Читать книгу System Reliability Theory - Marvin Rausand - Страница 97

This section describes how a system function (SF) can be modeled by a reliability block diagram (RBD). An RBD is a success‐oriented graph with a single source (a) and a single terminal (b). The nodes of the RBD are called blocks or functional blocks. Each block represents a component function (or a combination of two or more functions). We assume that the blocks are numbered , where is known. This numbering is for convenience. In practical applications, a combination of letters and digits are often used to identify component functions. An RBD with blocks is called an RBD of order .

Each block is either functioning or failed, but the terms up and down are also used. Intermediate states are not allowed. To block (for ) is connected a binary state variable , defined as follows:

(2.1)

Observe that means that the specified function of block is up. It does not mean that all the functions of the component associated with block are up.

Blocks are drawn as squares or rectangles, as shown is Figure 2.8 for component function . Connection between the end points (a) and (b) in Figure 2.8 means that block is functioning (i.e. ). It is possible to enter more information into the block and include a brief description of the required component function. An example is shown in Figure 2.9, where the component is a safety shutdown valve that is installed in a pipeline. A label is used to identify the block.

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 .