It is an outstanding problem in engineering application to solve problems related to time truncated zero-failure data. In this paper

a method of reliability analysis for time truncated zero-failure data based on Weibull distribution was presented

which can making an high confidence assessment for the reliability of product with time truncated zero-failure data when the lower limit of shape parameter and the one-side lower confidence limits of reliability and life were provided. Large mount of Monte Carlo simulation results show that this method can combine the zero-failure data that contributing to Weibull distribution together and make full use of information of time truncated zero-failure data

the precision of forecasting is obviously improved. The method introduced in this paper was used for analyzing the time truncated zero-failure data provide by the life test of one kind of high pressure vessel.