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### 8 Reliability block diagrams

A reliability block diagram (RBD) is a diagrammatic method for showing how component reliability contributes to the success or failure of a complex system. A RBD is drawn as a series of blocks connected in parallel or series configuration. Each block represents a component of the system with a failure rate. Parallel paths are redundant, meaning that all of the parallel paths must fail for the parallel network to fail. (Compare [Wikipedia])

Mathematically, a (standard) reliability block diagram is just a negated fault tree, only consisting of AND and OR gates: Parallel paths in a RBD represent redundancies, i. e. they are equivalent to conjunctions (AND-gates) in a fault tree, whereas serial connections are represented by OR-gates.

Consequently in Functional Safety Suite a reliability block diagram is internally represented by fault tree data, and evaluated according to fault tree rules. Thus all characteristics and options described in section 7 apply for reliability block diagrams as well, except of a few deviations explained hereafter.

#### 8.1 Conjunctions Properties Panel

Figure 50: Changing the type of a conjunction in a reliability block diagram

Since in Functional Safety Suite a reliability block diagram is internally represented by a fault tree, even the additional conjunction types Inhibit (only the 2-input variant), PAND and Combination can be used in an reliability block diagram. These types of conjunctions are indicated by INH, PRIO or the number of paths that must fail on top of the vertical line on the right side of the block(s) that are children of this gate, see figure 50.

NOT-gates, Reduced Combination gates and 3-input Inhibit gates are not allowed in reliability block diagrams, but this is only because graphical representation would be very inconvenient for most readers and therefore potentially misleading. If you need those conjunction types, you should use a fault tree instead.

Unfortunately providing different types of conjunctions goes along with a graphical problem in RBDs, see section 8.4.

#### 8.2 Transfer-In gates

Also Transfer-In gates can be used in reliability block diagrams. However since gates are only indicated as lines in reliability block diagrams, Transfer-In gates have to be shown as blocks, i. e. similar to basic events. Therefore in order to create a Transfer-In gate, first add a new block, then convert the block to a Transfer-In gate by Edit – Convert to Transfer-In. The properties panel will change so that you can select the referred model, see figure 51. The reference of the Transfer-In gate can either be another reliability block diagram or another fault tree.

Figure 51: Representation and properties of a Transfer-In gate

Note that in contrary to fault trees, the reference will always be the top event of the referred reliability block diagram or fault tree.

#### 8.3 Editing of reliability block diagrams

Create a reliability block diagram by File – New Model. Select a name and package for the new reliability block diagram that will be created. Finally a simple reliability block diagram, consisting of one block only, is created.

Create a new generic basic event by Library – New Generic Basic Event. Usually you should create the generic basic event in the local package, which hence is the default location.

Click on the block to select it.

Add a new block referring to the latest generic basic event by Edit – Add Block Serial or Edit – Add Block Parallel. You can select any other existing generic basic event by selecting it via its name and package.

Multiple blocks can be selected by drawing up a selection rectangle by pressing the left mouse button and pulling the mouse, or by clicking on multiple blocks while pressing the left mouse button.

The sequence of blocks in a series can be changed by ‘Shift+→’ and ‘Shift+←’, the sequence of parallel blocks can be changed by ‘Shift+↑’ and ‘Shift+↓’. You can select one or multiple blocks for moving.

A single block or a selection of multiple blocks can be deleted with the ‘Delete’ key.

If you want to assign a new (not yet existing) generic basic event to an existing block, select Library – New Generic Basic Event. The name of the block will change to the name of the new generic basic event, showing that it now refers to the new generic basic event.

You can copy or cut selections of one or multiple blocks by pressing ‘Ctrl+C’ or ‘Ctrl+X’. The selection saved like this can be pasted by Edit – Paste Serial or Edit – Paste Parallel. ’Ctrl+V’ is equivalent to Edit – Paste Serial. Don’t forget to change the suffixes when coping blocks if necessary.

#### 8.4 NULL blocks

In a standard RBD, it is impossible that two “AND-gates” are directly linked, i. e. that one is the parent gate of the other, because the two “And-gates” would just be merged to one.

However if we have different types of conjunctions following each other, e. g. an Inhibit and a normal And, we have to distinguish the “gates” graphically. This is done by introducing NULL blocks, see figure 52. A NULL block is a generic basic event with no failure rate (h = 0) and no unavailability (Q = 0).

In figure 52 the Inhibit conjunction is OR’ed with the NULL block just in order to put it below an AND conjunction. Mathematically the NULL block has no effect of course.

Figure 52: The NULL block

If you need to add a NULL block, you’ll find it in the global library.

When deleting blocks in a serial structure, a NULL block is automatically inserted where necessary. When converting a fault tree to a reliability block diagram, NULL blocks are automatically inserted where necessary as well. However even this automatism doesn’t guarantee that you will always be able to visually distinguish all different combination gates in some structures. Therefore you should be careful using combination gates different from AND, or prefer using a fault tree instead.

#### 8.5 Pro’s and Con’s of RBDs versus FTAs

Pro’s RBD:

- Block diagrams are obviously a good method to present the structure of a system. This is why they are used in thousands of variants, in all fields of engineering and even other sciences.

Con’s RBD:

- A technical system doesn’t consist of “series” and “parallel” structures only, but other structures (such as enabling/disabling components) are not supported by (standard) RBD’s.
- The RBD only shows the logical structure (and even this only as long as it is similar to the physical structure) on global level. There is no way of describing the behavior or functionality of a group of components in the RBD, because the “gates” are not explicitly shown and therefore no descriptions can be added to the “gates”.
- When using different types of conjunction gates, it isn’t automatically safeguarded that you will actually see the different types. Therefore if you want to use conjunction gates different from AND, you should use a fault tree.

Pro’s FTA:

- The “top-down” approach allows to analyze even very complex systems, without increasing the risk of introducing errors in the structure. This approach is supported (or even only enabled) by the explicit presentation of gates, allowing for additional intermediate descriptions.
- The explicit presentation of gates allows nice graphical representation of additional gate types.

Con’s FTA:

- More abstract than a block diagram, thus the structure is not immediately visible.

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