This study aims at developing a model that would enable us to predict the failure times of machines in cement manufacturing process. The knowledge of machine failures is very vital in maintenance of machines in order to enhance production and minimize on costs of maintenance. In this context, Weibull distribution, Least Squares (LS) method and Maximum Likelihood Estimation (MLE) method are applied to assess failure distributions. 167 machine failure data were used in this study and analyzed with Minitab the software. It was concluded that the failure times follow Weibull distribution and the LS and MLE methods were used to estimate the parameters of the distribution in order to check the fitness. Thus, applying LS method, it is possible to get β = 2.07 and η = 971.7, while applying MLE method, results obtain as β = 2.17 and η = 966. It was noted that these values are rather close and both methods gave almost the same results.