Abstract: The concept of failure rate in the theory of reliability has been introduced to the study of earthquake prediction, and an attempt has been made to draw a set of new reliability function w1(t)=exp-taecsin(lnt+)It is found that:1. The parameter a may take as a numerical criterion to judge the three stages of seismic activity, i.e. a 1 for the principal energy release stage.2. The failure rate function can represent adequately the fluctuation of the seismic activity in each of the stages mentioned-above and can be used to judge the activity level in each stage.3. When c = 0, the new reliability function will be degenerated into the Weibull reliability function, that is, the latter is a special case of the former.A test has been made by applying the new reliability function to the Tangshan Earthquake (Ms =7.8), the Xinfengjiang Earthquake (Ms= 6.1), and to the seismicity of the seismic zones of Eastern Yunnan and of SB China coastal region with satisfactory results.