The article “Numerical Prediction of Surface Wear and Roughness Parameters During Running-In for Line Contacts Under Mixed Mixed Lubrication” (J. Tribol., Nov. 2018) proposes probability models for several variables that arise in studying the wear of mechanical components like gears and piston rings. These variables include X = wear particle thickness (microns) and W = wear loss (cubic microns).
a. The article’s authors make mathematical arguments that (1) X should follow an exponential distribution and (2) the pdfs of W and X should be related by

What distribution are the authors specifying for W? Identify the name and parameter values of the distribution.

b. If the variance of W is 3.0 (one of several values considered in the article), what are the numerical values of the parameters of W’s distribution, and what is the value of the λ parameter for X’s exponential distribution?

Transcribed Image Text:

fw (w) x w².fx (w)