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A series-parallel system consists of m subsystems that are connected in series, with ni units connected in parallel in each subsystem, i=1,…,m. The reliability block diagram of a series-parallel system is shown in Figure 1.10.

Figure 1.10 Reliability block diagram of a series-parallel system.

Denote pij as the reliability of component j in subsystem i, 1≤i≤m, 1≤j≤ni. Let Pi be the reliability of the subsystem i, 1≤i≤m. First, the reliability of each subsystem is derived as for the parallel system, that is,

(1.51)

The reliability of the series-parallel system is, then,

(1.52)