Cubic mean

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

\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][3]

It is used for predicting the life expectancy of machine parts.[3][4][5][6]

It can be understood as the generalized mean with p=3.

References

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