, m , m£4-5. , , .
(. 3.24) l1 l2.
. 3.24
(t)=1-(1-P1(t))×(1-P2(t))= P1(t)+ P2(t) - P1(t)×P2(t)
, ( ) ""
= P1+ P2 - P1×P2
Pi(t)=exp{-lit}, i=1, 2,
(t)= .
l1=l2=l
(t) = 2P(t) P2(t)= 2×-lt - -2lt
, . tHc
: .
, . , l
.. l=tH 1,5 (. . 4)
m=2.
fc(t)=2×l×e-lt - 2×l×e-2lt
- tg. l g 2×e-lt - 2×e-2lt = t.
l1, l2, l3 (. 3.25)
. 3.25 -
(t) t .
"" l3 (. 3.26). =1+2-12. = I = 1 + 2-12.
. 3.26
I (. 3.27), "" l3 3. :
(t)= I +P- I P = P 1+P2-P1P2+P3-P1P3- P2P3+ P1P2P3
, Pi=e-lit, i=1, 2, 3.
. 3.27 -
|
|
(t)=3×-lt - 3×-2lt + -3lt
f(t)=3×l×-lt - 6×l×-2lt + 3×l×-3lt
(t)
(t)=1-(1-P1(t))×(1-P2(t)×(1-P3(t))= P1+P2-P1P2+P3-P1P3- P2P3+ P1P2P3
l1 l2 l3 l4 (. 3.28).
. 3.28
Pi(t)=e-lit, i=1, 2, 3, 4.
(t) l1, l2 I I(t)= 1(t)×2(t) (. 3.29).
. 3.29
II II(t)= 3(t)×4(t).
(. 3.29), (t)=PI(t)+PII(t)-PI(t)PII(t) (t)=P1P2+P3P4 - P1P2P3P4= =
, l1=l2=l3=l4=l:
(t)=2×-2lt - -4lt
f(t)=4×l×-2lt - 4×l×-4lt
l1, l2 l3, l4, (. 3.30)
. 3.30
, .
Pi=e-lit, i=1, 2, 3, 4 (. 3.31).
. 3.31
. 3.31 . 3.28 , .
. 3.30 I II (. . 3.30) . 3.32.
. 3.32
I II I II:
I(t)=P1+P3 - P1P3 II(t)=P2+P4 - P2P4
I II (. 3.33).
. 3.33
. 3.33 (t) t.
(t)=I(t)×II(t)=(P1+P3 - P1P3)×(P2+P4 - P2P4)= P1P2+ P1P4+ P2P3+P3P4 - P1P2P3 - P1P2P4 - P1P3P4 - P2P3P4 + P1P2P3P4
(t)=
l:
(t)=42 43 + 4=4×-2lt - 4×-3lt + -4lt
4 ( l) , "" . , "" :
|
|
t=0,75 tH t=0,916 tH
t 22% "". , l1, l2, l3, l4.
(. 3.34)
I 1 2 3 4 I 1 2 3 4
II 1 2 II 1 2
III 3 4 III 3 4
IV 1 4
V 2 3
. 3.34 : t=0,75 tH, t=0,916 tH
I, II, III . IV V!. , l1, l2, l3, l4, , . .
, , (. 3.35)
. 3.35
(t)=23 6 (t)=(2 2)3= 83 124 + 65 6
. , , .
"" (. 3.36 ).
. 3.36
"" "", l l . l . 3.36 .
. t l1=l2=l3=l4=l=l, 1 5 (. . 3.37)
. 3.37
, , . :
5
NN | |||||
I II III IV V |
I-IV:
I=×P×P×P×P= 5
II=5××P×P×P×Q=5×4 ×(1-P)=5×P4-5×P5
III=8×P×P×P×Q×Q=8×3×Q2 =8×3×(1-P)2=8×P3 - 16×P4 - 8×P5
IV=2×P×P×Q×Q×Q=2×2×Q3 =2×2×(1-P)3=2×P2 + 6×P4 - 6×P3 - 2×P5
(t)= -lt, Q=1-P.
I, II, III, IV I, PII, PIII, PIV :
(t)= I + II + III + IV = 25 54 + 23 + 22
, 12,5% .
|
|
"" . l, "" l, t.
(t)= 4×P + 4×3 ×P (1-P) + 4 (1-P) + 4×3 (1-P)× (1-P) + 42 P (1-P)2 + 2×2 (1-P)2× (1-P) =
= 22 + 22×P 43×P + 24 ×P - 4 = 2e-2lt + 2e-(2l+2l)t - 4e-(3l+2l)t + 2e-(4l+l)t - e-4lt
l=0 . l¥ . , l=l tHc=0,816tH
"" () " " (). "" (. 3.38).
. 3.38
() (. 3.39).
. 3.39
:
( P(t))
"" ( Q0(t))
( Q(t))
, :
P(t) + Q0(t) + Q(t) = 1
1 "" 1 2 (. 3.40).
. 3.40
P(t), Qc(t), tHc P(t), Q0(t), Q(t) .
:
I 1 2;
II 1 2 ("");
III 2 1 ("");
Pc(t) = P(t)×P(t) + P(t)×Q0(t) + P(t)×Q0(t) = P2(t) + 2×P(t)×Q0(t)
Q(t) , . , Q0(t) = 1- P(t) - Q(t),
(t)= 2(t) 2(t) - 2(t)×Q(t)
Q(t)= 1 - 2(t) + 2(t) + 2(t)×Q(t)
Qp(t)=Pc(t)/ P(t)
:
Qp>1 Pc(t)> P(t)
=2+2Q0,
2+2Q0³P(t)
: +2Q0>1.
Q0(t) = 1- P(t) - Q(t) :
Q0(t) > Q(t)
, , "" , " ". , "" ( 3-4 ) .
"" , . "" , - (. 3.41)
|
|
. 3.41 -
k P(t), Q0(t), Q(t), m. , "" , , "" . , "" .
(. 3.41) :
Pc(t)=[ 1-Qk(t)]m - { 1-(1-Q0(t))k}m
- "" ( Q=Pc(t)/P>1)
Q+(1-Qk)m>(1-Q0)+{ 1-(1-Q0)k}m
, , . , , , .
N=2m+1 ( m=1, 2, 3, .) (), m+1 (. 3.42)
. 3.42
(t) l, (t). (t) 2m+1.
I II, 2m+1 , (. 3.43)
. 3.43
(. 3.44),
(t)=PI(t)×PII(t),
PI(t) I, PII(t) = P(t), P , , l.
. 3.44
PI(t) P(t)=exp{-lt} N. m=1 N=3.
I . 6.
6
3
NN | I | ||||
I II III |
I(t)=×P×P+3Q= 3 + 3P2(1-P)=P3+3P2 - 3P3=3P2 2P3
Q=1-P,
:
c(t)= I(t)×II(t)= 32×P 23×P = 3e-(2l+l)t - 2e-(3l+l)t
l=l =3e-3lt 2e-4lt;
m=2 N=5. I .7.
7
5
NN - | I | ||||
I II III IV |
I(t)=×P×P×P×P +5 P×P P×P Q + 10 P×P×P×Q×Q = 5 + 5P4(1-P) + 10P3(1-P)2 =6P5 - 15P4 + 10P3
1:
:
c(t)= I(t)×II(t)= 65×P 154×P + 103×P
P = exp {-lt},
|
|
c(t)= I(t)×II(t)= 66 155 + 104
, m N=2m+1, m=1,2,3 .8.
8
N=2m+1
NN | I | ||||
I II III i+1 m | N N-1 N-2 N-i m | i<m+1 N-m |
iN N i; , 0!=1, 1!=1.
I
I(t)=N + N PN-1×Q + + CiN×PN-i×Qi + +CmN×m×QN-m
Pc(t)=PI(t)×II(t)=N×P + N PN-1×Q×P + + CiN×PN-i×Qi×P + +CmN×m×QN-m×P
l=l,
Pc(t)=PI(t)×II(t)=N+1 + N PN×(1-) + + CiN×PN-i+1×(1-)i + +CmN×m+1×(1-)N-m
. S1, S3, S5 S7, , , l (t) ( . 9).
: Pc1, tH1; Pc3, tH3; Pc5, tH5, P7, t7.
. 9
9
N= 1, 3, 5, 7
N=1 | N=3 | N=5 | N=7 | |
tHc(N) , 8,8% 3 7. , ?
, (t).
, g=3, 5, 7
, : ( ) g(t)>1,
( ) g(t)<1,
g(t)º1 g(t)=1 ( ( 3, 5, 7 ) )
g(t) t g(t)><1 t.
:
P(t)=e-lt 1 0.
P(t0)=0,5 :
3(t0)=1, 5(t0)=1, 7(t0)=1
t<t0 P(t)>0.5 , 3(t)>1, 5(t)>1, 7(t)>1, tÎ[0, t0].
t>t0 P(t)<0.5 3(t)<1, 5(t)<1, 7(t)<1, tÎ[0, t0].
. 3.45 3.46.
3.45
3.46
, t, t<t0, P(t)>0.5, P(t), ( 8-9%) tH.
<0,5 ( ) P(t) P(t) ( 8-9%), .
, "" P(t)>0.5 m , . ( P(t)) .
(t), t. i () :
, ,
i i- , i=1, 2, ( i l i (t) λi , i (t)).
() , () t0, (). , .
, m λi, i (t); (t) t.
(t), t λi, :
, ,
, λi, t ( ). , :
,
ViP, Vit ΨiP, Ψit :
,
Ψit, Vit , .
m λi, i (t), i=1,m. (t), t t 0, 0< t 0<¥ λi i.
(t) m i, i=1,m:
(t)= f ( 1, 2, , i, , m).
Pc(t),
(t) t λi ( i) t 0 :
, ,
:
, ,
; , t 0 t.
.
m λi, (. 3.47).
. 3.47
m
:
li t:
,
,
, li, .
:
,
,
, ΨiP, Ψit , li .
l1, l2, l1 l2 (. 3.48) (t)= 1 + 2 1 2 =
,
li, t :
,
,
. 3.48
i,, l i.
l1¹l2 :
,
,
, l1=l2=l 1= 2= , :
, ,
, ,
- , . :
,
,
Dl i l i.
ViP, Vit .
3.3.
() .
, , .. , , . , .
:
,
,
,
.
. :
t,
Pc(t0)
t0, 0<t0<¥.
={t (t0)} : S ; (); L , , ..
=(S, , L)
S , : . S1 , S2 2 , .. , Sn n ( n - ).
Sj, 1<j<n, , , . Sj h, h=1,2,3,, dj, .. Sjh. S1 (. 3.49).
. 3.49 S1
S2 (. 3.50)
. 3.50 S2
S3 8 (. 3.51)
. 3.51 S3
, Sj j. 6-8 .
dj Sj. , , :
1. ;
2. ;
3. .
1 2 - S2 S21;
S3 S31 , S32, S35 ( 1 2).
2: - - S1, S2 d3 4- S3 (. 3.52):
. 3.52 S3
n (, , l - ) n l.
S , Sjh, j=1,2,,n; h=1,2,,dj, - (Sjh) Sjh.
. (Sjh) Sj Sjh, . , , S5 l , =1,2,3,4,5. . 10 , 1 5 t .
10
Pc | tc | |
5 | 0.200 | |
5p4-4p5 | 0.45 | |
6p5-15p4+10p3 | ||
-4p5+15p4-20p3+10p2 | ||
1-(1-p)5 |
, () , .. . - (S, , l), , (t0) tc .
l. , Sj, -
Lj(t)={ l1(t), l2(t),, lj(t)}
, , ,
Lj={l1, l2,, lg,,lj}
lg
- .
.
L* , . ( ), lg ,
.
, . k ( ) , k<3-5. lg (, (Sjh) S), ( , ).
(t0) t - I-
Sjh, j=1,2,, n, h=1,2,,dj
lgm, g=1,2,,j; ; m=1,2,,k
, (Sjh, lgm).
. lg, Sj dj:
n+ dj+, j=1,2, - () .
.