System Reliability Theory. Marvin Rausand
Parallel or redundant paths can be installed for a single block, for a selection of blocks, or for the entire system function, SF.
For hardware, redundancy may be achieved by installing one or more extra hardware items in parallel with the initial item. The redundant items may be identical or diverse. Adding redundancy increases the cost and makes the system more complicated, but if the cost of failure is high, redundancy is often an attractive option.
2.8.5 Voted Structure
A
A 2oo3 voted structure is shown in Figure 2.14. Two different diagrams are shown. The diagram to the left is a physical diagram that shows the 2oo3 logic, whereas the RBD to the right is a series–parallel structure. In the RBD, we see that the system is functioning when block 1 AND block 2 are functioning OR block 1 AND block 3 are functioning OR block 2 AND block 3 are functioning. Observe that each block appears in two different places in this RBD. This shows that an RBD is not a physical layout diagram, but a logical graph illustrating the specified function of the system.
Figure 2.14 Voted structure 2oo3, (left) a physical diagram and (right) an RBD.
2.8.6 Standby Structure
Redundancy may either be active, in which case the redundant items operate simultaneously in performing the same function (as for the parallel structure), or standby, such that the redundant items are only activated when the primary item fails. With standby redundancy, the standby items may be in cold standby or in partly loaded standby. With cold standby, the redundant item is considered to be as‐good‐as‐new when activated. With partly loaded standby, the item may be failed or worn when activated.
A simple standby structure with two blocks is shown in Figure 2.15. Initially, block 1 is functioning. When block 1 fails, a signal is sent to the switch
Figure 2.15 Standby structure.
2.8.7 More Complicated Structures
Many of the structures, we study in this book, can be represented by a series–parallel RBD. A simple example of such a structure is shown in Figure 2.16.
Figure 2.16 RBD for a series–parallel structure.
Remark 2.2 (Series–parallel structures)
The term series–parallel structure is not used in the same way by all authors. Some authors use the term to describe a series structure, where one or more of the blocks have added redundancy, that is, have parallel paths. The same authors use the term “parallel‐series structure” to describe a parallel structure where two or more blocks appear in at least one of the parallel paths. In this book, we use the term series–parallel structure to describe a structure, where the blocks are arranged in any combination of series and parallel structures (as indicated in Figure 2.16).
2.8.8 Two Different System Functions
The fact that different system functions give rise to different RBDs is illustrated in Example 2.2.
Example 2.2 (Pipeline with safety valves)
Consider a pipeline with two independent safety valves
Figure 2.17 Two safety valves in a pipeline: (a) physical layout, (b) RBD for the safety barrier function, and (c) RBD for spurious closure.
The two blocks in Figure 2.17b represent the valve function “stop flow” for valve 1 and 2, respectively. This means that each valve is able to close and stop the flow in the pipeline. To achieve the system function “stop flow,” it is sufficient that at least one of the individual valves can “stop flow.” The associated RBD is therefore a parallel structure with respect to the system function “stop flow.”
The valves may close spuriously, that is, without a control signal, and stop the flow in the pipeline. The two blocks in Figure 2.17c represent the valve function