System Reliability Theory. Marvin Rausand

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Figure 2.8 Component function shown as a block.

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 and .

      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 blocks are functioning. This means that the structure fails as soon as one block fails. The RBD of a series structure of blocks is shown in Figure 2.12. A path is seen to be available between the end points (a) and (b) – and the system is functioning – if and only if all the blocks are functioning. The system function can be represented by the Boolean expression: The series structure is functioning if block 1 AND block 2 AND AND block are all functioning. As mentioned above, the sequence of the blocks in Figure 2.12 is not important, and we might have drawn the RBD with the blocks in any sequence.

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 blocks is able to function. The RBD of a parallel structure is shown in Figure 2.13. For this structure, there are different paths between the end points (a) and (b). The structure is functioning if any one of these paths is functioning. This means that the structure is functioning if at least one of the blocks is functioning. The parallel structure can be represented by the Boolean expression: The parallel structure is functioning if block 1 OR block 2 OR block is functioning.

Figure 2.13 Parallel structure.

      2.8.4 Redundancy

      Redundancy is a means to improve the reliability of a structure. Redundancy may be defined as follows:

      Definition 2.9 (Redundancy)

      The provision of more than one means or parallel paths in a structure for performing a given function such that all means must fail before causing system failure.

      The parallel structure in Figure 2.13 has redundancy because all the blocks have to fail to cause the specified system failure, SF. Because blocks have to fail, the system is said to have redundancy of order Скачать книгу