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A I I E Transactions Determining the Mean Time to Failure for Certain Redundant Systems
Determining the Mean Time to Failure for Certain Redundant Systems
Jumonville, Philip, Lesso, William G.Quanto ti piace questo libro?
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Volume:
1
Lingua:
english
Rivista:
A I I E Transactions
DOI:
10.1080/05695556908974418
Date:
March, 1969
File:
PDF, 122 KB
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This article was downloaded by: [McGill University Library] On: 09 February 2015, At: 15:21 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 3741 Mortimer Street, London W1T 3JH, UK A I I E Transactions Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/uiie19 Determining the Mean Time to Failure for Certain Redundant Systems a Philip Jumonville & William G. Lesso a b University of Texas , b University of Texas , Published online: 06 Jul 2007. To cite this article: Philip Jumonville & William G. Lesso (1969) Determining the Mean Time to Failure for Certain Redundant Systems, A I I E Transactions, 1:1, 8182, DOI: 10.1080/05695556908974418 To link to this article: http://dx.doi.org/10.1080/05695556908974418 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sublicensing, systematic supply, or distribution in any form; to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/termsandconditions Determining the Mean Timeto Failure for Certain Redundant Systems PHILIP; JUMONVILLE University of Texas Downloaded by [McGill University Library] at 15:21 09 February 2015 WILLIAM G. LESSO, Associate Member, AIIE University of Texas Abstract: A relatively simple relationship is presented for determining the mean time to failure for systems with redundancy of the type where r out of n units must be operating for the system to be operating. The special case is for units that have constant failure rates. parallel to achieve a certain level of reliability and mean tirrle to system failure. If the reliability function of each unit can be described by the exponential distribution and the units can be considered identical, then the mean time to failure of the system can be determined by a relatively simple relationship. If the requirement is for r units out of N to operate satisfactorily for the system to be operative, then the system reliability is given by There are several methods that can be used to improve the reliability of a system. Besides improving the basic design of the components, it is also possible to add identical units in parallel. These parallel units can be in either an active or standby mode. In the latter case, the redundant units are operated only if some other active units fail. Then it is necessary to consider the reliability of the switching devices to bring in the standby units. In this note, only systems using active redundant units will be considered. This means of improving system reliability becomes feasible when the cost of the units is relatively less than the cost of a failure or downtime and repair. Also, in some systems, it may be a requirement that more than one identical unit in parallel operate satisfactorily for the total system to be considered operative. For example, a remote power station may be required to supply a quantity of power such that a t least three units are needed. For reliability, seven may be on line to carry the load. For the case where more than one unit is required, the problem is to determine how many units should be added in where R is the reliability of a single unit. For the case where the exponential distribution can be used, Equation 1 becomes The system mean time to failure can be expressed in terms of the system reliability (2) : Substituting Equation 2 into Equation 3, it was found that the form for ONST takes on a relatively simple form: Table 1 : Mean time to failure factors r units out of n required @*,,=l/hkn,~ nr 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 1 .ooo 1.500 1.833 2.083 2.283 2.450 2.593 2.718 2.829 2.929      0.500 0.833 1.083 1.283 1.450 1.593 1.718 1.829 1.929   March 1969 0.333 0.583 0.783 0.950 1.093 1.218 1.329 1.439  0.250 0.450 0.617 0.760 0.855 0.996 1.096  0.200 0.367 0.510 0.635 0.746 0.846 0.167 0.310 0.435 0.546 0.646 AIIE Transactions  7  0.143 0.268 0.379 0.479 8 /  L 0.125 0.236 0.336 9 10    0.111 0.211    0.100 81 as "majority systems." Here, r takes on a value of (N+1)/2. That is, the output from N units is compared and the composite output is based on a "majority vote." In Table 2, the mean time to failure for majority systems, that is, two out of three, three out of five, etc., are given. Again, the mean time to failure decreases, asymptotically approaching O.693/X (1). Table 2: Mean time to failure for majority systems 0, ,, 63.2 %,a 07.4 @9,5 011,~ k n ,r 0.833 0.783 0.760 0.746 0.737 0.730 b. Downloaded by [McGill University Library] at 15:21 09 February 2015 In Table 1, the values for the sum l/j are given for values of N and r from 1 to 10. To determine the mean time to failure, it is necessary to know only the failure rate A, and the values of N and r. Then For values beyond the scope of the table, Equation 4 can be used directly. It is interesting to note that, for any level of required units, the mean time to failure will increase as X is increased but at a decreasing rate. However, since the sum is a harmonic series, there is no limit as X becomes infinite. If the number of units in parallel, N , is fixed, then the mean time to failure decreases as the required number, r, increases. A special type of system in this category is known (1) GAVER,D. P., "Time to Failure and Availability of Paral leled Systems with Repair," I E E E Transactions on Reliability, Volume R12, June, 1968. (2) VON ALVEN, W. H., editor, Reliability Engineering, A R I N C Research Corporation, PrenticeHall, Inc., Englewood Cliffs, New Jersey, 1964. Dr. Lesso i s a n Associate Professor in the Department of Mechanical Engineering at the University of Texas. His current research activities include work in availability ~oncepts,new plant facilities investments and optimizing ofshore drilling platforms. He was previously afiliated with General Electric's Flight Propulsion Division. He holds a B S M E f r o m the University of Notre Dame, a n M B A from Xavier University and a n M S and a P h D in Operations Research from the Case Institute of Technology. He i s a member of T I M S and O R S A . Phillip Jumonville is currently a student i n the Department of Physics at the University of Texas. . AIIE Transactions Volume I No. 1