49
9,89
15
3,33
5,86
3,32
7,65
4,40
9,94
6,70
14,69
2,60
3,77
2,57
4,11
3,90
5,36
3,05
6,87
2,55
4,55
3,16
5,90
3,20
6,50
4,50
9,31
3,62
5,21
3,29
7,79
4,83
9,57
6,41
14,34
2,46
3,27
2,45
4,88
3,99
5,98
3,48
6,40
2,527
4,44
3,40
5,13
3,14
6,75
4,47
9,11
3,65
5,56
3,14
7,10
4,75
9,59
6,34
14,54
2,20
3,85
2,57
4,65
3,96
5,40
3,04
6,04
3,59
4,28
4,43
5,76
4,61
5,64
5,27
6,12
2,83
4,69
3,00
5,69
3,42
6,70
4,68
9,86
2,82
3,54
3,23
3,63
3,44
4,25
3,10
4,53
3,29
5,98
3,99
7,43
4,99
9,21
6,39
14,74
136
8,41
12,98
10,80
15,99
11,14
17,36
14,15
22,75
17
7,04
10,50
9,68
11,21
9,06
12,40
11,97
14,76
18
7,03
12,56
9,14
15,11
11,83
19,40
14,08
26,30
19
3,09
4,80
4,53
5,32
4,78
5,87
5,36
6,13
20
3,04
3,61
3,83
3,70
3,52
4,47
3,77
4,47
8,42
12,78
10,88
15,69
11,59
17,81
14,62
22,99
8,47
8,44
12,18 12,08
10,79 10,37
15,04 15,86
11,57 11,84
17,09 17,63
14,54 14,173
22,79 22,569
8,40
8,73
7,16
10,78 10,73 10,31
9,34
9,49
9,06
12,06 11,44 11,98
9,98 10,97 10,73
12,95 13,047 13,16
11,13 11,61 11,254
14,86 14,75 13,52
7,80
7,19
12,04 12,037
10,72
9,10
15,71 15,55
11,94 11,21
19,31 18,38
14,94 14,86
26,07 26,37
7,50
12,09
9,76
15,91
11,74
19,42
14,49
26,81
3,45
4,74
4,42
5,14
4,77
5,67
5,23
6,63
3,68
4,84
4,30
5,46
4,10
5,61
5,68
6,98
3,40
4,45
4,75
5,82
4,58
5,90
5,21
6,75
2,84
3,51
3,53
3,84
3,39
4,05
3,55
4,72
2,88
3,17
3,99
3,64
3,28
4,53
3,80
4,50
2,96
3,50
3,29
3,04
3,24
4,52
3,59
4,13
. .
. .
, . .
30.05.2017.
60×84 1/16.
.
. . 7,0.
2017 .
, .
.
.- . . 7,63.
100
.
,
137
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