In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fi...In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.展开更多
In order to obtain the life information of the vacuum fluorescent display （VFD） in a short time, a model of constant stress accelerated life tests （CSALT） is established with its filament temperature increased, an...In order to obtain the life information of the vacuum fluorescent display （VFD） in a short time, a model of constant stress accelerated life tests （CSALT） is established with its filament temperature increased, and four constant stress tests are conducted. The Weibull function is applied to describe the life distribution of the VFD, and the maximum likelihood estimation （MLE） and its iterative flow chart are used to calculate the shape parameters and the scale parameters. Furthermore, the accelerated life equation is determined by the least square method, the Kolmogorov-Smirnov test is performed to verify whether the VFD life meets the Weibull distribution or not, and selfdeveloped software is employed to predict the average life and the reliable life. Statistical data analysis results demonstrate that the test plans are feasible and versatile, that the VFD life follows the Weibull distribution, and that the VFD accelerated model satisfies the linear Arrhenius equation. The proposed method and the estimated life information of the VFD can provide some significant guideline to its manufacturers and customers.展开更多
In this note,the tampered failure rate model is generalized from the step-stress accelerated life testing setting to the progressive stress accelerated life testing for the first time.For the parametric setting where ...In this note,the tampered failure rate model is generalized from the step-stress accelerated life testing setting to the progressive stress accelerated life testing for the first time.For the parametric setting where the scale parameter satisfying the equation of the inverse power law is Weibull,maximum likelihood estimation is investigated.展开更多
Inthispaper,theoptimumtestplanandparameterestimationfor3-stepstep-stress accelerated life tests in the presence of modified progressive Type-I censoring are discussed.It is assumed that the lifetime of test units foll...Inthispaper,theoptimumtestplanandparameterestimationfor3-stepstep-stress accelerated life tests in the presence of modified progressive Type-I censoring are discussed.It is assumed that the lifetime of test units follows a Lomax distribution with log of characteristic life being quadratic function of stress level.The maximum likelihood and Bayesian method are used to obtain the point and interval estimators of the model parameters.The Bayes estimates are obtained using Markov chain Monte Carlo simulation based on Gibbs sampling.The optimum plan for 3-step step-stress test under modified progressive Type-I censoring is developed which minimizes the asymptotic variance of the maximum likelihood estimators of log of scale parameter at design stress.Finally,the numerical study with sensitivity analysis is presented to illustrate the proposed study.展开更多
In this paper, we consider the statistical analysis for the dependent competing risks model in theconstant stress accelerated life testing (CSALT) with Type-II progressive censoring. It is focusedon two competing risk...In this paper, we consider the statistical analysis for the dependent competing risks model in theconstant stress accelerated life testing (CSALT) with Type-II progressive censoring. It is focusedon two competing risks from Lomax distribution. The maximum likelihood estimators of theunknown parameters, the acceleration coefficients and the reliability of unit are obtained by usingthe Bivariate Pareto Copula function and the measure of dependence known as Kendall’s tau.In addition, the 95% confidence intervals as well as the coverage percentages are obtained byusing Bootstrap-p and Bootstrap-t method. Then, a simulation study is carried out by the MonteCarlo method for different measures of Kendall’s tau and different testing schemes. Finally, a realcompeting risks data is analysed for illustrative purposes. The results indicate that using copulafunction to deal with the dependent competing risks problems is effective and feasible.展开更多
基金supported by the National Natural Science Foundation of China(1150143371473187)the Natural Science Basic Research Plan in Shaanxi Province of China(2016JQ1014)
文摘In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.
基金Undergraduate Education High land Construction Project of Shanghaithe Key Course Construction of Shanghai Education Committee (No.20075302)the Key Technology R&D Program of Shanghai Municipality (No.08160510600)
文摘In order to obtain the life information of the vacuum fluorescent display （VFD） in a short time, a model of constant stress accelerated life tests （CSALT） is established with its filament temperature increased, and four constant stress tests are conducted. The Weibull function is applied to describe the life distribution of the VFD, and the maximum likelihood estimation （MLE） and its iterative flow chart are used to calculate the shape parameters and the scale parameters. Furthermore, the accelerated life equation is determined by the least square method, the Kolmogorov-Smirnov test is performed to verify whether the VFD life meets the Weibull distribution or not, and selfdeveloped software is employed to predict the average life and the reliable life. Statistical data analysis results demonstrate that the test plans are feasible and versatile, that the VFD life follows the Weibull distribution, and that the VFD accelerated model satisfies the linear Arrhenius equation. The proposed method and the estimated life information of the VFD can provide some significant guideline to its manufacturers and customers.
基金This research is by the National Natural Science Foundation of China(69971016, 10271079) the Science and Technology Development Foundation of Shanghai(00JC14507) the Major Branch of Learning Foundation of Shanghai.
文摘In this note,the tampered failure rate model is generalized from the step-stress accelerated life testing setting to the progressive stress accelerated life testing for the first time.For the parametric setting where the scale parameter satisfying the equation of the inverse power law is Weibull,maximum likelihood estimation is investigated.
文摘Inthispaper,theoptimumtestplanandparameterestimationfor3-stepstep-stress accelerated life tests in the presence of modified progressive Type-I censoring are discussed.It is assumed that the lifetime of test units follows a Lomax distribution with log of characteristic life being quadratic function of stress level.The maximum likelihood and Bayesian method are used to obtain the point and interval estimators of the model parameters.The Bayes estimates are obtained using Markov chain Monte Carlo simulation based on Gibbs sampling.The optimum plan for 3-step step-stress test under modified progressive Type-I censoring is developed which minimizes the asymptotic variance of the maximum likelihood estimators of log of scale parameter at design stress.Finally,the numerical study with sensitivity analysis is presented to illustrate the proposed study.
基金This work is supported by the National Natural Science Foundation of China[grant number 71571144],[grant number 71401134],[grant number 71171164],[grant number 11701406]Natural Science Basic Research Program of Shaanxi Province[grant number 2015JM1003]Program of International Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province[grant number 2016KW-033].
文摘In this paper, we consider the statistical analysis for the dependent competing risks model in theconstant stress accelerated life testing (CSALT) with Type-II progressive censoring. It is focusedon two competing risks from Lomax distribution. The maximum likelihood estimators of theunknown parameters, the acceleration coefficients and the reliability of unit are obtained by usingthe Bivariate Pareto Copula function and the measure of dependence known as Kendall’s tau.In addition, the 95% confidence intervals as well as the coverage percentages are obtained byusing Bootstrap-p and Bootstrap-t method. Then, a simulation study is carried out by the MonteCarlo method for different measures of Kendall’s tau and different testing schemes. Finally, a realcompeting risks data is analysed for illustrative purposes. The results indicate that using copulafunction to deal with the dependent competing risks problems is effective and feasible.
