Statistical inferences for the geometric process (GP) are derived when the distribution of the first occurrence time is assumed to be inverse Gaussian (IG). An alpha-series process, as a possible alternative to the GP, is introduced since the GP is sometimes inappropriate to apply some reliability and scheduling problems. In this study, statistical inference problem for the alpha-series process is considered where the distribution of first occurrence time is IG. The estimators of the parameters alpha, mu, and sigma(2) are obtained by using the maximum likelihood (ML) method. Asymptotic distributions and consistency properties of the ML estimators are derived. In order to compare the efficiencies of the ML estimators with the widely used nonparametric modified moment (MM) estimators, Monte Carlo simulations are performed. The results showed that the ML estimators are more efficient than the MM estimators. Moreover, two real life datasets are given for application purposes.