Residual lifetime prediction model of nonlinear accelerated degradation data with measurement error

For the product degradation process with random effect (RE), measurement error (ME) and nonlinearity in step-stress accelerated degradation test (SSADT), the nonlinear Wiener based degradation model with RE and ME is built. An analytical approximation to the probability density function (PDF) of the product's lifetime is derived in a closed form. The process and data of SSADT are analyzed to obtain the relation model of the observed data under each accelerated stress. The likelihood function for the population-based observed data is constructed. The population-based model parameters and its random coefficient prior values are estimated. According to the newly observed data of the target product in SSADT, an analytical approximation to the PDF of its residual lifetime (RL) is derived in accordance with its individual degradation characteristics. The parameter updating method based on Bayesian inference is applied to obtain the posterior value of random coefficient of the RL model. A numerical example by simulation is analyzed to verify the accuracy and advantage of the proposed model.

MULTIVARIATE SURVIVAL DISTRIBUTIONS OF AGE AND RESIDUAL LIFETIME PROCESSES IN NONHOMOGENEOUS POISSON PROCESS

Let {V(t),t≤0} be the nonhomogeneous Poisson process with cumulative intensituy parameter A(t). |δ,t≥0 the, age process, and y, t≥0} the residual lifetime process. In the present-paper the expressions of n-dimensional survival distribution functions of the processes {δ and γ, and their Lebesgue decompositions are derived.

Smoothed Estimator of Quantile Residual Lifetime for Right Censored Data

It is of great interest to estimate quantile residual lifetime in medical science and many other fields. In survival analysis, Kaplan-Meier（K-M） estimator has been widely used to estimate the survival distribution. However, it is well-known that the K-M estimator is not continuous, thus it can not always be used to calculate quantile residual lifetime. In this paper, the authors propose a kernel smoothing method to give an estimator of quantile residual lifetime. By using modern empirical process techniques, the consistency and the asymptotic normality of the proposed estimator are provided neatly.The authors also present the empirical small sample performances of the estimator. Deficiency is introduced to compare the performance of the proposed estimator with the naive unsmoothed estimator of the quantile residaul lifetime. Further simulation studies indicate that the proposed estimator performs very well.

MOMENT-METHOD ESTIMATION BASED ON CENSORED SAMPLE

In reliability theory and survival analysis, the problem of point estimation based on the censored sample has been discussed in many literatures. However, most of them are focused on MLE, BLUE etc; little work has been done on the moment-method estimation in censoring case. To make the method of moment estimation systematic and unifiable, in this paper, the moment-method estimators(abbr. MEs) and modified momentmethod estimators(abbr. MMEs) of the parameters based on type Ⅰ and type Ⅱ censored samples are put forward involving mean residual lifetime. The strong consistency and other properties are proved. To be worth mentioning, in the exponential distribution,the proposed moment-method estimators are exactly MLEs. By a simulation study, in the view point of bias and mean square of error, we show that the MEs and MMEs are better than MLEs and the “pseudo complete sample” technique introduced in Whitten et al.(1988). And the superiority of the MEs is especially conspicuous, when the sample is heavily censored.

MULTIVARIATE LIKELIHOOD RATIO ORDERING OF CONDITIONAL ORDER STATISTICS

Multivariate likelihood ratio order of order statistics conditioned on both the right tail and the left tail are built. These results strengthen and generalize those conclusions in terms of the univariate likelihood ratio order by Khaledi and Shaked （2007）, Li and Zhao （2006）, Hu, et al. （2006）, and Hu, Jin, and Khaledi （2007）.

Generalized Multivariate Gumbel Distributions——Dependence,Aging Properties and Applications

This paper introduces a generalized multivariate Gumbel(GMG) distribution using a survival copula.Various dependence properties of the GMG distribution and some analytical properties of the generators of the GMG distribution are studied.Furthermore,the authors also investigate the dependence behavior of the residual lifetime vector of the GMG distribution.As an illustration,the GMG distribution is applied to fit a real data set.