The purpose of this study is to understand the tendency of point machines failures by using periodic inspection data. Since the inspection data are discrete evaluations, the application of the conventional Weibull hazard model is considered effective. However, we can only obtain information on the condition at the time of inspection from this data, and the failure occurrence interval is not known. Therefore, we developed a method to construct a failure occurrence prediction model from incomplete inspection data by formulating the likelihood of the model as the difference between the survival probability at the time of defect observation and that at the previous inspection. The proposed method shows that the survival probability of an average converter after 90 days is about 10% lower than that of the conventional method, indicating that the conventional method may underestimate the occurrence of initial defects.