Statistical Inference For The Exponential Distribution With Two-parameters In The Situation Of Zero-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 research aspect in the reliability engineering. In the situation of zero-failure data, how to analyze the reliability of production is very difficult for the existing reliability engineering theory which is based on the failure data. In the situation of zero-failure data, some methods just as the maximum likelihood estimation and the approximate unbiased linear estimation which are often used in the Type-I life testing is invalid. So the zero-failure data research is an important field. At present, most researches about the zero-failure data aimed at the exponential distribution with one parameter and the Weibull distribution. So this paper tries to use the existing theories and methods to study the exponential distribution with two parameters in the situation of zero-failure data. First, this paper introduces the statistical inference for the exponential distribution with two parameters under type-I censoring. And the estimation under multiply type-I censoring is given out. Secondly, this paper discusses the estimation for the exponential distribution with two parameters in the situation of zero-failure data from the view of classical statistics and Bayes statistics. At last, this paper discusses the Bayesian zero-failure reliability demonstration testing procedure for the exponential distribution with two parameters and designs the demonstration testing procedure.