Abstract: Based on random censoring data whose life follows exponential distribution, unit and system reliability evaluation methods are studied, and a method of estimating the reliability lower limit is proposed in the case of the exponential distribution under random censoring data, which is also applicable to type Ⅰ censoring data and type Ⅱ censoring data. Firstly, the censoring data are complemented into virtual complete data by use of the quantile-filling algorithm. Based on the fiducial inference, the failure rate distribution of each unit is given. According to the characteristics of the exponential distribution, in view of the failure rate, unit failure rate samples are randomly extracted by Monte Carlo method. In addition to system reliability model, the distribution of system failure rate is obtained, therefore the upper limit of the system failure rate at the given confidence level, and the lower confidence limit of the system reliability are obtained.