January 2016
Intermediate to advanced
300 pages
6h 54m
English
book
Fluctuation Mechanism and Control on System Instantaneous Availability
by Yi Yang, Yong-Li Yu, Li-Chao Wang
Content preview from Fluctuation Mechanism and Control on System Instantaneous Availability
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50 ◾ System Instantaneous Availability
Prove: e following formula can be obtained according to definitions of
reliability and mean time to the first failure of system:
R(k) = P{X > k} = P{Z(k) = Z(k − 1) = … = Z(0) = 0}.
In other words, R(k) = P
0
(k, k).
…
……
TE
XjPZ Zj Zj
jP ZZjPZj ZZj
jP jj
M
j
j
j
010, 1
0101|0
10
01,1
1
1
0
1
∑
∑
∑
{}
{}
{}
() ()
() () ()
()
() ()
() ()
()
== == −= =
===−==== −=
=λ −−
=
∞
=
∞
=
∞
4.1.2.2 System Availability
Definition 4.3: e probability that the system is in normal status at the time of k
is defined as instantaneous availability; that is,
A(k) = P{X(k) = 0}.
eorem 4.2: e model established in Section 4.1.1 is used to obtain follow-
ing formula:
∑
=
=
() (,
)
0
0
Ak Pkj
j
k
.
Prove: Use the probability analysis method according to the definition of ...
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