The Crack Lifetime distribution is the combination of one parameter and the two-parameter Inverse Gaussian distribution and two-parameter Length Biased Inverse Gaussian distribution. Birnbaum-Saunders distribution, two-parameter fatigue life distribution, is the special case of the Crack Lifetime distribution. Ahmed et al (2008) had studied parametric estimation for the parameters of Birnbaum-Saunders lifetime distribution based on a new parameterization. The new parameterization of the two-parameter Birnbaum-Saunders lifetime distribution is to be considered. The new parameterization is important since it fits the physical phenomena of fatigue cracks.