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 system is equal to the product of the reliability of its component subsystems, if their failure modes are known to be statistically independent. For a series of n components, this is expressed as:

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

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

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.