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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
70 System Instantaneous Availability
Obviously, B
1
B
2
. en, P{B
1
} = P{B
2
} P{B
1
|B
2
}. And
P{B
1
} = P
1
(k + 1, j + 1)
P{B
2
} = P
1
(k, j)
P{B
1
|B
2
} = 1 − μ
1
( j).
us,
P
1
(k + 1, j + 1) = P
1
(k, j)(1 − μ
1
(j)), j k.
Similarly,
P
2
(k + 1, j + 1) = P
2
(k, j)(1 − μ
2
(j)), j k
P
0
(k + 1, j + 1) = P
0
(k, j)(1 − λ(j)), j min(T
0
− 1, k).
us, Formula 4.6 is proven.
When the unit has worked normally and continuously for T
0
time, preventive
maintenance is carried out for the system. us, the probability that the unit is
continuously in 0 status for j(> T
0
) unit time is zero. According to the definition of
P
0
(k, j), P
0
(k, j) = 0 and j > T
0
. us, Formula 4.7 is proven.
Because
P
0
(k + 1, 0) = P{Z(k + 1) = 0, Z(k) 0}
= P{Z(k + 1) = 0, Z(k) = 1} + P{Z(k + 1 ...
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Publisher Resources

ISBN: 9781498734684