Cubic mean

The cubic mean ${\displaystyle {\bar {x}}_{\mathrm {cubic} }}$ of ${\displaystyle n}$ real numbers ${\displaystyle x_{i}\in \mathbb {R} }$ is defined as:

${\displaystyle {\bar {x}}_{\mathrm {cubic} }={\sqrt[{3}]{{\frac {1}{n}}\sum _{i=1}^{n}{x_{i}^{3}}}}={\sqrt[{3}]{{x_{1}^{3}+x_{2}^{3}+\cdots +x_{n}^{3}} \over n}}.}$   [1][2]

It is used for predicting the life expectancy of machine parts.[2][3]

It can be understood as the generalized mean with ${\displaystyle p=3}$.

References

1. • "calculation formulas" (PDF).
   • Svarovski, Ladislav. Solid-Liquid Separation. google books. Retrieved 2015-01-20.
2. "Equivalent Load". Creative Motion Control. Archived from the original on 2015-01-20. Retrieved 2015-01-19.
3. • "ISO 4301-1-1986 Cranes and lifting appliances; Classification; Part 1 : General". www.iso.org. 1986. also available from "freestd.us". Retrieved 2015-01-20.
   • Babu & Sridhar. Design of Machine Elements. google books. Retrieved 2015-01-20.
   • Essential Concepts of Bearing Technology, Fifth Edition. google books. Retrieved 2015-01-20.