Statistical Inference On The Reliability Of Progressively Censored Data

Reliability and quality of products are firmly linked like the hinges.In recent years,reliability analysis has received a lot more interest in the fields of engineering application and academic research.To acquire the failure data as well as control the product quality accurately,mankind developed a variety of lifetime testing schemes,such as the complete life-testing,Type-I and Type-II censored testing,among others.With the advancement of manufacturing technology,many products feature strong reliability and long-term service life,hence the progressive censoring scheme has been proposed to improve the efficiency of life-testing.This thesis focused on the reliability analysis under various types of progressively censored data and explored the statistical inference of different lifetime distributions.The specific studied contents are listed as follows.(1)Under progressively Type-II censored data,we explored the inference question on the stress-strength reliability(SSR)for a general class of lower truncated models.When the stress and strength variables have the same and different model parameters,maximum likelihood estimators and Bootstrap confidence intervals of SSR are constructed.Furthermore,based on the proposed pivotal quantities,the generalized estimators of SSR under different cases are investigated as well.Simulation results indicated that the generalized estimation outperforms traditional likelihood-based results.(2)Under the generalized progressive hybrid censoring scheme,we assumed that the failure time of product is distributed in the Weibull model,and the estimation of model parameters is discussed.From the frequentist view,respectively,the maximum likelihood estimation(MLE)and the asymptotic confidence intervals of model parameters are constructed,and the existence and uniqueness of MLE are certified as well.Moreover,the model parameters are further estimated under the Bayesian perspective.The Bayes estimators and the corresponding credible interval are obtained by the M-H sampling algorithm.Simulation results showed that the accuracy of Bayes method is superior to the classical method,and the MCMC sampling has a good convergence.(3)To test the lifetime of similar products,we introduced a joint adaptive progressive censoring scheme.Under the general family of inverse exponentiated distributions,various approaches to the statistical inference of model parameters and reliability indices are discussed.The maximum likelihood and maximum spacing products estimators are constructed,and the approximate confidence intervals are also obtained by using the asymptotic theory as well as the delta method.In addition,the Bayes estimators based on the likelihood and spacing products functions are investigated under Linex loss,respectively.The component-wise M-H algorithm is provided for the complex posterior computation as well.The numerical results indicated that the spacing products-based methods appear more effective under both classical and Bayesian perspectives,which are valuable complements to the likelihood-based approaches.