In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially acc...In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration factor.The average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.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
This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of t...This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of the parameters is obtained through the numerical method for solving the likelihood equations. Approxi- mate confidence interval （CI）, based on normal approximation to the asymptotic distribution of MLE and percentile bootstrap Cl is derived. Finally, a numerical example is introduced and then a Monte Carlo simulation study is carried out to illustrate the pro- posed method.展开更多
Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditio...Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress,such as pressure,temperature,vibration,voltage,or load to induce early failures.In this paper,a step stress partially accelerated life test(SSPALT)is regarded under the progressive type-II censored data with random removals.The removals from the test are considered to have the binomial distribution.The life times of the testing items are assumed to follow lengthbiased weighted Lomax distribution.The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax.The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix.The Bayesian estimators cannot be obtained in the explicit form,so the Markov chain Monte Carlo method is employed to address this problem,which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters.The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations.In addition,to compare the performance of the considered confidence intervals for different parameter values and sample sizes.The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter,for different sample sizes,observed failures,and censoring schemes,in most cases.Also,the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes,observed failures,and censoring schemes,in most cases.Further performance comparison is conducted by the experiments with real data.展开更多
Partly interval censored data frequently occur in many areas including clinical trials,epidemiology research,and medical follow-up studies.When data come from observational studies,we need to carefully adjust for the ...Partly interval censored data frequently occur in many areas including clinical trials,epidemiology research,and medical follow-up studies.When data come from observational studies,we need to carefully adjust for the confounding bias in order to estimate the true treatment effect.Pair matching designs are popular for removing confounding bias without parametric assumptions.With time-to-event outcomes,there are some literature for hypothesis testing with paired right censored data,but not for interval censored data.O’Brien and Fleming extended the Prentice Wilcoxon test to right censored paired data by making use of the PrenticeWilcoxon scores.Akritas proposed the Akritas test and established its asymptotic properties.We extend Akritas test to partly interval censored data.We estimate the survival distribution function by nonparametric maximum likelihood estimation(NPMLE),and prove the asymptotic validity of the new test.To improve our test under small sample size or extreme distributions,we also propose a modified version using the rank of the score difference.Simulation results indicate that our proposed methods have very good performance.展开更多
电迁移(ElectroMigration)效应是集成电路中重要的可靠性项目。本文提出了测试思想从传统的"测试到失效"(Test to Fail)到"测试到目的"(Test to Target)的转变,详细讨论了定数与定时截尾(Censored)测试在封装级电...电迁移(ElectroMigration)效应是集成电路中重要的可靠性项目。本文提出了测试思想从传统的"测试到失效"(Test to Fail)到"测试到目的"(Test to Target)的转变,详细讨论了定数与定时截尾(Censored)测试在封装级电迁移测试中的应用,分析了实际测试当中可能碰到的各种情况并提出了处理方法,总结了一个完整的截尾测试处理流程。展开更多
This paper first proposes a random effects generalized linear model to evaluate the storage life of one kind of high reliable and small sample-sized products by combining multi-sources information of products coming f...This paper first proposes a random effects generalized linear model to evaluate the storage life of one kind of high reliable and small sample-sized products by combining multi-sources information of products coming from the same population but stored at different environments. The relevant algorithms are also provided. Simulation results manifest the soundness and effectiveness of the proposed model.展开更多
基金Supported by National Natural Science Foundation of China(11271039)
文摘In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration factor.The average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.
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(7117116470471057)
文摘This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of the parameters is obtained through the numerical method for solving the likelihood equations. Approxi- mate confidence interval （CI）, based on normal approximation to the asymptotic distribution of MLE and percentile bootstrap Cl is derived. Finally, a numerical example is introduced and then a Monte Carlo simulation study is carried out to illustrate the pro- posed method.
基金This work was funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,under Grant No.FP-190-42.
文摘Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress,such as pressure,temperature,vibration,voltage,or load to induce early failures.In this paper,a step stress partially accelerated life test(SSPALT)is regarded under the progressive type-II censored data with random removals.The removals from the test are considered to have the binomial distribution.The life times of the testing items are assumed to follow lengthbiased weighted Lomax distribution.The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax.The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix.The Bayesian estimators cannot be obtained in the explicit form,so the Markov chain Monte Carlo method is employed to address this problem,which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters.The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations.In addition,to compare the performance of the considered confidence intervals for different parameter values and sample sizes.The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter,for different sample sizes,observed failures,and censoring schemes,in most cases.Also,the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes,observed failures,and censoring schemes,in most cases.Further performance comparison is conducted by the experiments with real data.
基金supported by grant 1R01 HS024263-01 from the Agency of Healthcare Research and Quality of the U.S. Department of Health and Human Services
文摘Partly interval censored data frequently occur in many areas including clinical trials,epidemiology research,and medical follow-up studies.When data come from observational studies,we need to carefully adjust for the confounding bias in order to estimate the true treatment effect.Pair matching designs are popular for removing confounding bias without parametric assumptions.With time-to-event outcomes,there are some literature for hypothesis testing with paired right censored data,but not for interval censored data.O’Brien and Fleming extended the Prentice Wilcoxon test to right censored paired data by making use of the PrenticeWilcoxon scores.Akritas proposed the Akritas test and established its asymptotic properties.We extend Akritas test to partly interval censored data.We estimate the survival distribution function by nonparametric maximum likelihood estimation(NPMLE),and prove the asymptotic validity of the new test.To improve our test under small sample size or extreme distributions,we also propose a modified version using the rank of the score difference.Simulation results indicate that our proposed methods have very good performance.
文摘电迁移(ElectroMigration)效应是集成电路中重要的可靠性项目。本文提出了测试思想从传统的"测试到失效"(Test to Fail)到"测试到目的"(Test to Target)的转变,详细讨论了定数与定时截尾(Censored)测试在封装级电迁移测试中的应用,分析了实际测试当中可能碰到的各种情况并提出了处理方法,总结了一个完整的截尾测试处理流程。
基金supported by National Natural Science Foundation of China (Grant No. 10571070)the China Postdoctoral Science Foundation (Grant No. 20060400514)
文摘This paper first proposes a random effects generalized linear model to evaluate the storage life of one kind of high reliable and small sample-sized products by combining multi-sources information of products coming from the same population but stored at different environments. The relevant algorithms are also provided. Simulation results manifest the soundness and effectiveness of the proposed model.
