It is a deviation reality that lifespan of some productsis described by common distributions. However，the ZZ distribution can better describe thelifespan distribution of this type of product. In order tostudy the reliabilityof the ZZ distribution under the condition of no failure data

and thereliability function is transformed

and the concavity and convexity is used toobtain a more precise relationship between the reliability of the products ateach detection time Further

under the prior distribution is the uniformdistribution or more general distribution

Bayesian Estimation of thereliability at each moment is given Meanwhile

according to the optimalconfidence lower limit formula of known function with confidence level of 1－α in the caseof no failure data

the optimal confidence lower limit expression of thereliability function is given

and the simplified form that is convenient touse is obtained in several special cases.