Lusser's law

Last updated December 15, 2020

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]

R_{s}=\prod _{i=1}^{N}r_{i}=r_{1}\times r_{2}\times r_{3}\times ...\times r_{n}

where R_s is the overall reliability of the system, and r_n is the reliability of the n^th 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]

R_{s}=r^{N}

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

R_{s}=0.95\times 0.8=0.76

which is lower than either of the individual components.

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References

↑ Collins, R. (July 14, 2003). "Lusser's Law". The American Spectator. Retrieved 10 August 2015.
1 2 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.

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[AmSpec-1] Collins, R. (July 14, 2003). "Lusser's Law". The American Spectator. Retrieved 10 August 2015.

[DeVale-2] 1 2 DeVale, J. (1998). "Basics of Traditional Reliability" (PDF). p. 8. Retrieved 11 August 2015.

[Kopp-3] Kopp, C. (1996). "System Reliability and Metrics of Reliability" (PDF). Peter Harding & Associates, Pty Ltd. p. 7. Retrieved 11 August 2015.

[Critchley-4] Critchley, Terry (2014). High Availability IT Services. CRC Press. p. 117. ISBN 9781482255911.

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