The explicit estimators of the parameters alpha, mu and sigma(2) are obtained by using the methodology known as modifiedmaximum likelihood (MML) when the distribution of the first occurrence time of an event is assumed to be Weibull in series process. The efficiencies of the MML estimators are compared with the corresponding nonparametric (NP) estimators and it is shown that the proposed estimators have higher efficiencies than the NP estimators. In this study, we extend these results to the case, where the distribution of the first occurrence time is Gamma. It is anotherwidely used andwell-known distribution in reliability analysis. A real data set taken fromthe literature is analyzed at the end of the study for better understanding the methodology presented in this paper.