On The Classical Parameters of the Crack Distribution

Abstract

The three parameter Crack distribution is a useful and effective tool in statistical analysis in conjunction with the desired interest of engineering studies relating to fatigue cracks that occur in materials used for numerous products such as lorry, air craft and other heavy machinery due to excessive load or when the force is exerted beyond the materials ability. This distribution contains as special cases: the Birnbaum-Saunders distribution, the Inverse Gaussian distribution, and the Length Biased Inverse Gaussian distribution, all of which are well known, have their own characteristics and are naturally related to each other. In this thesis, we derive new direct and more mathematically appealing methods for obtaining the distribution function and the moment generating function for the Crack distribution in the classical parameters. A random number generation procedure is described which simulates Crack numbers. The main idea is to use the composition method, that is, a Crack random number is obtained by the initial generation of Inverse Gaussian and Length Biased Inverse Gaussian random numbers. After this we combine them in a special way to obtain a Crack random number.