3 1
.
 ,
| (1.1) |
n(t) - , t; N- , ; *(t) - .
 ,
| (1.2) |
N-n(t)- , t; q*(t) - .
 ,
| (1.3) |
n(t) - (t, t+t); f*(t) - ; t - e.
 ,
| (1.4) |
n(t)- , t; n(t) - (t, t+t); *(t)- .
 ,
| (1.5) |
ti - i- ; N- , ; mt* - .
mt* (1.5) N . mt*
 ,
| (1.6) |
ni - i- ;
t.i = (ti-1+ti)/2; m=tk/t; t=ti+1-ti; ti-1 - i- ; ti- i- ; tk - , ; t- .
 ,
| (1.7) |
Dt*- .
1.1. 1000 , 3000 . 80 . P*(t), q*(t) t = 3000 .
ee. N= 1000; n(t)=1000-80=920; N-n(t)=1000-920=80. (1.1) (1. 2)
1.2. 1000 . 3000 . 80 , 3000 - 4000 . 50 . 3000 - 4000 .
. N=1000; t=3000 ; t =1000 ; n(t)=50; n(t)=920.
(1.3) (1.4)
1/
1.3. N = 400 . t = 3000 200 , .. n(t) = 400-200=200. (t, t+t), t= 100 , 100 , .. n(t)= 100. *(3000),
|
|
|
P*(3100), f*(3000), *(3000).
. (1.1)
(1.3) (1.4),
(1/)
(1/)
1.4. 6 . ti (ti - 6 i- ): t1 =280 ; t2 = 350 ; t3 =400 ; t4 =320 ; t5 =380 ; t6 =330 .
.
. (1.5) 
.
1.5. 7 . :
t1 =12.; t2=23.; t3 =15.; t4=9.; t5=17.; t6=28.; t7=25.; t8=31. 
.
.
.
1.6. 45 45 , .1.1. m*.
1.1
| ti,. | ni | ti,. | ni | ti,. | ni |
| 0-5 | 30-35 | 60-65 | |||
| 5-10 | 35-40 | 65-70 | |||
| 10-15 | 40-45 | 70-75 | |||
| 15-20 | 45-50 | 75-80 | |||
| 20-25 | 50-55 | ||||
| 25-30 | 55-60 |
. 
(1.6),
.
1.7. 100 . 4000 . 50 . 4000 - 4100 . 20 . f*(t),*(t) t=4000 .
1.8. 100 .
4000 . 50 . p*(t) q*(t) t=4000 .
1.9. 1000 10 2. 1000 - 1100 . . f*(t), *(t) t =1000 .
1.10. 1000 . 3000 . 80 . 3000 - 4000 . 50 . p*(t) q*(t) t=4000 .
1.11. 1000 . t=1300 . 288 . 1300-1400 . 13 . p*(t) t=1300.
t=1400 .; f*(t), *(t) t =1300 .
1.12. 45 . t=60 . 35 . 60-65 . 3 . p*(t) t=60. t=65 .; f*(t), *(t) t =60 .
1.13. 45 , 80- , 45 , .1.2. mt*.
1.2.
| ti,. | ni | ti,. | ni | ti,. | ni |
| 0-10 | 30-40 | 60-70 | |||
| 10-20 | 40-50 | ||||
| 20-30 | 50-60 |
1.14. 8 . ti (ti - i- ):
t1 =560.; t2=700.; t3 =800.; t4=650.; t5=580.; t6=760.; t7=920.; t8=850.
|
|
|
.
1.15. 6 . : t1 =15.; t2=20.; t3 =10.; t4=28.; t5=22.; t6=30.
.
1.16. 1000 . t=11000 .
410 . 11000-12000 . 40 . p*(t) t=11000 . t=12000 ., f*(t), *(t) t=11000 .
3 2
.
,
(2.1)
(2.2)
(2.3)
(2.4)
(2.5)
p(t) - 0 t; q(t) - 0 t; f(t)- ;
(t)- c ; mt - .
(2.1) - (2.5)
 ;
| (2.6) |
 ;
| (2.7) |
 ;
| (2.8) |
 ;
| (2.9) |
 .
| (2.10) |
(2.1) - (2.5) 
|  ;
| (2.11) |
|  ;
| (2.12) |
 ;  ;
| (2.13) | |
 ,
| (2.14) |
(U) - ,
(0)=0; (2. 15)
(-U) =-(U); (2.16)
()=0.5. (2.17)
mt - ; t2 - ; - .
(2.1) - (2.5)
 ;
| (2.18) |
 ;
| (2.19) |
 ;
| (2.20) |
 ;
| (2.21) |
 ,
| (2.22) |
a,k - . (x) - - (2.1) - (2.5)
 ;
| (2.23) |
 ;
| (2.24) |
 ;
| (2.25) |
 ;
| (2.26) |
 ,
| (2.27) |
t - ; - .
.
2.1. =2.510-5 1/.
p(t),q(t),f(t),mt t=1000.
. (2.6), (2.7), (2.8), (2.10) p(t),q(t),f(t),mt.
1. :
.
.7.14 [ 1 ]
.
2. q(1000).
q(1000)=1-p(1000)=0.0247.
3.
; 
1/.
4.
.
2. 2. mt =8000 , t =2000 . p(t),f(t),(t),mt t=10000 .
. (2.11), (2.12), (2.13),(2.14) p(t), f(t), (t),mt.
1.
p(t)=0.5(U); U=(t-mt)/t;
U=(10000-8000)/2000=1; (1)=0.3413;
p(10000)=0.5-0.3413=0.1587. 2. f(t)
.
.
f(t)=(U)/t; U=(t-mt)/t 
;
f(1000)=(1)/2000=0.242/2000=12.110-5 1/.
3. (t)
(t)=f(t)/p(t);
(10000)=f(10000)/p(10000)=12.110-5 /0.1587=76.410-5 1/.
4.
mt = 8000 .
2.3. . p(t),f(t),(t),mt t=1000, t=1000 .
|
|
|
. (2.23), (2.25), (2.27),(2.26) p(t),f(t),
mt,(t).
1. p(t)
2. f(t)
f(t)=tp(t)/t2 ;
f(1000)=10000.606/10002=0.60610-3 1/.
3.
(t)= t/t 2;
(1000)=1000/10002 =10-3 1/.
4.
.
2.4. k=1.5; a=10-4 1/, t=100 . p(t),f(t),(t),mt.
. 1. p(t) (2.18).
p(t)=exp(-atk); p(100)=exp(-10-4 1001.5); x=1001.5;
lg x=1,5lg 100=3; x=1000; p(100)=e-0,1 =0,9048.
2. f(t)
f(t)=aktk-1 p(t);
f(100)=10-4 1,51000,5 0,90481,3510-3 1/.
3. (t)
(t)=f(t)/p(t);
(100)=f(100)/p(100)=1,3510-3 /0.90481,510-3 1/.
4. mt
.
z(z)=(z+1),
;
x=10-2,666;lg x=-2,666lg10=-2,666= 
; x=0,00215.
m t =0,90167/0,00215=426 .
2.5.
.
: p(t), (t),mt.
. 1. . (2.1)
1+ 2 
,
.
2.
.
3. . (2.5)
.
2.6. 120 0.9. , . t =120 ., .
2.7. 640 . , . 120 ., t=120 .
2.8.
mt = 8000 ., t =1000 . p(t), f(t), (t), mt t=8000 .
2.9. t= 1860 . (t), f(t),(t) t = 1000 .
2.10. =2,6; = 1,65*10-7 1/.
(t), f(t), (t) t=150 . .
2.11. t=1000 . (1000)=0,95. . f(t), (t), mt.
2.12. 1260 . . P(t), f(t), (t) t=1000 .
2.13. , f(t)=2e-t (1-e-t). P(t), (t), mt.
|
|
|
2.14. , P(t)=3e-t-3e-2t+e-3t.
P(t), (t), mt.
2.15. t = 1300 , mt=1500 . t= 100 .
3
.
, . , .
t
Pc(t) =P1(t)*P2(t)...Pn(t)= 
(3.1) i(t) - i- t.
i (t) =(t),
Pc(t)=Pn(t). (3.2)
(t) i(t) .
:
(3. 3)
(3.4)
(3.5)
i(t) - i- ; (t) - .
(0, t)
(3.6)
fc(t)
(3.7)
(3.8)
:
(3. 9)
. (3.10)
; (3.11)
; (3.12)
; (3.13)
; (3.14)
; (3.15)
; (3.16)
, (3.17)
mti - i - .
, . (t), , :
(3.18)
qi (t) -- i - .
.
3.1. . 1=0,16*10-3 1/ = const.
2=0,23*10-4t 1/, 3=0,06*10-6t2,6 1/.
100 .
. (3.3)
t=100
.
3.2. , : mt1=160 ; mt2 =320 ; mt3 = 600 .
. .
. (3.17)
i - i - . (3.11)
1/.
c - .
(3.16) :
.
3.3. 12600 , =0,32*10-6 1/. Pc(t), qc(t), fc(t), mtc, t=50 .
Pc(t) - t;
qc(t) - t;
fc(t) - T ;
mt - .
. (3.11)
= *n = 0,32*10-6*12600 = 4,032*10-3 1/.
(3.13)
(t) = e-ct; (50) = e-4,032*0,001*50 0,82.
(3.15)
qc(t)= 1- Pc(t) = cPc(t); qc(50)=1-Pc(50) 0,18.
(3.14)
fc(t) = ce-ct = cPc(t); fc(50) = 4,032*10-3*0,82 = 3,28*10-3 1/.
(3.16)
mt=1/c=1/4,032*10-3250 .
3.4. . t = 100 : 1(100) = 0,95; 2(100) = 0,97. . .
. :
(100)=1(100)*2(100)=0,95*0,97=0,92.
,
(t)=e-ct
(100)=0,92=e-c100 .
.7.14[1]
*1000,083 =0,83*10-3 1/.
mt=1/c=1/(0,83*10-3)=1200 .
3.5. t P(t) = 0,9997. , n = 100 .
|
|
|
. c(t)= Pn(t)=(0,9997)100.
c(t) , (3.18). q(t)=1-P(t)=1-0,9997=0,0003.
c(t) 1-nq(t)=1-100*0,0003=0,97.
..6. t c(t)=0,95. n= 120 . .
. , 
(t) , (t) (3.18).
qc(t)=1- c(t)=1-0,95=0,05.
3.7. 12600 , =0,32*10-6 1/.
t = 50 .
. (.11)
=*n=0,32*10-6*12600=4,032*10-3 1/.
(.13)
c(t)= -ct
c(50)= -4,032*0,001*50 0,82.
3.8. 2000 , = 0,33 * 10-5 1/.
t = 200 .
3.9. 200000 , =0,2 * 10-6 1/. t = 24
.
3.10. 6000 , . = 0,16*10-6 1/. t = 50 .
3.11. n = 5 . t, : P1(t)=0,98; P2(t)=0,99; P3(t)=0,998; P4(t)=0,975; P5(t)=0,985. .
3.12. , : mt1=83 ; mt2=220 ; mt3=280 ; mt4=400 ; mt5=700 . . .
.1. . t = 50 : P1(50)=0,98; P2(50)=0,99; P3(50)=0,998; P4(50)=0,975; P5(50)=0,985. . .
4
.
1,2,.... () . , , . qc(t)
(4.1)
qj(t) - j - .
(4.2)
j(t) - j - .
j(t) =(t), j = 0, 1,..., m,
(4.3)
(4.4)
, , n . .4.2. n . m, . . m.
( ).
j -
(4.5)
ij(t), j=0,1,2,...m; i=1,2,3,...,n - ij.
j -
. (4.6)
. (4.7)
. (4.8)
: , ..
ij(t)=Pi(t). (4.9)
(4.10)
(4.11)
, . .
Pi(t)=e-it. (4.12)
(5.10), (5.11)
qc(t)=(1-e-0t)m+1, (4.13)
Pc(t)=1-(1-e-0t)m+1, (4.14)
, (4.15)
0 - , n .
6
. (4.16)
(4.17)
, (4.18)
0 = 1/0 - .
.
4.1. 10 , mt = 1000 . , . mtc, fc(t) (t) t = 50 :
) ,
) .
.
)
,
- ; i - i - ; n = 10.
i=1/mti = 1/1000=0,001; i = 1,2,...,n; =i;
c=n=0,001*10=0,01 1/;
mtc=1/c=100 ;
fc(t)=c(t) Pc(t);
c(50)=c; Pc(t)=e-ct;
fc(50)=ce-ct=0,01*e-0,01*506*10-3 1/;
c(50)=0,01 1/.
) 
; m=1; 
;
; 0 =c =0.01 1/;
;
;
;
fc(50)4.810-3 1/; c(50)5.710-3 1/.
4.2. . =10-2 1/. (t) t=10 , mtc, fc(t), (t) .
. n=1; i=; 0=n=;m=1. (4.14)
(t)=1-(1-e-t)2;
(10)=1-(1-e-0,1)2.
e-0,1=0,9048.
c(10)=1-(1-0,9048)2 =1-0,095221-0,01=0,99.
mt. (4.4)
.
fc(t).
(t).
3 4.. n = 5000 . . (t) = 0,9 t =10 ., .
.
Pc(t)=1-(1-e-nt)2
Pc(t)=1-[1-Pn(t)]2,
P(t)=e-t.
(t) - .
1-[1-Pn(t)]20,9,
.
1/n ,
, P(t)= (-t)1-t,
1-t1-6,32*10-5
(6,32*10-5)/t=(6,32*10-5)/10=6,32*10-6 1/.
.
3 4.4. . : , . : 1= 4*10-4 1/; 2= 2,5*10-4 1/; 3= 3*10-4 1/. t=100 :
) ; ) .
4.5. .4.3. Pc(t), mtc, fc(t), c(t). , .
4.6. , (n = 3) . =5*10-4 1/. Pc(t), mtc, fc(t), c(t) .
4. 7. .4.4. (t). , .
4.8. I,II,III. : 1, 2, 3. Pc(t) :
) ;
) .
4.9. .4.5. , . : 1= 0,3*10-3 1/; 2= 0,7*10-3 1/. t = 100 c, , t=100 .
4.10. , , .
=2*10-3 1/, =1*10-3 1/, . .4.6. c(t), mt, fc(t), (t).
4.11. .4.7. , . , 1, 2.
4.12. n = 4000 . (t) = 0,9 t = 100 . , , : ) ; ) 6.
4.13. 6 . 6 y(ti) (0, ti) 0,9. , (0, ti)
: ) ; ) ; ) .
4.14. , 1=120,54*10-6 1/ 2=185,66*10-6 1/.
( 1 2) (..4.8). (t) , mt, fc(t) (t) . (t) t = 20 .
5
()
() .
.
. , .
(5.1)
(5.2)
1 - ; 0 - ; m - .
(5.3)
.
(5.4)
(5.5)
fc(t) .
(5.6).
(t) .
(5.7)
1 =0 () .
(5.8)
(5.9)
.
(5.10)
fc(t) .
(5.11)
(t) .
(5. 12)
.
5.1. 10 , mt = 1000 . , . (t), mt, fc(t) (t)
t = 50 :
) ,
) ( ).
:
) 
- , i - i - ; n = 10,
1/,
; pc(t)= 
;
fc(t)=c(t)pc(t); c(50)=c;
fc(50)=c =0.01e-0.0150610-3 1/;
c(50)=0.01 1/.
) mtc= 
; m=1;
mtc= 
=200 .
c(t)
0=,
Pc(t)=e-t(1+ct).
fc(t).
c (t).
c(t)= 
0 Pc(50), fc(50), c(50).
pc(50)=e-0.0150(1+0.0150)=e-0.51.5=0.60651.50.91,
fc(50)=0.01250e-0.0150=0.010.5e-0.5310-3 1/,
c(50)= 
1/.
5.2. 0=0,4*10-3 1/. , ( ).
1= 0,06*10-3 1/. t = 100 ., mt, fc(t) (t).
. m = 1. (5.),
;
; 
.
(5.13)
(5.13)
0.96[1+6.67-6.67(1-0.006)]0.998.
mt (5.4.).
= 
4668 .
fc(t).
= 
(5.13)
(t).
5.3. t=1000 . 0,95, . . (1000) = 0,95. , ( ). , , fc(t) (t) .
. m = 1. (5.9),
(5.14)
,
, (5.15)
(t)- ; 0 - .
(5.15)
P(1000)=e-o1000 =0,95.
.7.14 [1]
0*1000=0,051,
0=0,051/10000,5*10-4 1/.
(5.14)
Pc(1000)=0,95(1+0,05)=0,9975.
mtc (5.10).
mtc = (m+1)/0=2/0=2/(0,5*10-4) = 40000 .
,
mtc =1/0=20000 .
fc(t) (5.11).
(t).
.
5.4. . (.5.1). . Pc(t), mtc, fc(t), (t).
5.5. .5.2. Pc(t), fc(t), (t) . (t) t = 0.
5.6. .5.3, ,,, - . Pc(t) .
5.7. .5.4. Pc(t) .
5.8. (=8*10-3 1/) (0 = 8*10-4 1/). Pc(t), mtc. Pc(t) t = 20 .
5.9. 1, 2 3, . 0=10-3 1/. 1 2, 2 3. 0.. ,
Pc(t) , mtc . Pc(t) t=100 .
5.10. . mt= 200 . mtc : ) ; ) .
6
.
(.6.1.). .
i - .
; 
(6.1)
qij(t) - ij (0, t).
j- .
; 
, (6.2)
Pij(t) - ij
(0,t); mi - j- .
(6.3)
mi=m=const
Pij(t)=P(t); (6.4)
P
