Reliability Block Diagram

A Reliability Block Diagram (RBD) is a method of graphically showing probability combinations. A drawing is done with boxes representing the components of a system. An RBD is quite effective for two-state reliability problems. Two-state means that the system has two operational states, success and failure. 

Although the two-state method could be used for multiple state problems such as safety instrumented systems, most find the technique confusing and error prone for such problems. The RBD technique is presented briefly here in order to build understanding of system reliability modeling. 

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A reliability block diagram can be developed for the system from the definition of adequate performance. The block diagram represents the effect of subsystem or component failure on system performance. In this preliminary analysis, each subsystem is assumed to be either a success or failure. A rehabihty value is assigned to each subsystem where the appHcation and a specified time period are given. The reUabiUty values for each subsystem and the functional block diagram are the basis for the analysis. 

A Reliability Block Diagram (RBD - ANSl/lEEE Std 352-1975) while laid out similarly to a flow diagram, represents the components as a series of interconnecting blocks. Com identified by the block labeling. System B in Figure 3 4.1-1 is shown as an RBD in Fig It is customai y to draw RBDs with the source on the left and the sink on the rij unquantified, RBDs are useful because they show the system s logic and how it can fail... 

Cutset means one combination of component failures that fail the system It 3d to have originated as cuts across the flow in reliability block diagrams . In Figure 3,4 3-1, Dugh... 

Reliability block diagram Model and evaluation of component.s or systems Quantitative... 

Activities during System Life 3.1. Reliability Block Diagram 1933... 

To analyze and measure the reliability and maintainability characteristics of a system, there must be a mathematical model of the system that shows the functional relationships among all the components, the subsystems, and the overil system. The reliability of the system is a function of the reliabilities of its components. A system reliability model consists of some combination of a reliability block diagram or cause-consequence chart, a definition of all equipment failure and repair distributions, and a statement of spare and repair strategies (Kapur 1996a). All reliability analyses and optimizations are made on these conceptual mathematical models of the system. 

A reliability block diagram is obtained from a careful analysis of the manner in which the system operates. An analysis has to be done of the effects on overall system performance of failures of the various components the support environment and constraints, including such factors as the number and assignment of spare parts and repairpersons and the mission for the system. 

The reliability block diagrams for many systems cannot be represented by the preceding three configurations. In general, the concept of coherent systems can be used to determine the reliability of any system (Barlow and Proschan 1975). The performance of each of the n components in the system is represented by a binary indicator variable, which takes the value 1 if the ith component functions and 0 if the ith component fails. Similarly, the binary variable 0 indicates the state of the system, and 0 is a function of x = (xj,. . . , xj. 

System reliability models, 1932-1937 fault tree analysis, 1936-1937 reliability block diagram, 1933-1936 Systems for Integrating Manufacturing... 

IEC 61078 and Annex B of IEC 61508-6 illustrate the reliability block diagram technique for calculating the probabilities of failure for safety instrumented functions designed in accordance with IEC 61511-4-ANSI/ISA-84.00.01-2004 Parti (IEC 61511-1 Modi and this standard. 

Reliability block diagrams (RBDs) are similar to block flow diagrams (BFDs) (described in Chapter 16). A BFD shows the flow of gases, liquids, and solids through the process. An RBD illustrates the flow of reliability from the front of the plant to the back. 

Figure 5-1. Reliability Block Diagram Showing Successful System With One Failed Component...

Figure 5-2. Reliability Block Diagram—Series System...

Figure 5-3. Reliability Block Diagram for Example Problem 5-1...

Figure 5-4. Reliability Block Diagram—Parallel System...

Comparison of the Reliability Block Diagram and the Fault Tree... 

A system has a series reliability block diagram as follows ... 

A system has a the reliability block diagram shown below. Availability of AC power = 0.99, Availability of the motor = 0.98 A B... 

A system has four components with the reliability block diagram shown below. If the power supply has a one-year reliability of 0.95 and the controller has a one-year reliability of 0.99, what is the system reliability for one year ... 

Fault Trees and Reliability Block Diagrams are both methods of showing probability combinations. There have been a number of solution techniques developed to solve probability combinations. These include Cut Sets, Tie sets. Event Space, Decomposition Method, Gate Solution Method, and many others. In this appendix three examples will be shown - the Event Space method and the Cut Set method, and the Gate Solution Method. Details and full development of the methods can be found in (Ref. 1) Chapter 5. 

Consider the example of a 2oo3 redundant power supply system as shown in Figure C-1. The system consists of three diverse power supplies each capable of providing 100 watts of power. The total load on the system is 175 watts. Therefore, the system can be successful in delivering 175 watts if only two of the three power subsystems are available. The fault tree for this system is shown in Figure C-2 and a reliability block diagram is shown in Figure C-3. 

To solve the fault tree or the reliability block diagram via the event space method one creates a list of all combinations of successful and failed components. For each line in the list, the probability is listed and the system operation (success or failure) is listed. By convention, this is done by quantity of failed units. 

The "Cut Set" method was named from the reliability block diagram. Notice in Figure C-3 that if one "cuts" across a set of blocks in parallel that the system fails. The reliability block diagram is draw in the "cut set" style to show those cut sets. 

Solution A fault tree can be drawn to show the probability combinations for failure to indicate a fire. A fault tree is a good tool to use for the problem compared to a reliability block diagram as this problem focuses on one failure mode, failure to indicate a fire. (Another failure mode might be false indication of a fire.) The fault tree is shown in Figure C-4. 

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