Lusser's law

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]

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

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]

${\displaystyle R_{s}=r^{N}}$

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

${\displaystyle R_{s}=0.95\times 0.8=0.76}$

which is lower than either of the individual components.