Statistical Inference For The Exponential Distribution In The Situation Of Only-one-failure Data

With the development of science and technology, the quality of production is better and better. So in the type- I life testing, the situation of Zero-failure data often occurs , especially in high reliability and small sampling tests. Therefore the problem of Zero-failure data becomes a new reserved aspect in the reliability engineering.Only-one-failure data includes one failure information of the products ,it can describe the products' characteristic better than Zero-failure data .So, in this paper, we try to apply basic theory and classical statistics to study only-one-failure data following Exponential distribution .First, this paper introduces some research work about reliability in Zero-failure data. So the readers can learn some basic theory to study high quality products in the reliability engineering.Secondly, this paper gives the hierarchical Bayesian estimation of the failure rate in case of only-one-failure data, and also gives the weighted Bayesian estimation of the reliability, then analyzes the result.At last, this paper designs the demonstration testing procedure for the exponential distribution of only-one-failure data.