11.3 Parallel systems
11.3.1 Two component system
Consider initially the case of a two component system for which the relevant state space diagram is shown in Figure 10.2. the probability of the system begin in the down state is given by Equation 10.7d, i.e.,
(11.12)
In this case the failure rate λp and repair rate μp of a single components in parallel is required. This is illustrated in figure 11.2
Fig. 11.2 Representation of a two component parallel system
The probability of the single component begin in the down state is
(11.13)
Since Equations 11.12 and 11.13 must be identical
(11.14)