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In a parallel system, the system functions or operates successfully when at least one component function is working. It implies that the failure of all components will cause the entire system to fail. The reliability block diagram of a parallel system is shown in Figure 1.9.

Figure 1.9 Reliability block diagram of a parallel system.

Denote Fs(t) as the probability of failure of the system. Denote Fi(t) as the probability of failure of component i. The system reliability can be expressed as

(1.49)

It follows that

(1.50)