In contrast to the analytical mode, the simulation mode takes into account repair and restoration actions, including behaviors of crews, spare part pools, throughput, etc. It can be used for highly complex scenarios involving a multitude of probabilistic events, such as corrective maintenance, preventive maintenance, inspections, imperfect repairs, crew response times, spare part availability, etc. These failure times are then combined in accordance with the way the components are reliability-wise arranged within the system. In the case of repairable systems, the failure distribution itself is not a sufficient measure of system performance, since it does not account for the repair distribution. to measure system reliability, outage rate goals, types of faults, and types of outages will be discussed. System reliability pertains to sustai interruptions and momentary interruptions. In this example, because the Weibull distribution is not a symmetrical distribution, the MTTFs do … First, identify the series and parallel sub -systems. What is the overall reliability of the system for a 100-hour mission? H��W�n[7�����p�c�ڭ��hA���ږ�Z\In���p��{�-Y�@ѡf㙅$(���[5�A�?ol�U��3^��v�b>�. Both of these methods will be explored in the chapters that follow. This does not necessarily mean that they cannot be repaired, but rather that it does not make economic sense to do so. applicable equations, terms and definitions along with an example of an Excel driven reliability calculator used to perform these calculations. Measurement 3. A new performance criterion called availability can be calculated, which accounts for both the failure and repair distributions. To accomplish this, the relationships between components are considered and decisions about the choice of components can be made to improve or optimize the overall system reliability, maintainability and/or availability. It is possible for each block in a particular RBD to be represented by its own reliability block diagram, depending on the level of detail in question. A reliability block diagram is a graphical representation of the components of the system and how they are reliability-wise related (connected). The overall results are analyzed in order to determine the behavior of the entire system. During this correct operation, no repair is required or performed, and the system adequately follows the defined performance specifications. for example Govil [ 1983] , Srinath [ 1985], Abdul Ameer [ 1998]. 1. It involves choosing a "key" component and then calculating the reliability of the system twice: once as if the key component failed (R=0) and once as if the key component succeeded (R=1). Ancillary analyses can be performed, such as optimized reliability allocation, reliability importance computation of components, etc. Power quality involves voltage fluctuations, abnormal waveforms, and harmonic distortions. The discrete event simulation also has the capabilities for: Examining resource usage, efficiency and costs. Each of these systems could have their own RBDs in which the blocks represent the subsystems of that particular system. It is calculated by dividing the total operating time of the asset by the number of failures over a given period of time. which is very reliable. 1.0 INTRODUCTION. These two probabilities are then combined to obtain the reliability of the system, since at any given time the key component will be failed or operating. Analyzing relationships between systems and components. Optimizing procedures and resource allocation. Case 1 - All three components are identical with times-to-failure that are described by a Weibull distribution with and hours. Analytical computations are discussed in RBDs and Analytical System Reliability and Time-Dependent System Reliability (Analytical). RBDs and Analytical System Reliability discusses RBDs and diagramming methods. A static block can be interpreted either as a block with a reliability value that is known only at a given time (but the block's entire distribution is unknown) or as a block with a probability of success that is constant with time. The level of granularity or detail that one chooses should be based on both the availability of data and on the lowest actionable item concept. As shown in the figure below, BlockSim includes two independent computation modes: analytical and simulation. Specifically, the components of the system are not repaired or replaced when they fail. They can also be used to describe the interrelation between the components and to define the system. The selection of this level (e.g., component, subassembly, assembly or system) determines the detail of the subsequent analysis. ]��B�F��$�˳W�_\����6���U?���������ں5sI����cB�#�z�� �{��������7��5�5�6��SjĀ6q�ݗ�3^���Y�U�� �6d=�B�����Dɟ�k���D��b���P�p!�`�M 0 fQ�0/�Ф �AV~"G�����"j����eĚqI��Bsm�Q��E� ��R|�Y�l���&�P�pd7z�lO Q�F �&��L��:W։B�"�WS% @���v8G���(�$�d���bIZ���Z���ؘ ���D�-i��8k�86ШO�&� �f'el�1S��Fd�2ӑ��3��n$f.-,fήf3s���jr��j�VZ�,���r���Ȭۨ)�ᶚ%���Ų@�j��T�nm�G� ��uGٯ�Z~���6��PG��/3)��mb�ds6۲q�'�@��%2�. Consider a system consisting of three components connected reliability-wise in series. When considering only the failure characteristics of the components, the analytical approach should be used. Fig. The official definition of reliability is "the probability of a device performing its intended function under given operating conditions and environments for a specified length of time." The reliability-wise arrangement of components is directly related to the derived mathematical description of the system. Both transient and permanent outages are included in the measurement of reliability. In repairable systems, two types of distributions are considered: failure distributions and repair distributions. There is a lack of repeatability in the results due to the random nature of data generation. The result is an analytical expression that describes the reliability of the system as a function of time based on the reliability functions of its components. Reliability (System) = R 1 x R 2 x R 3 x R 4 x ….R N; Reliability (Active Redundant Parallel System) = 1 – (1 – R 1)(1 – R 2) Now that the Reliability formulas are understood, the … Course material for the RCAM course on Reliability Evaluation of Electrical Power Systems 1 Reliability calculations for power networks Problem 1.1 Introduction to reliability calculations for power networks a) Explain the difference between primary and secondary failures in a power system. Static calculations can be performed both in the analytical mode and the simulation mode. Unfortunately, poor understanding of the relationship between a system and its constituent components can result in statements like this being accepted as factual, when in reality they are false. Availability. Examples of various types of distribution systems will show how outage rates can be reduced and system reliability improved by the application The RBD provides a visual representation of the way the blocks are reliability-wise arranged. However, when both the failure and maintenance characteristics need to be considered, the simulation method must be used to take into account the additional events. When the computer manufacturer finds out that the hard drive is not as reliable as it should be and decides not to try to improve the reliability of the current hard drive but rather to get a new hard drive supplier, then the lowest actionable item is the hard drive. This page was last edited on 5 January 2016, at 20:28. 2.2 The reliability of a system : it is probability that the system will The probability that a PC in a store is up and running for eight hours without crashing is 99%; this is referred as reliability. In other words, the analytical approach involves the determination of a mathematical expression that describes the reliability of the system in terms the reliabilities of its components. PNF - probability of no-failure operation of the element, unit or system. Failure data for this resistor can be obtained by performing in-house reliability tests and by observing the behavior of that type of resistor in the field. Reliability and Unavailability of a System The reliability of a system, which was defined in the previous section, describes the probability that the system is function­ ing for a specified period of time. Thecombined system is operational only if both Part X and Part Y are available.From this it follows that the combined availability is a product ofthe availability of the two parts. For example, if all components in a system must succeed in order for the system to succeed, the components will be arranged reliability-wise in series. Combination System Example 4: Find the reliability of the system shown on the next page. Because the failure properties of a component are best described by statistical distributions, the most commonly used life distributions are available in BlockSim. 1. 2. It should be noted that this may differ from how the components are physically connected. Availability is the likelihood that a system will provide service over the course of its lifetime. When events such as these are considered, analytical solutions become impossible when dealing with real systems of sufficient complexity. For example, Supplier 1's reliability at 10,000 miles is 36.79%, whereas Supplier 2's reliability at 10,000 miles is 50.92%. If the automobile is rendered inoperative when a component or subsystem fails, that component is typically repaired or replaced rather than purchasing a new automobile. Static analytical calculations are performed on RBDs that contain static blocks. [/math] . The hard drive supplier will then have actionable items inside the hard drive, and so forth. The parameters of that distribution represent the life distribution of that resistor block in the overall system RBD. The available distributions are: The same distributions are also available as repair distributions and in other probabilistic property windows that we will discuss later. Analyses that involve repairable systems with multiple additional events and/or other maintainability information are very difficult (if not impossible) to solve analytically. One of the most important is that in many situations it is easier and less expensive to test components/subsystems rather than entire systems. In system reliability analysis, one constructs a "System" model from these component models. the reliability of diesel engine using failure data. Why it’s important When you devise a set of questions or ratings that will be combined into an overall score, you have to make sure that all of the items really do reflect the same thing. These block properties can then be used to perform a variety of analyses on the overall system to predict and/or optimize the system's reliability, maintainability, availability, spare parts utilization, throughput, etc. The advantages of the analytical approach are: The disadvantage of the analytical approach is: Two types of analytical calculations can be performed using RBDs (and BlockSim): static reliability calculations and time-dependent reliability calculations. All three components have the same feasibility value of Moderate (5). The blocks are connected with direction lines that represent the reliability relationship between the blocks. There are many specific reasons for looking at component data to estimate the overall system reliability. To illustrate this concept, consider the aforementioned computer system shown earlier. 0,992 - incorrect format. In these cases, analysis through simulation becomes necessary. RELIABILITY . You can calculate internal consistency without repeating the test or involving other researchers, so it’s a good way of assessing reliability when you only have one data set. References: 1. For example, the following statement is not valid: All of the components in a system have a 90% reliability at a given time, thus the reliability of the system is 90% for that time. Systems can be generally classified into non-repairable and repairable systems. (For more information about these distributions, see Life Distributions.) These equations were built by analyzing a huge amount of field data over a long period of time. The time scale in BlockSim can assume any quantifiable time measure, such as years, months, hours, minutes or seconds, and also units that are not directly related to time, such as cycles or miles of use. For example, if F1 = 0.1 and F2 = 0.2, then R1 = 0.9 and R2 = 0.8 and R = 0.9 × 0.8 = 0.72. PNF enter with a dot, not a comma. The results are dependent on the number of simulations. %PDF-1.2 %���� As an example, let us assume a very simple system, consisting of … An automobile is an example of a repairable system. Remember also that [math]cdf(t)=1-R(t)\,\! An RBD of a simplified computer system with a redundant fan configuration is shown below. In life data analysis and accelerated life testing data analysis, as well as other testing activities, one of the primary objectives is to obtain a life distribution that describes the times-to-failure of a component, subassembly, assembly or system. Reliability follows an exponential failure law, which means that it reduces as the time duration considered for reliability calculations elapses. RBDs are constructed out of blocks. Let’s say we are interested in the reliability (probability of successful operation) over a year or 8,760 hours. This is a considerable difference in reliability. Conditional reliability, warranty time and other calculations can be performed. Improvement The following formula is for calculating the probability of failure. Difference between Reliability and Availability Let’s say a Car may break down and require … The advantages of the simulation approach are: The disadvantages of the simulation approach are: Simulation is discussed in the Repairable Systems Analysis Through Simulation and Throughput Analysis chapters. Systems can contain static blocks, time-dependent blocks or a mixture of the two. Once the data set has been obtained, the life distribution of a component/subsystem can be estimated using ReliaSoft's Weibull++ or ALTA software. A system is a collection of components, subsystems and/or assemblies arranged to a specific design in order to achieve desired functions with acceptable performance and reliability. Let’s say the motor driver board has a data sheet value for θ (commonly called MTBF) of 50,000 hours. Reliability Testing can be categorized into three segments, 1. Repairable systems and availability will be discussed in Introduction to Repairable Systems and Repairable Systems Analysis Through Simulation. In a reliability block diagram, such blocks represent the component, subsystem or assembly at its chosen black box level. In fact, the system's reliability function is that mathematical description (obtained using probabilistic methods) and it defines the system reliability in terms of the component reliabilities. Time-Dependent System Reliability (Analytical), Repairable Systems Analysis Through Simulation, https://www.reliawiki.com/index.php?title=Basics_of_System_Reliability_Analysis&oldid=62406, 1 and 2 parameter exponential distributions, 1, 2 and 3 parameter Weibull distributions, Mixed Weibull distribution (with 2, 3 or 4 subpopulations), Generalized-Gamma (i.e., G-Gamma) distribution, The mathematical expression for the system's. 12 0 obj << /Length 13 0 R /Filter /FlateDecode >> stream Fig 5 shows probability density function on basis of … Assume the objective reliability for the system is 90% for a mission time of 100 hours. Reliability is the likelihood that a system will continue to provide service without failure. Non-repairable systems are those that do not get repaired when they fail. Bazovsky, Igor, Reliability Theory and Practice 3. In simulation, random failure times from each component's failure distribution are generated. Subsystem 1 has a reliability of 99.5%, subsystem 2 has a reliability of 98.7% and subsystem 3 has a reliability of 97.3% for a mission of 100 hours. For example, consider a resistor that is part of a larger system to be analyzed. When used in this fashion, the block diagram is then referred to as a reliability block diagram (RBD). This module is suitable for reliability analysis of large-scale systems of general configurations. For any life data analysis, the analyst chooses a point at which no more detailed information about the object of analysis is known or needs to be considered. A system consisting of n components or subsystems, of which only k need to be functioning for system success, is called a “k-out-of-n” configuration. The following figure shows two blocks, one representing a resistor and one representing a computer. [/math] ) may be utilized. The resultant reliability of two components is R = R1 × R2. Taking the example of the AHU above, the calculation to determine MTBF is: 3,600 hours divided by 12 failures. The result is 300 operating hours. PNF 2 gearbox = 0.996. Example 7:Find the reliability of a system with three components, A, B, and C in parallel. Chapter 1: Basics of System Reliability Analysis, More Resources: BlockSim Examples Collection, Download Reference Book: System Analysis (*.pdf), Generate Reference Book: File may be more up-to-date. The analytical mode uses the exact reliability solutions for the system, employing the system's reliability function or cumulative density function (cdf). Each Reliability Prediction standard offers a set of mathematical formulas to model and calculate the failure rate of a variety of electromechanical components that make up a product or system. If using failure rate, lamb… If one includes information on the repair and maintenance characteristics of the components and resources available in the system, other information can also be analyzed/obtained, such as system availability, throughput, spare parts usage, life costs, etc. Block diagrams are widely used in engineering and science and exist in many different forms. In other words in system reliability analysis we are concerned with the construction of a model (life distribution) that represents the times-to-failure of the entire system based on the life distributions of the components, subassemblies and/or assemblies ("black boxes") from which it is composed, as illustrated in the figure below. Using this definition, the probability of a device working for 100 hours and the reliability of a device designed to work for 100 hours are two ways to make the same statement. 3 shows the failure rate but failure rate is not constant due to repairable system it may increase, constant or decreasing. 1 0 0004 0 9996 1 1 0 95 1 0 92 1 0 90 1 1 1 1 2 13..) ()()() = − = = − − − − R p = − −r −r −r Graunt studied the probability of survival for humans to different ages [Graunt, 1662, p. 75]. This could continue down through many levels of detail, all the way down to the level of the most basic components (e.g., fasteners), if so desired. The mathematical description of the system is the key to the determination of the reliability of the system. These chapters also offer derivations of needed equations and present examples. The reliability function for the exponential distributionis: R(t)=e−t╱θ=e−λt Setting θ to 50,000 hours and time, t, to 8,760 hours we find: R(t)=e−8,760╱50,000=0.839 Thus the reliability at one year is 83.9%. MTBF is a basic measure of an asset’s reliability. This can be accomplished through discrete event simulation. A variety of online tools and calculators for system reliability engineering, including redundancy calculators, MTBF calculators, reliability prediction for electrical and mechanical components, simulation tools, sparing analysis tools, reliability growth planning and tracking, reliability calculators for probability distributions, Weibull analysis and maintainability analysis calculations. For example, for a system of three units (n=3), with one unit required (m=1) for success and two units that are cold standby spares (n-m=2): The first term represents the probability of no failures, the second term the probability of exactly one failure (requiring one switching action) and the third term the probability of two failures (requiring a second switching action). For example, repairing a four-year-old microwave oven is economically unreasonable, since the repair would cost approximately as much as purchasing a new unit. After defining the properties of each block in a system, the blocks can then be connected in a reliability-wise manner to create a reliability block diagram for the system. In the same manner, other types of information can also be obtained that can be used to define other block properties, such as the time-to-repair distribution (by analyzing the times-to-repair of each block instead of the times-to-failure), other maintenance requirements, throughput properties, etc. Statistical Background, RBDs and Analytical System Reliability and Time-Dependent System Reliability (Analytical) discuss this further. Modeling 2. Calculation of reliability for serial connection of elements. The first examples of reliability calculations and estimates can be found in the investigations of John Graunt in 1662. If one of two components must succeed in order for the system to succeed, those two components will be arranged reliability-wise in parallel. On the other hand, repairable systems are those that get repaired when they fail. A block is usually represented in the diagram by a rectangle. As stated above, two parts X and Y are considered to be operating in series iffailure of either of the parts results in failure of the combination. Most household products, for example, are non-repairable. At that point, the analyst treats the object of analysis as a "black box." This information will allow the reliability engineer to characterize the life distribution of each component. Data can be obtained from different sources, including: Additionally, component life data may also be provided by the manufacturer or supplier of the component/subsystem. Time-dependent analysis looks at reliability as a function of time. In other words, this diagram demonstrates the effect of the success or failure of a component on the success or failure of the system. In the analytical (or algebraic analysis) approach, the system's pdf is obtained analytically from each component's failure distribution using probability theory. An interruption of greater than five minutes is generally considered a reliability issue, and interruptions of less than five minutes are a … Example: Calculating Reliability of a Series System Three subsystems are reliability-wise in series and make up a system. Calculate the system reliability. For example, in an RBD of a car, the top level blocks could represent the major systems of the car, as illustrated in the figure below. 2.Some Definition and Concepts 2.1 Complex System: is a collection of devices or subsystem interconnected to fulfill complex operation . This is done by repairing or replacing the failed components in the system. Having segmented a product or process into parts, the first step in evaluating the reliability of a system is to obtain life/event data concerning each component/subsystem (i.e., each block). 2. Using the above formula and setting the reliability of each element at 0.9, we find. Where, R = Reliability as a function of time (sometimes shown as R(t)) e = Euler’s constant (≈ 2.71828) λ = Failure rate (assumed to be a constant during the useful life period) t = Time Knowing that failure rate is the mathematical reciprocal of mean time between failures (MTBF), we may re-write this equation in terms of MTBF as a “time constant” (τ ) for random failures during the useful life period: The probability of failure has increased to 1 – 0.72 = … See Mettas . In many of the discussions and examples that follow, and to maintain generality, time units may be omitted or a general time unit ( [math]tu\,\! In other words, reliability of a system will be high at its initial state of operation and gradually reduce to its lowest magnitude over time. It’s expensive to add redundant parts to a system, yet in some cases, it is the right solution to create a system that meets the reliability requirements. For such a system, k is less than n. An example of such a system might be an air traffic control system with n displays of which k must operate to meet the system reliability requirement. Example for data entry: PNF 1 engine = 0.995. The following figure illustrates a static RBD. It is very important to remember that even though any time unit may be used, the time units used throughout an analysis must be consistent in order to avoid incorrect results. MIL-HDBK-338, Electronic Reliability Design Handbook, 15 Oct 84 2. As shown below, a life distribution is then fitted to the data and the parameters are obtained. A repair distribution describes the time it takes to repair a component (time-to-repair instead of time-to-failure). BlockSim can resolve even the most complex systems analytically and this method should be used when one is performing reliability analysis. Considering only the failure characteristics of the system adequately follows the defined performance.... 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