Reliability Estimation Of Weibull Distribution With Zero Failure Data

In the process of production and application of products,it is very important to study the reliability of products.The research method is to carry out the life test of the product.With the increasing number of products with high reliability,the possibility of no failure for a long time is increased in the life test of products.On the other hand,in order to control the cost of the test,the experimental method of timing truncation is often adopted.These make the life test data collected in the test of the product basically have no failure data.It becomes the focus of our research to estimate the reliability parameters scientifically and reasonably based on the no-failure data.This paper mainly studies the estimation of reliability parameters of Weibull distribution in the case of no failure data.The main research contents are as follows:At present,the distribution curve method is widely used to estimate the reliability parameters of Weibull distribution without failure data.This makes the method of solving point estimation and interval estimation disjointed.Based on this,this paper improves the traditional distribution curve method,and uses the posterior distribution of the failure probability to obtain the estimation of the confidence upper limit with the confidence level as,so as to obtain the estimation of the reliability at the confidence level as the confidence lower limit.By using the method in this paper,the point estimation and interval estimation of the local reliability of Weibull distribution without failure data can be obtained based on the same step.With distribution curve method on the reliability of parameter estimation accuracy of determining factor is the failure probability estimates,based on the theory point of view,the posterior distribution of the failure probability is used to adjust its prior distribution or to calculate the failure probability estimates in scope,again by the relationship between failure probability and the failure time in fixed failure probability values range.Through the concrete example of bearing experiment,the robustness and feasibility of the method proposed in this paper are verified.