The Underlying Driving Forces of Continuous Probability Density and Distribution Functions  
Author Zhigang Wei

 
Co-Author(s) D. Gary Harlow; Burt Lin; Fulun Yang

 
Abstract Continuous probability density and distribution functions are commonly used in statistics and reliability analyses. There are many different distribution functions coming from a wide variety of families from which an engineer choose. Therefore, the basic understanding of the characteristics of distribution functions is crucial to the selection of a distribution function in engineering designs. In this paper, the underlying driving forces of the commonly used distribution functions are investigated. It is found that all of the widely used distribution functions can be thought of as the result of two competing forces: a short-range repulsive force and a long-range attractive force with proper boundary condition imposed. The possible distribution functions resulted from bimodal and multiple-modal failures are also discussed.

 
Keywords Reliability, Probabilistic density function, Multiple-modal failure, Driving force, Yin and Yang
   
    Article #:  1821
 
Proceedings of the 18th ISSAT International Conference on Reliability and Quality in Design
July 26-28, 2012 - Boston, Massachusetts, U.S.A.