This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units re...This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.展开更多
This article deals with the case of the failure-censored constant-stress partially accelerated life test （CSPALT） for highly reliable materials or products assuming the Pareto distribution of the second kind. The ma...This article deals with the case of the failure-censored constant-stress partially accelerated life test （CSPALT） for highly reliable materials or products assuming the Pareto distribution of the second kind. The maximum likelihood （ML） method is used to estimate the parameters of the CSPALT model. The performance of ML estimators is investigated via their mean square error. Also, the average confidence interval length （IL） and the associated co- verage probability （CP） are obtained. Moreover, optimum CSPALT plans that determine the optimal proportion of the test units al- located to each stress are developed. Such optimum test plans minimize the generalized asymptotic variance （GAV） of the ML estimators of the model parameters. For illustration, Monte Carlo simulation studies are given and a real life example is provided.展开更多
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
基金supported by the National Statistical Science Research Project of China(2019LZ32)
文摘This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.
基金supported by the King Saud University,Deanship of Scientific Research and College of Science Research Center
文摘This article deals with the case of the failure-censored constant-stress partially accelerated life test （CSPALT） for highly reliable materials or products assuming the Pareto distribution of the second kind. The maximum likelihood （ML） method is used to estimate the parameters of the CSPALT model. The performance of ML estimators is investigated via their mean square error. Also, the average confidence interval length （IL） and the associated co- verage probability （CP） are obtained. Moreover, optimum CSPALT plans that determine the optimal proportion of the test units al- located to each stress are developed. Such optimum test plans minimize the generalized asymptotic variance （GAV） of the ML estimators of the model parameters. For illustration, Monte Carlo simulation studies are given and a real life example is provided.
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.
