Statistical Inference On The Reliability Of Competing Risk Data Under Ranked Set Sampling

With the development of science and technology,people pay more and more attention to the reliability of products,reliability analysis and evaluation is the focus of industrial quality control.In the reliability analysis of products,simple random sampling is usually used to obtain the required life time data.However,it is a costly and time-consuming work to measure the lifetime data of a large number of random samples.The ranked set sampling is an efficient and flexible life time information collection method,which can save time and cost.Therefore,it is of great significance and practical value to study the reliability statistical analysis based on the ranked set sampling method.Based on the competing risk lifetime data of the ranked set sampling,this paper conducts a statistical analysis.The specific research contents are as follows:(1)An independent competing risk model is proposed based on the minimum ranked set sampling with unequal samples.The statistical inference of model parameters and reliability indexes is studied when the competing risk lifetime data follow exponential distribution.The maximum likelihood estimation of the parameters are obtained by using the classical method,and the approximate confidence intervals are constructed according to the asymptotic theory.Secondly,under the general prior information,the Bayesian estimation and the high posterior density credible intervals are established,and the corresponding algorithm is given.Finally,the proposed method is simulated and the results show that the Bayesian estimation is superior to the classical estimation.(2)Based on the assumption that the dependent competing risk lifetime data follow the proportional hazard rate distribution,the estimation problem of lifetime model parameters and reliability indexes is studied based on the minimum ranked set sampling with unequal samples.Firstly,based on the characteristics of Marshall-Olkin bivariate generalized distribution family,a dependent competing risk model is established,and the point estimation and interval estimation results of model parameters are obtained by classical and Bayesian method,respectively.Furthermore,the point estimation equations of model parameters are given by using E-Bayesian theory under different loss functions,and the interval estimation results are obtained by efficient E-Bayesian sampling algorithm.Finally,a lot of simulation is carried out to compare the advantages of different estimation methods.The results show that the E-Bayesian estimation is better than the other two estimation methods.