Lusser's law: Difference between revisions
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'''Lusser's law''' in [[systems engineering]] is a prediction of [[reliability (engineering)|reliability]]. Named after engineer [[Robert Lusser]],<ref name="AmSpec">{{cite web | url=https://spectator.org/51313_lussers-law/ | title=Lusser's Law | work=The American Spectator | date=July 14, 2003 | accessdate=10 August 2015 | author=Collins, R.}}</ref> and also known as ''Lusser's product law'' or the ''probability product law of series components'', it states that the reliability of a [[Series circuit|series of components]] is equal to the [[product (mathematics)|product]] of the individual reliabilities of the components, if their [[failure causes|failure modes]] are known to be [[statistically independent]]. For a series of '' |
'''Lusser's law''' in [[systems engineering]] is a prediction of [[reliability (engineering)|reliability]]. Named after engineer [[Robert Lusser]],<ref name="AmSpec">{{cite web | url=https://spectator.org/51313_lussers-law/ | title=Lusser's Law | work=The American Spectator | date=July 14, 2003 | accessdate=10 August 2015 | author=Collins, R.}}</ref> and also known as ''Lusser's product law'' or the ''probability product law of series components'', it states that the reliability of a [[Series circuit|series of components]] is equal to the [[product (mathematics)|product]] of the individual reliabilities of the components, if their [[failure causes|failure modes]] are known to be [[statistically independent]]. For a series of ''N'' components, this is expressed as:<ref name="DeVale">{{cite web | url=http://users.ece.cmu.edu/~koopman/des_s99/traditional_reliability/presentation.pdf | title=Basics of Traditional Reliability | date=1998 | accessdate=11 August 2015 | author=DeVale, J. | pages=8}}</ref><ref name="Kopp">{{cite web | url=http://www.ausairpower.net/PDF-A/Reliability-PHA.pdf | title=System Reliability and Metrics of Reliability | publisher=Peter Harding & Associates, Pty Ltd | date=1996 | accessdate=11 August 2015 | author=Kopp, C. | pages=7}}</ref> |
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:<math>R_s=\prod_{i=1}^N r_i=r_1 \times r_2 \times r_3 \times ... \times r_n</math> |
:<math>R_s=\prod_{i=1}^N r_i=r_1 \times r_2 \times r_3 \times ... \times r_n</math> |
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If the failure probabilities of all components are equal, then as Lusser's colleague [[Erich Pieruschka]] observed, this can be expressed simply as:<ref name="DeVale" /> |
If the failure probabilities of all components are equal, then as Lusser's colleague [[Erich Pieruschka]] observed, this can be expressed simply as:<ref name="DeVale" /> |
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:<math>R_s= |
:<math>R_s=r^N</math> |
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Lusser's law has been described as the idea that a series system is "weaker than its weakest link", as the product reliability of a series of components can be less than the lowest-value component.<ref name="Critchley">{{cite book | url=https://books.google.co.uk/books?id=ltAqBgAAQBAJ&pg=PA117&lpg=PA117&dq=Lusser%27s+law&source=bl&ots=SNPCKYZh-o&sig=NUsUd9m3e45m87gG_bSxWjA7kps&hl=en&sa=X&ved=0CFEQ6AEwB2oVChMI0ZO-5qOfxwIVh4kaCh3oaw9V#v=onepage&q=Lusser's%20law&f=false | title=High Availability IT Services | publisher=CRC Press | author=Critchley, Terry | year=2014 | pages=117 | isbn=9781482255911}}</ref> |
Lusser's law has been described as the idea that a series system is "weaker than its weakest link", as the product reliability of a series of components can be less than the lowest-value component.<ref name="Critchley">{{cite book | url=https://books.google.co.uk/books?id=ltAqBgAAQBAJ&pg=PA117&lpg=PA117&dq=Lusser%27s+law&source=bl&ots=SNPCKYZh-o&sig=NUsUd9m3e45m87gG_bSxWjA7kps&hl=en&sa=X&ved=0CFEQ6AEwB2oVChMI0ZO-5qOfxwIVh4kaCh3oaw9V#v=onepage&q=Lusser's%20law&f=false | title=High Availability IT Services | publisher=CRC Press | author=Critchley, Terry | year=2014 | pages=117 | isbn=9781482255911}}</ref> |
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Revision as of 02:33, 27 November 2018
Lusser's law in systems engineering is a prediction of reliability. Named after engineer Robert Lusser,[1] and also known as Lusser's product law or the probability product law of series components, it states that the reliability of a series of components is equal to the product of the individual reliabilities of the components, if their failure modes are known to be statistically independent. For a series of N components, this is expressed as:[2][3]
where Rs is the overall reliability of the system, and rn is the reliability of the nth component.
If the failure probabilities of all components are equal, then as Lusser's colleague Erich Pieruschka observed, this can be expressed simply as:[2]
Lusser's law has been described as the idea that a series system is "weaker than its weakest link", as the product reliability of a series of components can be less than the lowest-value component.[4]
For example, given a series system of two components with different reliabilities — one of 0.95 and the other of 0.8 — Lusser's law will predict a reliability of
which is lower than either of the individual components.
References
- ^ Collins, R. (July 14, 2003). "Lusser's Law". The American Spectator. Retrieved 10 August 2015.
- ^ a b DeVale, J. (1998). "Basics of Traditional Reliability" (PDF). p. 8. Retrieved 11 August 2015.
- ^ Kopp, C. (1996). "System Reliability and Metrics of Reliability" (PDF). Peter Harding & Associates, Pty Ltd. p. 7. Retrieved 11 August 2015.
- ^ Critchley, Terry (2014). High Availability IT Services. CRC Press. p. 117. ISBN 9781482255911.