Lusser's Law

Lusser's law in systems engineering is a prediction of reliability. Named after engineer Robert Lusser, 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:

:$R_s=\prod_^N r_i=r_1 \times r_2 \times r_3 \times ... \times r_n$

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:

:$R_s=r^N$

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.

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.

References

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Engineering failures
Reliability analysis
Reliability engineering
Statistics articles needing expert attention
Survival analysis
Systems analysis