Under Type-Ⅱ progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed tha...Under Type-Ⅱ progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed that the lifetime of the component in hybrid systems follows independent and identical modified Weibull distributions. The maximum likelihood estimations(MLEs)of the unknown parameters, acceleration factor and reliability indexes are derived by using the Newton-Raphson algorithm. The asymptotic variance-covariance matrix and the approximate confidence intervals are obtained based on normal approximation to the asymptotic distribution of MLEs of model parameters. Moreover,two bootstrap confidence intervals are constructed by using the parametric bootstrap method. The optimal time of changing stress levels is determined under D-optimality and A-optimality criteria.Finally, the Monte Carlo simulation study is carried out to illustrate the proposed procedures.展开更多
The inference for the dependent competing risks model is studied and the dependent structure of failure causes is modeled by a Marshall-Olkin bivariate Rayleigh distribution. Under generalized progressive hybrid censo...The inference for the dependent competing risks model is studied and the dependent structure of failure causes is modeled by a Marshall-Olkin bivariate Rayleigh distribution. Under generalized progressive hybrid censoring(GPHC), maximum likelihood estimates are established and the confidence intervals are constructed based on the asymptotic theory. Bayesian estimates and the highest posterior density credible intervals are obtained by using Gibbs sampling. Simulation and a real life electrical appliances data set are used for practical illustration.展开更多
Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the depend...Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the dependent competing risks model by using the Marshall-Olkin bivariate Weibull(MOBW) distribution.The maximum likelihood estimations(MLEs), midpoint approximation(MPA) estimations and approximate confidence intervals(ACIs) of the unknown parameters are obtained. In addition, the Bayes approach is also considered based on the Gamma-Dirichlet prior of the scale parameters, with the given shape parameter.The acceptance-rejection sampling method is used to obtain the Bayes estimations and construct credible intervals(CIs). Finally,two numerical examples are used to show the performance of the proposed methods.展开更多
基金The project was supported by the National Natural Science Foundation(Grant Nos.7117116471401134+1 种基金7157114411701406),the Natural Science Basic Research Program of Shaanxi Province(GrantNo.2015JM1003).
基金supported by the National Natural Science Foundation of China(71401134 71571144+1 种基金 71171164)the Program of International Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province(2016KW-033)
文摘Under Type-Ⅱ progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed that the lifetime of the component in hybrid systems follows independent and identical modified Weibull distributions. The maximum likelihood estimations(MLEs)of the unknown parameters, acceleration factor and reliability indexes are derived by using the Newton-Raphson algorithm. The asymptotic variance-covariance matrix and the approximate confidence intervals are obtained based on normal approximation to the asymptotic distribution of MLEs of model parameters. Moreover,two bootstrap confidence intervals are constructed by using the parametric bootstrap method. The optimal time of changing stress levels is determined under D-optimality and A-optimality criteria.Finally, the Monte Carlo simulation study is carried out to illustrate the proposed procedures.
基金supported by the China Postdoctoral Science Foundation(2019M650260)the National Natural Science Foundation of China(11501433)。
文摘The inference for the dependent competing risks model is studied and the dependent structure of failure causes is modeled by a Marshall-Olkin bivariate Rayleigh distribution. Under generalized progressive hybrid censoring(GPHC), maximum likelihood estimates are established and the confidence intervals are constructed based on the asymptotic theory. Bayesian estimates and the highest posterior density credible intervals are obtained by using Gibbs sampling. Simulation and a real life electrical appliances data set are used for practical illustration.
基金supported by the National Natural Science Foundation of China(71571144 71401134)the Program of International Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province(2016KW-033)
文摘Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the dependent competing risks model by using the Marshall-Olkin bivariate Weibull(MOBW) distribution.The maximum likelihood estimations(MLEs), midpoint approximation(MPA) estimations and approximate confidence intervals(ACIs) of the unknown parameters are obtained. In addition, the Bayes approach is also considered based on the Gamma-Dirichlet prior of the scale parameters, with the given shape parameter.The acceptance-rejection sampling method is used to obtain the Bayes estimations and construct credible intervals(CIs). Finally,two numerical examples are used to show the performance of the proposed methods.
