By E. Hinton, et al.,
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5 A union of n non-disjoint events. According to the inclusion–exclusion expansion formula, the probabilities of all single events are first added. However, this means that the probability of the intersections of any pair of events has been added twice and should therefore be subtracted. Next, the probabilities of all intersections of two events are subtracted from the previous result. tex 28/9/2006 16: 24 Page 37 37 3. Methods for Analysis of Complex Reliability Networks these operations however, the contribution of the intersection of any three events has been added 3 times by adding the probabilities of the single events and subsequently subtracted 3 times by subtracting the probabilities of the twofold intersections.
The SC component in Fig. 16(c) is a cold standby component. Its description requires specifying the cumulative distribution of the time to failure FO (t) and FC (t) for the basic failure modes of the switch (failed open and failed closed), and the number n of switched in standby components characterised by n cumulative distributions of the times to failure. The SW component in Fig. 16(d) is a warm standby component. While the life of a cold standby component starts to be consumed only after the component has been switched in, for a warm standby component, its life starts to be consumed immediately after installing it (this also applies to the hot standby component SH in Fig.
2 Reliability associated with 2 years operation as a function of the size (order) of the system of type ‘quasicomplete graph’. 5 × 75 × (75 − 1) − 1 = 2774), the computational time remains in the range of few seconds. With increasing the size of the system of type ‘almost-complete graph’, reliability increases monotonically. With increasing the size of the system however, the rate of the reliability increase diminishes significantly.
Analysis and Optimization of Prismatic and Axisymmetric Shell Structs. by E. Hinton, et al.,