A reliability application of a mixture of inverse gaussian distributions

A mixture of inverse Gaussian distributions (IGDs) is examined as a model for the lifetime of components. The components differ in one of three ways: in their initial quality, rate of wear, or variability of wear. These three cases are well represented by the parameters of the IGD model. The mechanistic interpretation of the IGD as the first passage time of Brownian motion with positive drift is adopted. The parameters considered are either dichotomous or continuous random variables. Parameter estimation is also examined for these two cases. The model seems to be most appropriate when the single IGD model fails due to heterogeneity of the initial component quality.