The analysis of reliabilities of process facilities often uses models based on the Weibull distribution. The parameters in these models are functions of operating conditions, and determined by experiments. Using these values, we calculate the reliability, mean time to failure, and standard deviation. The conventional method assumes that the operating condition is constant, and thus treats the model parameters as constants. In this paper, a reliability function is proposed which is applicable when the scale parameter is a function of time, and an analysis method based on this is also presented. A case study on a cooling fan resulted in a big difference from the conventional method to which the average operating conditions were applied. The proposed method is also applicable to other process facilities, and expected to effectively take into account the effects of changes in the operating conditions on the reliabilities of the facilities.