nadezhnost ees
DESCRIPTION
Надежность структурная энергетических системTRANSCRIPT
-
______________ .. ______ ______________2007 .
140200 - 140205 " ",
" , , , , "
2007
-
2
621.311.019.3 : .. : , e. .. : / .. : -, 2007. . .: . . .
"- "
- , 2007
: 6084 1/16 ... .-. . 100 "
- 620002, . , ., 19
-
3
..
-
4
1. ......................................................................................................................... 4
1.1. .......................................................................................................................... 7 1.1.1. .............................................................................. 8 1.1.2. ............................................................................ 12 1.1.3. ..................................................................................................... 17
1 . 2 . . ..................................................................... 17 2. ............................................................................................... 19
2.1. ............................................................................................................ 19 2.1.1. ......................................................................................... 21 2.1.2. .................................................................................................................. 24 2.1.3. ................................................................................... 26 2.1.4. m/n ................................................................................................................. 28 2.1.5. ........................................................................................................ 28 2.1.6. ...................................................................................... 29 2.1.7. ............................................................................................. 32 2.1.8. .......................................................................................................... 34 2.1.9. ........................................................................................................................ 35
2.2. - ............................................................................................................. 38 2.3. ................................................................................................. 41 2.4. ....................................................................................... 45 2.5. ...................................................................................................................................... 46
1.
-. , , -, , , -.
- . , - - , -, , .
- . , - . , - , -.
-
5
, , .
, , - , - ( ) - . , . - , - , . , , .
. -, .
, - ( , - , - ( , , .) - .
- . , , - . - - - , - .
, , -, , .
-
6
- , . , , , , -. .
. , - , , , - .
. , , - .. , . -, . -, -.
(), , , , - . - . , - () , , - .
. . - . , -
-
7
. 80- . - , .
- . . , . . , . . , . . , . . , . . , .., . . , . . , . . , .., .., .., .
1.1.
. , . - , - . : - () F(t), ( - ) R(t)=1-F(t), () f(t) )(t = f(t)/R(t). . 1.1.
1.1
F(t) R(t) f(t) )(t
F(t) t
0 dtf(t) 1-R(t)
t
0 dtf(t)
xdtt
0)(exp1
R(t) 1-F(t) 1-F(t)
t dtf(t)
xdtt
0)(exp
f(t) )(tFdtd )(tF
dtd )(tR
dtd
xdttt
0)(exp)(
-
8
)(t )()(
xRxf ( )
1 ( )F t
F t
[ ]ln ( )d R tdt t
dtf(t)
tf )(
1.1.1.
, -, .
( , )q n k k=0,1,,n n - q
( , ) k k n knq n k C q p= , (1.1)
p=1-q - ; !
! ( )!kn
nCk n k
= - n k. -
nqp )( + q 1)(
0==+
=n
k
knkkn
n pqCpq . (1.2)
-
1( , ) ( , 1)1
n k qq n k q n kk q
+= . (1.3) , -
, M=nq. D=npq. 1.2
( , )q n k k - 50 q =0,04 q=0,1.
1( , ) ( , )
k
iQ n k q n i
== -
, k. 1.2
q=0,04 q=0,l
-
9
-
-
,
( , )q n k
( , )Q n k
( , )q n k
( , )Q n k
0 0 0,8443 0,8493 0,6561 0,6561
1 50 0,1416 0,9909 0,2916 0,9477
2 100 8,84710-3 0,9997 0,0486 0,9963
3 150 2,45810-4 0,999998 3,610-3 0,9999
4 200 2,56010-6 1 1, 10-4 1
, k= 1, q=0,04 q(4,1) = 40,040,963 = 0,141558. k= 2 q(4,2) = 60,0420,962 = 0,0088.
1.2 , q(n,k) . - - (.
1.1. ). , - - = nq D = npq ( - ). - , 9D .
- . , (n+1)q. , - k. . 1.1. n=20 q=0,1 - =int(210,1)=2, n=40 =4. - . -, , ,
. 1.1. -
00,10,20,30,40,50,60,7
0 2 4 6 8 10
k
n=4n=20
n=40n=60
-
10
, , ( "n-1").
- . q>n/(n+1), - ( , )q n k , q
-
11
- .
- , :
nq= .
( )( , )!
knqnqq n k e
k .
1.3 (n= 20, q = 0,001 0,1). 1.3
k
q=0,001 q=0,1
0 0,980 0,980 0% 0,121 0,135 -11%
1 0,020 0,020 0% 0,270 0,271 0%
2 1,87E-04 1,96E-04 -5% 0,285 0,271 5%
3 1,12E-06 1,31E-06 -17% 0,190 0,1801 5%
4 4,77E-09 6,53E-09 -37% 0,09 0,090 0%
5 1,53E-11 2,61E-11 -71% 0,032 0,0361 -13%
6 3,82E-14 8,71E-14 -128% 0,009 0,0121 -36%
, - . k - ( k=20 1,6107 %), ,
- . , - 10-6 , .
- (. 1.2. ). -
. 1.2. -
-150%
-100%
-50%
0%
50%
0 1 2 3 4 5 6 7k
-
12
, - , (, , , ), .
, - . - - . , L { }, , , , 1,...,j j j j j jn q P n q j L = =L , Pj - j, - , :
xPkekkk
xFL
jjj
k k k L
kkkL
L
L
-
20.11.2007 13
1.4
F(x), R(x) f(x) (x) -
duuxF
mx
=
/)( 2
2exp
21)(
2
2
2)(exp
21
mx
m 2 -
-
)exp()( xxR = )exp( x /1 2/1 0x
( )= )(exp)( xxR ( ) )(exp)( 1 xx
1)( x
+1
11 0x
),()( xxF = ( ) xe
x
)(
1
2
0x
( ) xa
r
r
erxxR
= = 1
0 !)(
( ) xa ea
x
)!1(
1
( )( )
=
1
0
1
!)!1(
a
r
r
a
rxa
x
a 2
a a- a>0
dueu u =0
1)( - -; dueu
t u =0
1
)(1),( -
-.
-
20.11.2007 14
(, - ) (). , - , -. ( ), - - . , (, .).
" ", - , - . " " , - 2, 4,6%, .
-. , - . - .
, .
() . ( ) - . - 1.4
=
xdttxR
0)(exp)( .
-
20.11.2007 15
1
t
, =)(t =const. tetR =)( . - , , .. - , (, , , , - .).
- ( , , - ). - - . - -. - .
, , - (. 1.3. ). - : A - ( - , ), (t) , B - ( - ), (t)const, C - , (t) .
( ) )(exp)( xxR = . - - . =1 , 1 - .
-
. 1.3. -
-
20.11.2007 16
- .
, , a- - a, 1.4
/1=M , 2/1 =D ( ),
, a- - a .
. -, a=1, - , , - .
, -. , -
)/()(* ssfe += ,
( ) ( )aea sfssf )()/()( ** =+= . -
, , ( .1.4 - ). -, -, - - .
- , =1 . - - -
-
20.11.2007 17
. , .
-, - - .
1.1.3.
F1(x), F2(x)
)()()()()( 1221 xFdxzFxFdxzFzF
== . (1.7)
, , z, , , x ( )(1 xdF ), z-x (- )(2 xzF ). :
dxxfxzfdxxfxzfzf )()()()()( 1221
== . (1.8)
(1.7) , . (1.8), , , - - .
1 . 2 . . -
i . . , - Pi i - Pi = Ti/T., fi=1/T,
fi = Pi/Ti. fi -
i -
-
20.11.2007 18
,
=ij
ii jff . , jPf iijij = , , - == jPjff iiii .
- i i
i= Pi / fi=
==ij
iiii jfPT /1/ , . . - .
. , , -
, , , . . 1.4. , J. - ( ):
J - Jj , - J:
==Jj JiJj Ji
J jijPjiff .
J i, J. - iJ , - i , i Jj , J i. -
===Jj
iJj
iJiiJ ijPijfPf ;
===Jj
jJj
JiJJi jiPjifPf .
. 1.4. - -
J
I
S
j i
-
20.11.2007 19
-
=Jj
iJ ij ; (1.9)
=
Jjj
JjjJi PjiP / . (1.10)
, - - , . - , - .
- ,
=
==
Iii
Ii JjiI
IiiJIIJIJ PijPPfPf /// ;
=
==
Jjj
Jj JjjijJ
jjjIJJIJI PPPfPf ///
(1.9), (1.10), .
- .
2.
, - . , . - , [14-17 .].
2.1. -
. - .
-
20.11.2007 20
- - , - - -. - - : -, , - , - .
, . - . - -. . 2.1. - , ab - a b, ba - - a b ..
- , : - ; - - - ( ); - , (- ).
. - , - , . , - -
. 2.1. -
a
ab
ba
ba
baa
b
b
a
ab
b
-
20.11.2007 21
, - .
- - . , , , - . - , , .
2.1.1. , ,
,
P'(t)=P(t)L; (2.1) ,1)( = tPi (2.2)
P ( t ) - ; L - , Lij = ij
ji
=ij
ijiiL . .
Hi, , t + t i. , - t - t (- ii) t j t i ( ji), j , ..
+= jiiii HHH . Hj Hi -
ji tijetF = 1)( , - t t=0: ttFP jiji = )( . ttFP ijij = )(
, , - t j, t + t
-
20.11.2007 22
i, j - j i ttPP jijji = )( .
+=+ij
jijij
ijii ttPttPttP )()1)(()( .
=+j
jjiii ttPtPttP )()()( , (2.3)
=
ijijii - -
, - . 0t (2.3) :
=j
jjii tPtP )()(' ,
(2.1). , L ,
det L=0, (
=ij
ijii ). , - ( ), - . - (2.2)
( ):
. 2.1 . - ( )(tPw - )(tPf - ) -
, , - .
. 2.2. (2.1), (2.2):
.1)()(
);()()('
=++=
tPtP
tPtPtP
fw
fww Pf(t)
, =++ )()()(' tPtP ww . (2.4)
. 2.2. -
w f
-
20.11.2007 23
tw etCtP
)()()( += . (2.5) (2.10)
(2.4), C(t):
1)(
)(
)()()(
)(
)('
))(())(()('
CetC
etC
etCetCetC
t
t
ttt
++==
=+++
+
++++
ttt
w eCeCetP)(
1)(
1)()(
+++ ++=
++=
1)0( =wP , ( ), +=1C .
.)(1)(
;)(
)(
)(
twf
tw
etPtP
etP
+
+
++==+++= (2.6)
.
, . - =2 . . , 3- .
. . 2.3. .
. 2.3. .
=1/=0,5 (1/).
L=
0 1 2 0 - 1 - 2
0 1 2
-
20.11.2007 24
:
=++=
=
1)()()(
),()()(
),()(
210
'10
'1
'0
'0
ttt
ttt
tt
PPP
PPP
PP
, tet =)(0P . -
0)()( 1'
1 =+ tett PP . (2.7)
tetCt = )()(1P (2.8) (2.8) (2.7),
( ) 0)()()()()('1 ==+= ttttt etCeetCetCetCt P .
ttC =)( ttet =)(1P
, t=3 5.10 )3(= eP =0,223; 5,11 35,0)3( = eP =0,335;
2(3)=1-0,223- 0,335=0,442. . G(, ) , - (=0,5) . ( ). =2. - =1/ = 2. - 2(3)=G(3,2,2)=0,442. ! . - . , . . 3(6)=0,577. , , .
2.1.2. -
, , , . . () -. ,
-
20.11.2007 25
(2.1) . (2.1)
Lt = 0, (2.9) , .
1)( = tPj . (2.10) -
(! .).
-(a+b) a b 0
L= a -(b+ a) 0 b b 0 -(a+b) a
0 b a -( a+ b) , -
- : -(a+b) P0 + a P1+b P2 =0; a P0 -(b+ a) P1+b P3=0; b P0 -(a+b) P 2+ a P3=0;
b P1+a P2-( a+ b) P3=0 (2.11)
, , -
P0 + P1+ P2+P3=1. . 2.2. (2.11) - : a=b=1, a+ b=10. , () -
2.1.
2.1
-2 10 10 0 0 0,826446 1 -11 0 10 0 0,082645 1 0 -11 10 0 0,082645 1 1 1 1 1 0,008264
(2.11)
P0= a b/(a+ a) (b +b)=b; P1=a b/(a+ a) (b +b)=b;
-
20.11.2007 26
P2=b a /(a+ a) (b +b)=b; P3=a b /(a+ a) (b +b)=b,
i = i/(i+i), i = i/(i+i)- - i.
=10/(1+10)= 0,909, =10/(1+10)=0,091. -
, . i (2.9)
=ij
jijij
iji tPtP )()( . (2.12)
ijiij tPf )(= j.
i (2.9)
=
ijjij
ijiji tPtP )()( . (2.12)
i:
=ij
jiij
ij ff (
). - (2.9). , 1 ( ba ) 31011310 ffff +=+ , 31301013101 )( +=+ PPP
baba PPP +=+ 301 )( , (2.11).
2.1.3.
- - , - (2.3). (. ! -.). :
)()( tPtP fw = )()( tPtP wf = , == / . (2.2) ( ) ( ) +==+== 1/)(;1/1)( fw KtPKtP .
-
20.11.2007 27
. 2.4. -
- , :
1 P0 = 1 P1; 2 P2=2 P1.
P0 + P1+ P2 =1;
P2=(2/ 2)P1. =2 P1.
P1= 1 P0. n
nPn-1.= nP n. (2.13) Pn= n Pn-1.
(n +n-1) Pn-1.= n-1P n-2 +nP n. P n-2. (2.13), Pn-1= n-1 Pn-2. ,
Pj= j Pj-1. (2.14) , Pj -
-
j =j/j=Kj/Kj, (2.15) j. , Pj -. - , 1= jP , , , - :
0 1 2 1 1 2 2
-
20.11.2007 28
= =
== +
==
n
sk
s
k
j
k
j
j
PP
1 1
1
10
1
2.1.4. m/n . ( -), ( ) . , m .
. 2.5. 11,...,1,/)1( =+=+= mniiin ii . miPP iii ,...,1,1 == .
= =
=
+= m
sj
s
j
j
m
jmn
P
1 1
1
1
.
m =
= =
=
+= m
sj
s
j
j
m
jmn
P
1 1
1
1
2.1.5. n . , , . n ().. , . ().
0 1 2 n1 (n-1)2
2 m
(n-m+1)m
m
-
20.11.2007 29
. 2.6.
A1: 1 P0 =2 P1; P1=(1/ 2)/P0; A2: 2 P1 =3 P2; P2=(2 /3)/P1=(1 /3)/P0;
Pi= (1 /i+1)/P0;
( )+=
+= 1
11 /1
1n
iis
sP
2.1.6. 1 2
a b . 2.7. -
( , . 2.7, ) - : A0 - -; Ai - i, i = 1,, (- - ), , . . - .
- .
, + 1 (. 2.8). - , - :
niPP ii ,...,1,0 == ; 10 =+ iPP ,
. 2.8. -
A0 A1
An
1
n+1
A0
An
i i
A0 A
Ai
A1
-
20.11.2007 30
iiiii == / .
;1/11
0
+== =
n
iiKP njP
n
iijj ,...,1,1/
1=
+=
=.
- - :
( );1/10 P += ( )P += 1/ .
- . ,
( )
+=+ =
n
ii
11/11/1
=
= ni
i1
. (2.16) ,
. , - . -, . - . ,
( )( ) ( )baba KKK +=++== 11
111 (2.17)
baba ++=
(2.16) - ba . , - , . - , - , - , (2.16). -
-
20.11.2007 31
. (2.17) , 1
-
20.11.2007 32
2.1.7.
n . - , - ( ).
. 2.1.2. , - - .
-
i
n
i KK
1== . (2.19)
n . 2.9, 0 , f- , i - i , i - - i .
- f ( ,
==
n
ii
1 ):
=
=n
ii Kf
1
.
0
1
i
n
s1
ji
kn
i i
j
j
f
1
i
n
i i
1
n
1
n
1
n
1
n
s 1
ij
nk
j
j
(1.10)
. 2.9. -
-
20.11.2007 33
=
=
fjj
fj jsjjj
fjj
fjjfj P
KKPP
/ .
, fw PKP == .
== ii
K
K , -
(2.16) - . . - . - (2.19) b,
b
b
a
a
K +
+
=+=
111
( )ba ++=+ /11)/11(1
/111 .
baba ++= /1/1/1/1 .
,
ba
ba ++
=1
-
20.11.2007 34
21 KKK = ; - 21 += ; - = /1 ;
)1/( KK = ; : = / . f=K=0,4992510-62103=0,998510-3
2.3
, (1/) , / =1/,(1/) =, .. =/(1+), .. 1 1 10-3 103 10-3 0,99910-3 2 0,5 10-3 103 0,510-3 0,4997510-3 0,998510-3 0,510-3 2103 0,4992510-3 0,4992510-6
2.1.8. , { }niBi ,...,1, =
{ }niQi ,...,1, = 11
==
n
iiQ ,
==
n
iii BAPQAP
1)/()( . (2.20)
- , (2.20) - , . 2.10, i, i, i, - Wi, - - Bi - /Bi.
- (Wi /Bi.) iQ , P(Wi)= )1/( iiQ + - , , Bi
iii
iiiii QK
QWPBA =+== 1
)()/(P .
. 2.10. -
Wi
W1
Wn
A/B1
A/Bi
A/Bn
A
1
i
n
1
i
n
1
i
n Bn
Bi
B1
-
20.11.2007 35
== +==n
ii
i
in
iiii QQKA
11 1)(
f . ( )
=
=== ni
ii
n
iiii
QK
QKAPAA
1
1)(/)()(
f .
( )
=
=
== n
iii
n
iiii
QK
QKAPAA
1
1
1)(/)()(
f .
2.1.9. , -
- - . , -, , (. 2.11), , - .
. 2.11. -
- (. . 2.11, )) (. . 2.11, b), c)) - ( . 2.11, )). - , . - . 2.10. -
. , . 2.11
. 2.12.
a
b
c
d
a
b
c
d
a
b
c
dx
a) b) )
B1
B0
A/B1
A/B0
A
1
0
1
0
1
0
x
x x
-
20.11.2007 36
. 2.12, , - (. . 2.11, b)), , (. . 2.11, c)).
. 2.12 (. 2.1.3). -: (0)=1/(1++0+1);. (1)= (/0); (/1)= 1(/0); (/0)= 0(/0).
f=(0 + 1 )(0). : =(0 + 1 )/(1+). =(00 +1 1) (0 + 1)=
=( 0 + 1) (0 + 1). . . 2.11, ), ,
: =1; =10; =0,1; =0,0909.
(. 2.11, b) :
=0,09092=0,00826; =1-0,00826=0,9917; =20; f=0,0082620=0,1652; =f / =0,1652/0,9917=0,1666; = /.= 0,1666/20=0,00833.
: 0=2=2*0,1666= 0,3332; 0 = 2 =2*0,00833=0,0167; 0.= 0/ 0 =0,33/0,0167=20;
. 2.11, ): : =2=2; =2=2 0,1=0,2;=/=2/0,2=10. : = [ /(1+ )]2 =[0,2/(1+ 0,2)]2 =0,02778; =1- =0,972; 1=2=20; f= 1=0,5556; 1= f/ =0,556/0,972= 0,5715; 1 = 1/1= 0,5715/20=0,02855
(0)=1/(1+ +0+1). =1/(1+0,1+0,01666+0,1*0,02855)=0,8932 Pf=(0)(0+1)= 0,8932*(0,01666+0,1*0,02855)=0,01743 =0,8932*1,1=0,9825 f=(0 + 1 )(0)=( 0,3332+0,1 0,5714)*0,8932=0, 3487
-
20.11.2007 37
: =(0+1)/(1+)=(0,3332+0,1*0,5714)/(1+0,1)=0,3549 =(0 + 1) /(0 + 1)=(0,3332+0,1*0,5714)/(0,01666+0,1*0,02855)=20,002. - (.0)
: ( Q0=1/(1+0,1)=0,909) ( Q1=0,1/(1+0,1)=0,091).
0 - 0 =0,01666/(1+0,01666)= 0,01639; 1=0,02778.
()= 0 Q0+ 1 Q1=0,01639*0,909+0,02778*0,091=0,01743. ( )
=)(A (00 Q0+11Q1)/()= 20*0,01743/0,01743=20. ,
. - .
-
20.11.2007 38
2.2. - .
- : -, 1 . 0 -. . - ( - - ), -.
( ) , . , . , - - , 2 > 5 -. () - (). - , : - . , = 1; , = 0.
( ). . , - - ( = 1) ( = 0). , (1 0), . - , - . - . , (1 0) - , ().
: , () (-). (), (F) 2.4.
-
20.11.2007 39
2.4
A B Not A A And B ( ( )BA A Or B T (1) T(1) F ( 01 = ) T ( 111 = ) T T (1) F (0) F (0) F ( 101 = ) T F (0) T (1) T ( 10 = ) F ( 110 = ) T F (0) F (0) T (1) F ( 000 = ) F
( ). - x x (: x). - x 10 ;01 == .
( ). 1 2 21 xx 1 + 2 ( 1 2). , . , - - :
111 ;101 ;110 ;000 ==== . ( ). -
1 2 21 xx 12 (- 1 2). , . , - :
111 ;001 ;010 ;000 ==== . :
=+==+==+==+=
.1 x;0 x; x;;00 x;00 x;11 x;1
xxxxxxxxx
() :
++=++=++==
.)()(;)()(
321321321
321321321
xxxxxxxxxxxxxxxxxx .
() : 12211221 ; xxxxxxxx +=+= .
() :
++=++=+
).)(()();()()(
3121321
3121321
xxxxxxxxxxxxxx .
: 21212121 )( ;)( xxxxxxxx =++= .
-
20.11.2007 40
).,...,,1(),...,,( );,...,,0(),...,,(
21211
211211
nn
nn
xxxxxxxxxxxxxxx
=+=++ (2.21)
11211211 )( ;)( xxxxxxxx =+=+ .
==++=+=+==++=+=+
.1)()()(;1)()()(
2211221212121
1122121212121
xxxxxxxxxxxxxxxxxxxxxxxxxx .
. 2.13
- (2.21). - , . 2.13, ) - ))((( 432121 xxxxxxs +++= ,
))(()))(10(()))((( 43214321432121 xxxxxxxxxxxxxxs ++=+++=+++= , . 2.13, ).
(2.22) (2.22)
-
- Z( Xr ), - xi.
1
2
3
4
1 2
3
4
-
20.11.2007 41
. 2.14. -
( ) () Z=x1x2 ( ); Z=x1+x2 ( ). , - , - -. , , . 3.4 , (. 3.4 ),
432412234214431423123 xxxxxxxxxxZ +++= , (2.23) ,
34342421213232424141343414132321213 xxxxxxxxxxxxxxxxxxxxxxxxZ +++= , , - -.
2.3. (2.23) , Z3
() , () . , , - (). .
V , -. () () () .
, , - . , -
-
20.11.2007 42
-
. {1,2} . 2.13 . , 2 - . {2,3} - , .
C , ( - ) .
, - , ( ).
???? . {1,2,3} . 2.13
, , 3 . {1,2} , .
vi , , - Vi , i , , i . - , - , . - s s -
nn kkksvvvs == ...;... 2121 . , s
}{ it , s - }{ ic . , iv it , )...({ 1 mii zztv = . s
imimiiii tzztzzttvt === )...(0{)...({ 11 , .. - . .
-
20.11.2007 43
. 2.15. : t1={e1,e4}; t2={e2,e5}; t3={e1,e3,e5}; t4={e2,e3,e4} ( . 2.16) - 1= 14, 2= 25, 3= 135, 4=135. 4321 ttttZ = .
. 2.16. - : ; b .
P(Z)= 1+ 2+ 3+ 4- P (t1, t2) - P (t1, t3) - P (t1, t4) - P (t2, t3) - P
(t2, t4) - P (t3, t4)+ P (t1, t2, t3) + P (t1, t2, t4) + P (t1, t3, t4) + P (t2, t3, t4) - P (t1, t2, t3, t4)= = 1+2+3+4 - P (e1,e2,e4,e5) - P (e1,e4,e3,e5) - P (e1,e2,e3,e4) -P (e1,e2,e3,e5) - P(e2,e3,e4,e5) + 2 P (e1,e2,e3,e4,e5)= = 14 + 25 + 135 + 135 - p1p2p4p5 - p1p4p3p5 - p1p2p3p4 -p1p2p3p5 - p2p3p4p5 + 2p1p2p3p4p5.
- P (Z)= 22 + 23 - 5p4 + 2p5. , =0,9091 ( . 2.1.9) P (Z)= 0,9823 ( 0,9826 ).
: s1={e1,e2}; s2={e4,e5}; s3={e1,e3,e5}; s4={e2,e3,e4} ( . 2.16) - Q1= q1q2, Q2= q4q5, Q3= q1q3q5, Q4=q1q3q5. 4321 ssssZ = .
. 2.15. -
1 4
2 5
1 3 5
2 3 4
1
2
4
5
1
3
5
2
3
4a) b)
1 4
2 5
3
-
20.11.2007 44
P ( Z ) = Q1+ Q2+ Q3+ Q4-P(s1, s2) - P (s1, s3) - P (s1, s4) - P (s2, s3)
- P (s2, s4) - P (s3, s4)+ P (s1, s2, s3) + P (s1, s2, s4) + P (s1, s3, s4) + P (s2, s3, s4) - P (s1, s2, s3, s4)= = Q1+ Q2+ Q3+ Q4 - P (e1,e2,e4,e5) - P (e1,e2,e3,e5) - P (e1,e2,e3,e4) - P (e1,e3, e4,e5) - P (e2,e3,e4,e5) + 2 P (e1,e2,e3,e4,e5)= = q1q2 + q4q5 + q1q3q5 + q1q3q5 - q1q2q4q5 - q1q2q3q5 - q1q2q3q4 -q1q3q4q5 - q2q3q4q5 + 2q1q2q3q4q5. q P ( Z ) = 2q2+2q3-5q4+2q5. q=0,0909 P ( Z ) =0,0177 ( 0,0174 ), P (Z)=1-0,0177=0,9823. , - .
-
20.11.2007 45
2.4. . 2.17, -
=1; =10; =0,1; q==0,0909.
. 2.17. - .
1. 3 (. 2.17, b). -
c,d f -
qf= qc+qd- qc qd =2*0,0909-0,0909^2=0,1735. 2. e, f. qg = qeqf =0,0909*0,1735=0,01577. 3 4 (. 2.17, c). -
b,g h -
qh= qb+qg- qb qg =0,0909+0,01577-0,0909*0,01577=0,1052. 4. a, h. q2 = qaqh =0,0909*0,1052= 0,00956 . 1. 4 -
2 (. 2.17, b). - q4 = q2 = 0,00956. ( ).
2. 3 - (. 2.17, d). x, y:
q4=qy*(qx+qw- qxqw); q2=qx*(qy+qw- qyqw), qw=q+qd- qcqd) =0,1735; q4-q2=qy*(qx+qw- qxqw) - qx*(qy+qw- qyqw)= (qy- qx) qw
a
b
c
de
4
2
3 1
a
be
4
1
2
f
a) b)
a
h1
2
c)
x
y
c
d4
2
1 3
d)
-
20.11.2007 46
qy = qx +R = qx +(q4-q2)/qw q4= (qx +R) *(qx+qw- qxqw)= qx2(1-qw)+ qx (qw + R- Rqw)+ Rqw.
R=(q4-q2)/qw=0. q4
qx2(1-qw)+ qxqw- q4 = 0,8265qx2+0,1735qx- 0,00956=0 qx=0,04532 qx=-0,2552.
. R=0 qy = qx =0,04532.
,
q3 =(qx +qc - qx qc) (qy +qd qy qd)=( 0,04532+0,0909-0,04532*0,0909)^2= =0,01745 - - (0,01743), .2.1.9
2.5. . - 1 2. . 2.18., a. 2.5.
. 2.18. .
2.5 .
, 1/ , .. 1 1 2 2 1 0,5 2 0,6 1 0,5 0,1 2 0,5 0,2
4 3
2
1
3
1
2 2
1
3
1
2
1
2
a) b)
-
20.11.2007 47
. 1. . 3, 4, 3 1 2, , "". -, , . - . 2.18., b.
2. 2 - 1 1 1, 1. 2,= (1+ 1)1+ 1=(1+0,5)*0,1+0,5=0,6 5/. 1,= 2+ 2)2+ 2=(2+0,6)*0,2+0,5=1,02/. -
1 2. . 2.19. a. 2.6
. 2.19. .
2.6 .
, 1/ , .. 1 1 2, 3 2 1 0,5 2 3 0,6 4 0,4 1, 4 0,5 0,1 2, 3 0,5 0,2 1 0,1
2
1 1
2 2
11 1
2
1
2
a) b)
4
4
56
5
3
3 3
2
3 3
4
-
20.11.2007 48
. 1. . - 5, 6, 5 2 , "". . 2.19. , b.
2. , 2 - 1 1 1, 1. , , 3 3 3, 3. -,
2,= (1+ 1)1+ 1+(3+ 3)3+ 3=0,6 5+1,02=1,67
1/. 1,= 2+ 2)2+ 2+(3+ 3)3+ 3=2*1,02=2,04 1/.
- 1,*=0,6 5 2,*=1,02 1/. , 1 4 4. 3,= (1,*+ 2,* +1+4)4+ 4 =(0,6 5+1,02+0,1+0,4)*0,1+0,5=0,717 1/.
(
) , , 1 (. 2.20). - (-) , : , , - . - , -, " - ".
-
20.11.2007 49
. 2.20.
(). - , , , - . . 2.21. , - .
. 2.21.
(. 2.20) 1 ( F) F= 2+ 3+ 22+ 23+ V222+ V233+ V2(1+ 1)+ +V3(4+T2+ 12+V124 +V4(2+ 5+ V5(6 +T3 + 13+ V135 + + V6(7 +T4 + 14+ V146+ V7(8 +3))))), i ( , ) i, Vi i
m/n
1
1 2 3
82 4 5 73 6
11 12 13
21 22 23
14
1 2 3 4
1 2 3 5 6
4
-
20.11.2007 50
- . , - - . . - . , m/n - . - . 2.22 , 250 . 480 .
q, - q3. , k n
knkkn pqCnkP
=)/( , p=1-q (. 2.22) )3/2()3/3( PPQ += , . - pqP 23)3/2( = . , , , -.
. 2.22
- m/n (. 2.23). n-i, (i=1,,n-m+1)
+=
+
== 11
1mn
sk
sk
jij
jij
nin
PP
.
( ) 1; +==
=
mnP
Pmen
mii
me
-
20.11.2007 51
. 2.23 m/n
. (. 2.22). =1, =10. . 2.24
. 2.24 2/3
1=3/=0,3; 2=2/2=0,1. - :
0226,0;226,0;752,033,11
1,03,03,011
2211323 ======++= PPPPP . e=2=20. -
462,0
226,0752,0226,022
23
2 =+=+= PP
Pe
. ( ) 452,0462,0978,023 ==+= ePPf
452,0200226,01 === ePf
3 2 1
3 2
2
1 2
n n-1 m m-1
n (n-1)
(n-m+1)
m
2
1 2
-
20.11.2007 52
1. .. . .: ,
1984.
2. . -
. .: , 1983.
3. .. -
: , 2002.
-
20.11.2007 53