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 Updating the Classic Reliability Block Diagram Methodology and Constructs Reliability block diagrams (RBDs) have been around for a long time, and have been widely used to model systems. A reliability block diagram is a graphical representation of how the components of a system are reliability-wise connected. As with any approach or methodology, reliability block diagrams have their advantages as well as disadvantages compared to competing methods. Some of these disadvantages are rooted in the basic elements and constructs used in a reliability block diagram. The constructs in the reliability block diagram methodology have not changed since its inception. This is unlike many other techniques/methodologies that have gone through multiple revisions and changes to improve upon their original capabilities (e.g., consider the improvements to the HTML markup language as the methodology has matured). In order to address some of the current inadequacies in reliability block diagrams, perhaps it is time to revise the standard to make the methodology easier to use and also more effective. This article reviews some of the existing techniques and introduces some new constructs to the tried and true reliability block diagram approach. Series, Parallel and Series Parallel Combination Configurations The simplest and most elementary configurations of an RBD are the series and parallel configurations. Items placed in series must all work for the system to work, as shown in Figure 1, where the system fails if either A, B or C fails. Items placed in parallel are considered to be redundant, as shown in Figure 2, where either D or B can fail and the system will continue to function. The concept can be expanded further, as shown in Figure 3, with combinations of series and parallel configurations in the same diagram. These elementary configurations form the basis of the reliability block diagram constructs. Figure 1: Series Configuration   Figure 2: Parallel Configuration   Figure 3: Combination of Series and Parallel Configurations Complex Configurations If one takes the approach a step further, “Complex” block diagrams can be created. “Complex” diagrams cannot be expressed as a simple combination of series and parallel blocks (such as the diagram in Figure 3) and thus require a more advanced analytical treatment. A network is a good example of system requiring a “Complex” reliability block diagram and Figure 4 illustrates an example of this RBD type. Figure 4: Complex System Configuration k-out-of-n Nodes The creation of reliability block diagrams with series, parallel, combination and complex configurations required the use of blocks and lines only. To extend the functionality of a block diagram, one needs to introduce some additional elements to the “tool kit.” One such element is the k-out-of-n node, which allows the analyst to specify an alternative form of redundancy known as k-out-of-n redundancy. A k-out-of-n node can have n paths leading into it, and requires that k of those n paths must function for the system to function. Figures 5 and 6 present RBDs that incorporate such nodes. The configuration in Figure 5 includes a k-out-of-n node where either B, C or D must operate for the system to function but any two of the other items may fail without causing system failure. With the traditional reliability block diagram methodology, k-out-of-n redundancy could have been specified for units drawn in parallel. However, with the introduction of the node element in the diagram, one can specify such redundancy for complex configurations, such as the one shown in Figure 6. Figure 5: k-out-of-n Node Configuration   Figure 6: Complex Configuration with 2-out-of-5 Node Standby Containers A Standby Container can be used to represent items configured with standby redundancy. Standby redundancy configurations consist of items that are inactive and available to be called into service when/if the active item fails (i.e., on standby). A container block, with other blocks inside, is utilized to better achieve and streamline the representation and analysis of standby configurations. The container serves a dual purpose. The first purpose is to clearly delineate and define the standby relationships between the active unit(s) and standby unit(s). The second purpose is to serve as the manager of the switching process. For this purpose, the container can be defined with its own probabilities of successfully activating standby units when needed. Figure 7 includes a standby container with three items in standby configuration where one component is active while the other two components are idle. One block within the container must be operating or, because the container block is part of a series configuration, the system will fail. Figure 7: Configuration with Standby Container Load Share Containers The container concept can be expanded to also represent load sharing configurations. As the name implies, load sharing configurations consist of a components that are in load sharing redundancy. Units in load sharing redundancy exhibit different failure characteristics when one or more fail. In Figure 8, units 1, 2 and 3 are in a load share container and have their own failure characteristics. All three must fail for the container to fail. However, as individual items fail, the failure characteristics of the remaining units change since they now have to carry a higher load to compensate for the failed ones. Figure 8: Configuration with Load Share Container In addition to Standby and Load Share containers, other new types of blocks can be used to increase the versatility of reliability block diagram constructions and facilitate more rapid creation of diagrams that are easier to read. These include Subdiagram Blocks, Multi Blocks and Mirror Blocks, which are described next. Subdiagram Blocks to Represent Inheritance A Subdiagram Block inherits some or all of its properties from another block diagram. This allows the analyst to maintain separate diagrams for portions of a system and incorporate those diagrams as components of another diagram. With this technique, it is possible to generate and analyze extremely complex diagrams representing the behavior of many subsystems, subsubsystems etc. in a manageable way. In Figure 9, Subdiagram Block A in the top diagram represents the series configuration of the subsystem reflected in the middle diagram, while Subdiagram Block G in the middle diagram represents the series configuration of the subsubsystem in the bottom diagram. Figure 9: Subdiagram Blocks to Represent Inheritance Multi Blocks to Save Time and Space By using Multi Blocks, a single block can represent multiple identical blocks in series or in parallel configuration. This technique is simply a way to save time when creating the RBD and to save space within the diagram. Each item represented by a Multi Block is a separate entity with identical reliability characteristics to the others. However, each item is not rendered individually within the diagram. In other words, if the RBD contains a Multi Block that represents three identical components in a series configuration, then each of those components fails according to the same failure distribution but each component may fail at different times. Because the items are arranged reliability-wise in series, if one of those components fails, then the Multi Block fails. It is also possible to define a Multi Block with multiple identical components arranged reliability-wise in parallel or k-out-of-n redundancy. Mirror Blocks to Simulate Bi-Directional Paths While Multi Blocks allow the analyst to represent multiple items with a single block in the RBD, Mirror Blocks can be used to represent a single item with more than one block placed in multiple locations within the diagram. Mirror Blocks can be used to simulate bi-directional paths within a diagram. For example, in a reliability block diagram for a communications system where the lines can operate in two directions, the use of Mirror Blocks will facilitate realistic simulations for the system maintainability and availability. It may also be appropriate to use this type of block if the component performs more than one function and the failure to perform each function has a different reliability-wise impact on the system. Conclusion As this article demonstrates, it is possible to update and expand the techniques available for reliability block diagrams in order to increase the effectiveness of the analysis tool and also improve the ease of creation and appearance of the diagrams. The proposed enhancements to the methodology include complex configurations, k-out-of-n nodes, Standby and Load Sharing containers, Subdiagram Blocks to represent inheritance from other diagrams, Multi Blocks to represent multiple identical blocks and Mirror Blocks to represent the same block in multiple locations within the diagram. ReliaSoft’s BlockSim 6 software supports all of the standard RBD techniques as well as the enhancements discussed in this article. On the Web at http://www.ReliaSoft.com/blocksim.

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