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Each block is either functioning or failed, but the terms up and down are also used. Intermediate states are not allowed. To block
(2.1)
Observe that
Blocks are drawn as squares or rectangles, as shown is Figure 2.8 for component function
Figure 2.8 Component function
Figure 2.9 Alternative representation of the block in Figure 2.8
An RBD with three blocks representing a system function, SF, is shown in Figure 2.10. The system function, SF, is up if block 1 is functioning and either block 2, block 3, or both are functioning.
Figure 2.10 A simple reliability block diagram with three blocks.
The blocks in Figure 2.10 are connected by arcs. Arcs are also called edges. The arcs are not directed, but directed arcs may sometimes be used to clarify the logic of the diagram. The system function, SF, is up if there exists a path from (a) to (b) through functioning blocks, otherwise, it is down. The RBD in Figure 2.10 is seen to have two paths
System Structure
The RBD is not a physical layout diagram of the system, but a logic diagram that shows how and when the system function, SF, is up. The sequence of failures is not important, and the RBD in Figure 2.10 is therefore equivalent to the RBD in Figure 2.11. The RBD shows the structure of the system with respect to a specified system function, SF. When discussing RBD, we talk about the structure instead of the system. Separate RBDs have to be established for each system function.
Figure 2.11 An alternative, and identical, version of the RBD in Figure 2.10.
Boolean Representation
Arranging several components along a path means connecting them by an AND‐ operation and arranging several components in parallel paths represents and OR‐operation. In essence, a RBD is a graphical representation of a Boolean expression. Boolean expressions are discussed further in Section 4.6. The system function SF in Figure 2.10 is seen to be up if block 1 is up AND block 2 OR block 3 is up.
2.8.2 Series Structure
A series structure is functioning if and only if all the
Figure 2.12 RBD for a series structure.
2.8.3 Parallel Structure
A parallel structure is functioning as long as at least one of its
