Reliability Estimation Of ZZ Distribution Under Zero Failure Data

In reliability statistics,there are usually four types of life distributions of the product: exponential distribution,Weibull distribution,extreme-value distribution and log-normal distribution.Under various sample forms,there are many studies of statistical inference about the four distributions both at home and abroad,including theory and application.However,there are some special cases in practical problems.For example,when the exponential distribution,Weibull distribution and other distributions are used to describe the life of some products(components),the results are found to be far from the actual ones.It shows that the life distribution of this kind of this products does not belong to the category of the above four distributions.However,ZZ distribution can better describe the life distribution of this kind of products.In recent years,the components have been characterized by high reliability,with little or no failure in a certain test period.In this paper,in order to study the reliability of the ZZ distribution under the condition of no failure data,and the reliability function is transformed,and the concavity and convexity is used to obtain a more precise relationship between the reliability of the products at each detection time.Further,under the prior distribution is the uniform distribution or more general distribution,Bayesian Estimation of the reliability at each moment is given.Based on Bayesian estimation of reliability,regression analysis were used to obtain the estimated value of ZZ distribution parameters.Besides,the estimation expressions of other reliability indexes(mean life,reliable life,etc.)are given.In addition,according to the optimal confidence lower limit formula of known function with confidence level of 1-? in the case of no failure data,the optimal confidence lower limit expression of the reliability function of the ZZ distribution isgiven,and the simplified form that is convenient to use is given in several special cases.Meanwhile,the above results are further simulated numerically.This paper extends the research on the type of life distribution.Meanwhile,the study of reliability estimation without failure data has certain theoretical significance and application value.