The Point Estimationand Lower Limit Confidence Interval Estimation of the Reliability in Weibull Distribution of Zero Failure Data

The point estimation and interval estimation of the reliability of Weibull distribution in the case of zero failure data are studied.First, by means of E-Bayes estimation, the point estimation of failure probability piof Weibull distribution with zero failure data was worked out, and then through the method of weighted least squares, the point estimation of the Weibull distribution parameters is realized and thus the point estimation of reliability is obtained.Next, by aid of the posterior distributionπ (pi|s|si) of the failure probability pi, the point estimation of piwhose upper confidence limit is piBu when the confidence level is at 1-αis obtained.Based on the distribution curve method, the estimation of the lower confidence limit RLwhen its conficence level is at 1-α.