Reliability Analysis For System With Masked Data

Reliability analysis for system with masked data is one of the important research contents of the reliability engineering.Based on the assumption that the system components have independent/dependent lifetime variables,masking is dependent/independent of the true cause of system failure,we discuss the reliability analysis of system with masked data under progressive interval and progressive hybrid censored life tests as well as the accelerated life tests.The main conclusions and innovations are as follows:In chapter 2,we discuss the reliability analysis of Burr XII series system with masked data under progressive interval censoring.Based on the system failure data,the probability density function for the system is derived.The latent variables are introduced to make the masked failure cause identify.EM algorithm is applied to compute the maximum likelihood estimates,and the missing information principle is used to obtain the observed fisher information matrix,which can be used for constructing the asymptotic confidence intervals.In addition,hybrid sampling algorithm is presented to obtain the Bayes estimates and Monte Carlo(MC)method is employed to construct the highest posterior density credible intervals.Finally,the effectiveness of the estimates is illustrated by numerical simulations under different masking probabilities and progressive removal schemes.In chapter 3,we research the statistical analysis of masked data in a series system with Marshall-Olkin Weibull distributed component.Based on progressive hybrid censored and masked system lifetime data,the likelihood function is established.We compute the maximum likelihood estimates for the parameter,and then the asymptotic unbiasedness and consistency are proved.By using Taylor expansion,the approximate maximum likelihood estimates of the unknown parameters are proposed.In addition,the Bayes approach is developed based on the assumption that the shape parameter has a log-concave function and the scale parameters have Gamma-Dirichlet priors.Finally,the effectiveness of the method is illustrated by numerical simulations.In chapter 4,we consider the reliability analysis of masked data in a hybrid system with dependent components,which are linked by a copula function.Based on type I progressive hybrid censored and masked system lifetime data,we drive some probability results for the hybrid system and then the maximum likelihood estimates as well as the asymptotic confidence intervals and bootstrap confidence intervals of the unknown parameters are obtained.Numerical simulations show that,the reliability evaluation model considering the dependence of components can better evaluate the reliability of the system.In chapter 5,we present the reliability analysis of log-normal system with masked data in constant stress accelerated life test under progressive hybrid censoring.Based on the system lifetime data,the likelihood function is established.The ‘latent vector for component lifetime' and the ‘latent variables for component-state' are introduced to simplify the likelihood function.The maximum likelihood estimates and Bayes estimates for the parameters are discussed by using the EM algorithm and the Gibbs sample algorithm,respectively.Finally,the least squares approach is used to obtain the estimates of the parameters in the accelerated function,and then the reliability of the components and system is evaluated under normal use stress level.In chapter 6,we consider the statistical analysis of masked data in step-stress partially accelerated life test under progressive hybrid censoring.TRV model is used to shift the failure time.Auxiliary variables are introduced to make the failure cause identify.Under the assumption that masking is independent and dependent of failure cause,the maximum likelihood estimates based on EM algorithm and the Bayes estimates based on hybrid sampling method are discussed,respectively.Finally,the developed techniques are illustrated by a numerical example.In chapter 7,we consider the Bayes analysis of Weibull system with masked data in multi-level step-stress accelerated lifetime test.For the series system with dependent component,Khamis-Higgins is used to shift the failure data,and then the likelihood function is established.Latent variables are introduced to make masked failure causes identify.We choose the restricted and unrestricted prior for the parameter,the sample steps from the posterior distribution are discussed,and then the Bayes estimates for the parameters and the Bayes prediction for the new sample are obtained.Finally,the least square approach is used to obtain the estimates of the parameters in the accelerated function,and then the reliability of the components and systems is evaluated under normal use stress level.