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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Discrete-Time System under General Probability Distribution ◾ 65
Also, when k ≤ t,
P
(i, j)
(k, t) = 0. i, j = 1, 2, …, n and i ≤ j. (4.5)
4.3.2 Common Reliability Index
A group of common reliability index of series repairable systems composed of n
different units under discrete time is derived through the models (4.1 through 4.5)
in Section 4.3.1.
4.3.2.1 System Reliability
e reliability function or the reliability of the system is R(k) = P{X ≥ k}. Obviously,
R(0) = 1.
When k ≥ 1, the following formula can be obtained:
R(k) = P{Z(0) = … = Z(k) = (0, 0)}
= P{Z(0) = … = Z(k − 1) = (0, 0)} P{Z(k) = (0, 0)|Z(0) = … = Z(k − 1) = (0, 0)}
= R(k − 1) P{Z(k) = (0, 0)|Z(k − 1) = (0, 0)}
Rk
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tj
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=−−λ −λ
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