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Fluctuation Mechanism and Control on System Instantaneous Availability
book

Fluctuation Mechanism and Control on System Instantaneous Availability

by Yi Yang, Yong-Li Yu, Li-Chao Wang
January 2016
Intermediate to advanced content levelIntermediate to advanced
299 pages
6h 54m
English
CRC Press
Content preview from Fluctuation Mechanism and Control on System Instantaneous Availability
96 System Instantaneous Availability
5.3.2 Stability Proving of Instantaneous Availability
According to features of matrix B and initial value P(0), the following conclusions
are set up.
eorem 5.10: e status of systems (5.8 and 5.9) only exists in finite set C,
in which,
)
(
=
=≤
=+++
++++++
C
Zzzz
Zz
innn
nnn
T
nn
ni
,,...,
|1
,0 1,
1, 2,..., 3
12 33,0
123
123123
.
Prove: Because
))
((
δ+ =
++++++
Pk BP kk
nnnnnn
1,
0, 1, 2,
...
3,03,0
123123
, for
matrix B, obviously,
B
nn
nn
nn
δ=δ
++
++
++3,
03,0
123123
.
us,
Pk Pk P
nnnnnn nnn
() ()
()
δ+ ==δ=
++++++ +++
1 ...
01
3,03,0 3,0
123123 123
.
en, for arbitrary nonnegative integer k, the status
()
()
=
++
,
12, ..., 2
12
Pk
pp p
nn
T
satisfies
()
δ=
=
+++
=
+++
1
3,0
1
3
123
123
Pk p
nn
ni
i
nnn
. (5.11)
According to definitions of failure rate, repa
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Publisher Resources

ISBN: 9781498734684