Research On Statistical Analysis And Reliability Evaluation Of Two Important Models

Stress-strength model and competing risks model are two important models in reliability theory and applied researches,which have been applied to the fields of engineering,medicine,economy,finance and so on.However,with development of intelligent manufactory industry,the original models are continually improving and enhancing with the exchanges of product structure and environmental factors.As to the stress-strength model,it usually assumes that stress variables and strength variables are independent identical distribution,then the statistical inferences are conducted based on the failure data of products.However,stress variables and strength variables have many different relationships in industrial products,which can't be treated as the same.In the research of competing risks model,people often assume that the failure rate function is monotonous and the failure causes are independent of each other.Then the statistical inferences are deduced based on the test data of products under usage stress level.However,many complex structures appear in industrial products nowadays,it is difficult to describe the lifetime characteristics of products by using the monotonous failure rate function.Furthermore,the independent competing risks model under usage stress level can't be applied to the accelerated dependent competing risks model.Motivated by the above mentioned,this dissertation discusses some new problems of the above two models,the main research contents and innovations are listed as follows:(1)Extending single-component product with independent stress-strength model to multicomponent product with dependent stress-strength model,the Gumbel copula is chosen as the connecting function between the stress variable and the minimum strength variable of the multicomponent product.Then the method-of-moment is used to obtain the dependent parameter in the model.Adopting the Newton-Rahpson method,the maximum likelihood estimators(MLEs)of the model parameters and reliability are obtained.Meanwhile,based on the asymptotic normal theory and the Bootstrap resampling method,the related asymptotic confidence intervals(ACIs)for the model parameters and reliability are computed.The influence of the dependent degrees on the results is analyzed.The results of simulation and real data analysis show that the method can be used to construct the relationship between the stress and strength variables.(2)Aiming at the problem of statistical analysis and reliability evaluation for different sources of strength variables,the stress-strength model with finite mixture exponential stress variables and Lindley strength variable is built,then the reliability of this model is deduced.The MLE and ACI of reliability are obtained by using the expectation-maximization(EM)algorithm and the bootstrap resampling method.Under squared error loss function,the Bayes estimators and the highest posterior density(HPD)credible intervals of reliability are acquired by using the Metropolis-Hastings algorithm with Gibbs.Finally,the hypothesis testing for the homogeneity of the finite mixture distributions is conducted.The numerical results declare that the proposed method can describe the relationship between different strength variables.(3)The lower truncated proportional hazard rate distributions are proposed to fit the failure data based on the statistical characteristics of test data.Then the stress-strength model for the lower truncated proportional hazard rate distributions is established.The reliability of this model is also derived.The MLEs and ACIs of the reliability are computed.Meanwhile,the pivotal quality estimators and the modified generalized pivotal quality confidence intervals of the reliability are obtained by adopting the pivotal quality method.Numerical results illustrate that the method can appropriately evaluate the stress-strength reliability of censored data.(4)Aiming at the problem of the monotone failure rate function cannot fit the lifetime of the complex system,extending the Chen distribution by the Marshall-Olkin extended method to obtain a more flexible failure rate function.Based on the adaptive progressively interval censored data,the likelihood function of the model parameters are deduced.The MLEs and ACIs of the model parameters are obtained by employing EM algorithm and bootstrap resampling method.The hypothesis testing for the consistency of the competing risks factors is performed.The numerical results state that the method can fit the data properly.(5)Using Marshall-Olkin exponential distribution to model the dependence structure of the competing risks,the reliability evaluation for the dependent competing risks model under constant stress accelerated life test(CSALT)is analyzed.The accelerated model is given as power rule model,and the likelihood function of the model parameters is given.Then,deduce the MLEs and the Bootstrap CIs of the model parameters,the pivotal quality estimators and the related pivotal quality confidence intervals of the model parameters,and the Bayes estimators and the HPD credible intervals under the squared error loss function for the model parameters.Meanwhile,the least squares estimators of the accelerated coefficients are computed,and the reliability under normal stress level and the mission time is obtained.The numerical results clarify that the method can be used to fit the accelerated dependent lifetime data.(6)Under the condition of the shape parameters and the scale parameters have relationship with stress levels,the reliability evaluation for the dependent competing risks model under CSALT is analyzed.Using Marshall-Olkin Weibull distribution to model the dependence structure of the competing risks.The accelerated model is given as logarithm linear model,and the likelihood function of the model parameters is given.Then,the MLEs and the ACIs of the model parameters are deduced.Meanwhile,under the squared error loss function,the Bayes estimators and the HPD credible intervals are computed by using the important sampling algorithm,as well as the least squares estimators of the accelerated coefficients based on Gauss-Markov theory are obtained.In addition,the fitting effects of Marshall-Olkin Weibull distribution and Gumbel copula are compared based on the real dataset.The numerical results indicate that in some cases the change of shape parameter due to accelerated levels can't be neglected.