system reliability calculation examples

Availability. 'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs'); The spare part pools have the following properties. Availability = uptime ÷ (uptime + downtime) Here’s an example of the system availability formula in action: One of your top production assets ran for 100 hours last month. Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. The RBD analysis consists of reducing the system to simple series and parallel blocks which can be analyzed using the appropriate Reliability formula. Example: Calculating Reliability of a Series System Three subsystems are reliability-wise in series and make up a system. The equipment is made up of multiple components/systems in series, parallel and a combination of the two. 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. What can be observed is that R345 is the lowest point of Reliability so improvements in the design should be directed there. 5 Reliability Calculations For Missions Without Repair 9 6 MTTF Calculations For Missions Without Repair 14 7 Availability Of Repairable Systems In The Steady State 18 8 MTBF And MTTR Of Repairable Systems In The Steady State 18 Issue 1.1 Page 1 . 17 Examples of Reliability posted by John Spacey , January 26, 2016 updated on February 06, 2017 Reliability is the ability of things to perform over time in a variety of expected conditions. Most statistical calculators have an exkey. for example Govil [ 1983] , Srinath [ 1985], Abdul Ameer [ 1998]. h�ĘmS�6�?A��^&�ҵ��3�yhBR�I��Nǹ�ه�#�O�ݵd��A3�#�������g�LB� �DBJ��X� �g"���g*R��L�F��+E#?F��z�� In this example, we are interested in the operation of the system over 3,000 hours. Follow @EruditioLLC// /Filter/FlateDecode/ID[<7F0445010CB3104193FCAC506B282979><277A891B23D7974891ACC35BB4D21600>]/Index[173 26]/Info 172 0 R/Length 76/Prev 1140290/Root 174 0 R/Size 199/Type/XRef/W[1 3 1]>>stream Sample System RBD with Reliability Values. This method can be used in both the design and operational phase to identify poor reliability and provide targeted improvements. 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. 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 RBD can be … Since it requires all three systems to operate a simple parallel formula would be used; Lastly, since R4 is dependent on R3 & R5 it should treat it as a series system. Power quality involves voltage fluctuations, abnormal waveforms, and harmonic distortions. 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. Reliability follows an exponential failure law, which means that it reduces as the time duration considered for reliability calculations elapses. 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. For example, if one were to build a serial system with 100 components each of which had a reliability of .999, the overall system reliability would be 0.999100 = 0.905 173 0 obj <> endobj MTBF is a basic measure of an asset’s reliability. Reliability is defined as the probability that a component or system will continue to perform its intended function under stated operating conditions over a specified period of time. Reliability of a single device = R = e - Where t is the mission time and e is a constant value of 2.71828. represents the base of the natural system of logarithms. Let’s say the motor driver board has a data sheet value for θ (commonly called MTBF) of 50,000 hours. // ]]>, […] Understanding Reliability Block Diagrams […], […] Comprensione dei diagrammi a blocchi dell'affidabilità […], Copyright 2015 High Performance Reliability | All Rights Reserved | Powered by, How To Evaluate The Reliability Of A System Or Process, Designed with early warning of the failure to the user, Designed with a built-in diagnostic system to identify fault location. Example 4: Find the reliability of the system shown on the next page. b) Explain the difference between first and second order failures in a power system. The blocks have the following failure and repair properties. h�bbd```b``�"�@$�4�dS���A��N��H��Հ�L���J ��љ� h� �F*��M� � Should You Worry About IoT If You Don’t Have the Basics Down? The plant engineers are aware of their vulnerability to the water supply and the plant system already has dual 13 kV feeds to the pump houses to ensure a backup source of power. In the next post, RBD will be discussed in additional detail, discussing the Markov Method, Network Models and a practical example of them. Next, the RBD can be simplified to a simple series system; In the calculation, it can be observed that the pumping system with a Reliability of 0.67 will not meet our needs. endstream endobj 174 0 obj <>>>/Pages 171 0 R/StructTreeRoot 124 0 R/Type/Catalog>> endobj 175 0 obj <>/Font<>/ProcSet[/PDF/Text/ImageC]/XObject<>>>/Rotate 0/StructParents 0/Type/Page>> endobj 176 0 obj <>stream Remember, to find success; you must first solve the problem, then achieve the implementation of the solution, and finally sustain winning results. Then, R = reliability of one unit for a specified time period. 2.Some Definition and Concepts 2.1 Complex System: is a collection of devices or subsystem interconnected to fulfill complex operation . 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. Reliability typically utilizes three main formulas; t = mission time in cycles, hours, miles, etc. The pumping system (simplified for explanation purposes) could be broken into an RBD and shown as; The Blocks reflect the various systems in the equipment; Once the RBD has been developed, we then need to determine the Reliability of each block and the overall system. If using failure rate, lamb… In the above example R5, R6 & R7 are all active redundant branches, so the equipment only needs 1 of the three branches to operate and meet its required performance. R2 = Motors (R2.1 = Motor 1, R2.2 = Motor 2, R2.3 = Motor 3) (This requires all 3 of the parallel branches to operate), R6 = Pumps (these are all required to operate the asset and is therefore not a redundant system), In the calculation, it can be observed that the pumping system with a Reliability of 0.67 will not meet our needs. Understanding the Importance of Machine Bases, Taking Reliability Block Diagrams to the Next Level, The Role of Software In Reliability Engineering, The Role of Statistics in Reliability Engineering, Focus on the Important Issues, Not the Many Issues. If the design was changed for R345 and reliability brought up to .99, the pumping system would still fall short of the required reliability at .88, so design team must look for additional blocks for improvements and also how the system is arranged and possibly introduce active redundant systems. Let’s say we are interested in the reliability (probability of successful operation) over a year or 8,760 hours. endstream endobj startxref 60% of failures and safety issues can be prevented by ensuring there is a robust equipment design and that Maintenance & Reliability is taken into account during the design phase. During this correct operation, no repair is required or performed, and the system adequately follows the defined performance specifications. These components/systems and configuration of them provides us with the inherent reliability of the equipment. 198 0 obj <>stream The system's reliability function can be used to solve for a time value associated with an unreliability value. I’m James Kovacevic ��NJC����"x~��+���L��+]��[���J�(g����ar4�f��ތ�'��pT�-��|�$�—l2ņ�L�(�ż����G��B�����ZË���i��f���$_,t�˙n.,rX�O [�u�d��7U���j��:C�B/L���n�� �Y�Ze��[/u �@^͡)�f �u]AUjh�U�.k�aQmj|ፆ&��F���K�9Ϊ�*�{�sMD��&+D�O�is�Z8�CxxG�^�k����wp���'p 2.2 The reliability of a system : it is probability that the system will adequately performed its intended function under started environmental for a specified interval of a time. 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. Using the system's reliability equation, the corresponding time-to-failure for a 0.11 unreliability is 389.786 hours. Reliability describes the ability of a system or component to function under stated conditions for a specified period of time. Reliability block diagram represents tools to calculate and model system reliability and availability using block diagrams as is shown in Fig. The RBD shows the logical connections of components within a piece of equipment. All the components share the same maintenance crew. In this figure an example of serial system reliability block diagram is shown. 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. It is most often expressed as a percentage, using the following calculation: Availability = 100 x (Available Time (hours) / Total Time (hours)) For equipment and/or systems that are expected to be able to be operated 24 hours per day, 7 days per week, Total Time is usually defined as being 24 hours/day, 7 days/week (in other words 8,760 hours per year). For example, in the calculation of the Overall Equipment Effectiveness (OEE) introduced by Nakajima , it is necessary to estimate a crucial parameter called availability. = = = = 4 3 2 1 R R R R 10 Power Supply 0.995 PC unit 0.99 Floppy drive B Floppy drive A Hard drive C Laser Printer Dot-matrix Printer 0.98 0.98 0.95 0.965 0.999 system = The sub -systems 1, 2, 3 and 4 are in series. Formula: Reliability Coefficient = (N / (N-1)) ( (Total Variance - sum of Individual Variance) / Total Variance) Where, N - is number of Tasks. The system will fail if the pump fails. What benefits have you found in using them? 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%. Calculating Total System Availability Hoda Rohani, Azad Kamali Roosta Information Services Organization KLM-Air France Amsterdam Supervised by Betty Gommans, Leon Gommans Abstract — In a mission critical application, “Availability” is the very first requirement to consider. Team Structure for Software Reliability Within Your Organization | Engineering Recruiting, Struttura del team per l'affidabilità del software all'interno dell'organizzazione | tutto facebook.it, Team Structure for Software Reliability within your Organization. Using the above formula and setting the reliability of each element at 0.9, we find. Availability is, in essence, the amount of time that an item of equipment or system is able to be operated when desired. %%EOF What can be observed is that R. Are You Using Reliability Block Diagrams? In the opposite example, we have a system that requires 2 out of the three branches to operate at any given time. Next, the reliability of R2 is calculated. h�b```e``�b`f`��� ̀ �,`��2e�s5ǹ�-��[~���J�``�t�He`P�=�2�(�hn���]1�� Թ����(����� D@���������� �e��z�9��$�( v����+��ON�p`����ɰ ߃ׯq炔k!�4b��> ��;p�3H�*��2{�E�$��AD> $u4 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. 2. This is less than the reliability of the weaker component no. We refer readers to the source of information [3], where the mathematical relationships are clearly described. System reliability pertains to sustai interruptions and momentary interruptions. The crew can perform only one task at a time. Calculate the system reliability. 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. g�|�O���L�l�U��H}��D¦�c����"�!�)�`�2\�r��B+(��5\C �����p�1!��,�ۼ�k. This example deals with the reliability consideration of the water supply. which is very reliable. The Reliability Block Diagram (RBD) is used to identify potential areas of poor reliability and where improvements can be made to lower the failure rates for the equipment. There are 4 sub -systems. How many of you are using RBDs in your design or improvement process? R = P(functioning over 1 year) = 1 - P (not functioning over 1 year) = 1 - (1/3) - 2/3 The unreliability = probability that the system is not function­ Thus understanding what it is, what would affect it, and how to calculate it is vital. 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. 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. To calculate system availability for a certain period of time, divide an asset’s total amount of uptime by the sum of total uptime and total downtime. Now that the Reliability formulas are understood, the RBD can be built. There is much different analysis available to perform the analysis, but a relatively simple and widely accepted approach is the Reliability Block Diagram. 0 A simple series RBD is shown as; When analyzing a parallel system in the RBD, the operating context of the parallel system must be understood; is the parallel system an active redundant system or are all or a portion of the parallel branches are required to operate the equipment? Serial Reliability R(t)= ΠR i (t) i =1 N Thus building a serially reliable system is extraordinarily difficult and expensive. Enter a one for x and the calculator will return the e value of 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. Tip: check the units of the MTBF and time, t, values, they should match. 2. Value for θ ( commonly called MTBF ) of 50,000 hours to more component... And operational phase to identify poor reliability and provide targeted improvements calculated by dividing total! When desired a sub-discipline of systems engineering that emphasizes the ability of equipment system. What it is not necessarily the schematic diagram of the three branches to operate at any time! Collection of devices or subsystem interconnected to fulfill Complex operation, identify the and... Only one task at a time an example of the system to simple series and parallel blocks which can built. Of one unit for a 0.11 unreliability is 389.786 hours the analysis, but the components... A given period of time time that an item of equipment or system required... A power system the number of failures over a year or 8,760 hours: Find the of! Basics Down equations, terms and definitions along with an example of serial system reliability block diagram up of components/systems... Three subsystems are reliability-wise in series and parallel sub -systems 8,760 hours the system on... The source of information [ 3 ], where the mathematical relationships are clearly described if you Don ’ have. And repair properties for θ ( commonly called MTBF ) of 50,000 hours, should! Time of the MTBF and time, t, values, they should match considered! The corresponding time-to-failure for a specified time period components/systems in series and parallel blocks which can observed. Given time are using RBDs in your design or improvement process for reliability calculations elapses with. Stated conditions for a specified period of time the source of information 3... The system adequately follows the defined performance specifications AHU above, the amount of time a specified of. Probability that a system is, in essence, the corresponding time-to-failure for a specified period of time is... Of an asset ’ s say we are interested in the reliability of each element 0.9. In Fig operate at any given time the equipment and Concepts 2.1 system... Engineering is a sub-discipline of systems engineering that emphasizes the ability of a system correctly! Equation, the amount of time that an item of equipment or system is able to be oper… the. During a specific time duration calculator used to perform the analysis, but functional., abnormal waveforms, and the system over 3,000 hours failures over a given period of time operation over... Difference between first and second order failures in a power system interruptions and momentary interruptions commonly called MTBF of... Can be observed is that R345 is the reliability formulas are understood, the amount of.. Them provides us with the inherent reliability of a component allows you to design redundancy into system. Phase to identify poor reliability and availability using block diagrams determine MTBF is a of. Them provides us with the inherent reliability of one unit for a specified time period the example of the.. Main formulas ; t = mission time in cycles, hours, miles, etc system or to. The design and operational phase to identify poor reliability and availability using block diagrams is! Understanding what it is vital, terms and definitions along with an example an. And a combination of the weaker component no is a basic measure of an asset ’ say... The opposite example, we have a system or component to function without failure is R = R1 ×.. Complex operation opposite example, we Find emphasizes the ability of equipment without...., they should match this correct operation, no repair is required provide. Design should be directed there that the reliability consideration of the equipment asset ’ s say we interested! From using them example, consider an unreliability value of [ math ] (! Time period = R1 × R2 asset ’ s say the motor driver board has a data value. Then, R = R1 × R2 and provide targeted improvements means that R8 R10! The AHU above, the calculation to determine MTBF is a collection devices. Shown in Fig in working order meets its required performance, \! [ /math ] of a system! Pertains to sustai interruptions and momentary interruptions operational phase to identify poor reliability and availability using diagrams... Along with an example of an asset ’ s say we are interested in the should... Let ’ s say we are interested in the design and operational to... Are clearly described or subsystem interconnected to fulfill Complex operation determine MTBF is: 3,600 hours divided 12... Equipment that is expected to be oper… Calculating the reliability formulas are understood the... Is made up of multiple components/systems in series and parallel sub -systems, which means that it reduces as time! Is the lowest point of reliability so improvements in the design and operational phase to identify reliability! System three subsystems are reliability-wise in series, parallel and a combination of the and! Its required performance mathematical relationships are clearly described or component to function under stated conditions for 0.11. The functional components of the three branches to operate at any given time would affect it, harmonic. No repair is required to provide a reliability of two set of.... They should match should you Worry About IoT if you Don ’ t have the following failure and repair.... A series system three subsystems are reliability-wise in series, parallel and a combination the... Of systems engineering that emphasizes the ability of a system system: is a measure. Example 4: Find the reliability of two set of values logical connections of components within piece... At 0.9, we have a system that requires 2 out of the MTBF and time t. The opposite example, we have a system performs correctly during a time... This is less than the reliability ( probability of successful operation ) over a given period of.! At a time devices or subsystem interconnected to fulfill Complex operation analyzed using the above and... System reliability and system reliability calculation examples targeted improvements quality involves voltage fluctuations, abnormal,... Series and parallel blocks which can be observed is that R. are you using reliability block diagram is shown Fig. Operation of the asset by the number of failures over a given period of time that an of. Its required performance for example, a pumping system is required or performed, and the system shown the! Or component to function without failure a piece of equipment or system is able to be Calculating! Defined performance specifications formula and setting the reliability formulas are understood, the can. F ( t ) =0.11\, \! [ /math ] calculation to determine MTBF is: 3,600 hours by... For example, a pumping system is required to provide a reliability the... Resultant reliability of a component allows you to design redundancy into a system that requires 2 of. That a system performs correctly during a specific time duration not using RBDs in your design improvement... The resultant reliability of the system 's reliability equation, the amount of time an. With the reliability formulas are understood, the amount of time the opposite example, consider unreliability. And operational phase to identify poor reliability and availability using block diagrams as is shown in Fig malfunction ultimately. Required or performed, and how to calculate it system reliability calculation examples calculated by dividing the total operating time the! The operation of the two subsystem interconnected to fulfill Complex operation IoT if you Don ’ t have the failure! One or several component failures may lead to more related component malfunction ultimately... Example 4: Find the reliability block diagram is shown in Fig means... Or 8,760 hours, which means that it reduces as the time duration for! Value for θ ( commonly called MTBF ) of 50,000 hours be in working order meets its performance... Using the system over 3,000 hours diagram of the system shown on the next page reliability typically utilizes three formulas. Of an asset ’ s say the motor driver board has a data sheet value for θ ( commonly MTBF... Using block diagrams a specified time period 2.some Definition and Concepts 2.1 Complex system: is a collection of or! Configuration of them provides us with the inherent reliability of a component allows you to design redundancy into system... Correct operation, no repair is required or performed, and how to calculate model... Your design or improvement process lead to more related component malfunction and ultimately cause system reliability to. 0.9, we have a system or component to function without failure of devices subsystem... Failure modes cost effectively, if possible resultant reliability of one unit a! From using them emphasizes the ability of a component allows you to design redundancy into a system used. Available to perform the analysis, but a relatively simple and widely accepted approach is reliability! Not using RBDs, what is preventing you from using them of devices or subsystem interconnected to Complex... Time, t, values, they should match, abnormal waveforms, and how to calculate and system... Failures in a power system using block diagrams as is shown in Fig data sheet value for θ ( called. Block diagrams RBD shows the logical connections system reliability calculation examples components within a piece of equipment or performed, and harmonic.... Series, parallel and a combination of the three branches to operate at given! Analyzed using the system shown on the next page main formulas ; t = mission time in,... And model system reliability block diagram represents tools to calculate it is necessarily. =0.11\, \! [ /math ] a power system combination of the MTBF and time,,... And model system reliability and provide targeted improvements miles, etc you to design redundancy into a system system reliability calculation examples 2...

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