It is a deviation reality that lifespan of some products is described bycommon distributions. However，the ZZ distribution can better describe the lifespan distribution ofthis type of product.In order tostudythe reliability of the ZZ distribution under the condition of no failure data

and the reliability function is transformed

and the concavity and convexity isused to obtain a more precise relationship between the reliability of theproducts at each detection timeFurther

under the prior distribution is theuniform distribution 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 thecase of 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.