The physical structural arrangement, even though clearly related to the reliability-wise arrangement, is not necessarily identical to it. Not every element of a system has to achieve high-reliability performance when not effectively making any different to the overall system reliability. It is clear that the highest value for the system's reliability was achieved when the reliability of Component 3, which is the most reliable component, was increased. The representative reliability block diagram for mode B is shown in Figure 5. Therefore it is important to know the system and how the model works. Reliability Block Diagrams Overview A reliability block diagram is a graphical and mathematical model of the elements of a system permitting the calculation of system reliability given the reliability of the elements. When this posts I should be just getting home from Nepal jet lag is no place to write posts.
In this simple drawing, there are n components in parallel and any one component is needed for the system to function. In real life, most systems or processes are not that simple and require a different level or type of models, often used in combination with other types. Subsystem 1 has a reliability of 99. This can be removed, yielding: Symbolic Solutions in BlockSim Several algebraic solutions in BlockSim were used in the prior examples. The exponential pdf is given by: And its mean is equal to: Therefore: The Arrhenius-exponential pdf can then be obtained by setting: The Arrhenius-exponential pdf is then represented by the following: Once the life-stress relationship has been established, we need to define the stresses loads. Similarly, by increasing the reliabilities of Components 2 and 3 in the third and fourth rows by a value of 10% while keeping the reliabilities of the other components at the given values, we can observe the effect of each component's reliability on the overall system reliability. Due to the lag time to assume the function, and the fact that standby equipment is not always properly maintained, the modeling of standby equipment can become complicated A standby block will typically have sub-blocks, but only one of the sub-blocks operates during the block operation.
Component Configurations In order to construct a reliability block diagram, the reliability-wise configuration of the components must be determined. Air Force for use with the Minuteman system. It can be seen that Component 1 has the steepest slope, which indicates that an increase in the reliability of Component 1 will result in a higher increase in the reliability of the system. This reference is also available online at. In mirrored blocks, the duplicate block behaves in the exact same way that the original block does.
The number K designate K 1 is the minimal number of failed sub blocks defining the block failure. This is illustrated in the following example. The probability of success for the system reliability can now be expressed as: This equation for the reliability of the system can be reduced to: or: If all three hard drives had the same reliability, , then the equation for the reliability of the system could be further reduced to: Or, using the binomial approach: The example can be repeated using BlockSim. BlockSim uses a 64K memory buffer for displaying equations. Each block represents a component of the system with a. There are a few different Reliability calculations for the system that requires x amount of y parallel branches to operate, and they are in the table below.
The system fails if both A and B fail. In the following table, we can examine the effect of each component's reliability on the overall system reliability. Note that since , the system equation above, can be reduced to: This is equivalent to. After the replacement, the new block is available for operation, and the replaced failed block may be discarded or repaired. Events T1 and T2 are more likely to occur in an older component than a newer product i. Subsystem 1 has a reliability of 99. The method is illustrated with the following example.
Block Conditioning Event A specific condition or restriction that can apply to any gate. Block that cannot fail or that is in a failed state. Such systems can be analyzed by calculating the reliabilities for the individual series and parallel sections and then combining them in the appropriate manner. Not all of the parameters need to be entered; some can be calculated from others. Selecting Unit 3 as the key component, the system reliability is: If Unit 3 survives, then: That is, since Unit 3 represents half of the parallel section of the system, then as long as it is operating, the entire system operates.
There is a saying that a chain is only as strong as its weakest link. Modes D, E and F have constant rates of occurrence exponential distribution with mean times of occurrence of 200,000, 175,000 and 500,000 hours, respectively. The first row of the table shows the given reliability for each component and the corresponding system reliability for these values. It is also possible to define a multi block with multiple identical components arranged reliability-wise in parallel or k-out-of- n redundancy. The reliability equation, as obtained from BlockSim is: The BlockSim equation includes the node reliability term which cannot fail, or. Likewise, a traditional fault tree cannot take into account both of the probabilities in a true standby configuration: the probability of occurrence when active and when on standby dormant, quiescent, inactive.
The system in the figure above cannot be broken down into a group of series and parallel systems. Doing so yields , shown next. The aspect of a self-correcting mode will be discussed in an upcoming Hotwire article. It is a basic event that does not need further resolution. Table 1: System Reliability for Combinations of Component Reliabilities This conclusion can also be illustrated graphically, as shown in the following figure.
To model this, you can think of a scenario similar to standby redundancy. In the following table, we can examine the effect of each component's reliability on the overall system reliability. To ensure that the equipment design is capable or yielding our requirements an analysis needs to be performed on the design to ensure the system or process can deliver. It is assumed that events S1 and S2 each have a constant rate of occurrence with a probability of occurrence of 1 in 10,000 and 1 in 20,000, respectively, in a single year 8760 hours. When considering the reliability of a system, the arrangement matters. This type of a configuration is also referred to as a complex system. Effect of the number of components in a parallel configuration Combination of Series and Parallel While many smaller systems can be accurately represented by either a simple series or parallel configuration, there may be larger systems that involve both series and parallel configurations in the overall system.
Unless explicitly stated, the components will be assumed to be statistically independent. This does not mean they are physically parallel in all cases , as capacitors in parallel provide a specific behavior in the circuit and if one capacitor fails that system might fail. This figure also demonstrates the dramatic effect that the number of components has on the system's reliability, particularly when the component reliability is low. Units 1 and 2 are connected in series and Unit 3 is connected in parallel with the first two, as shown in the next figure. For this equation, you need the reliability or probability of success given the primary unit has failed. It is clear that the highest value for the system's reliability was achieved when the reliability of Component 1, which is the least reliable component, was increased by a value of 10%.