The competing risks analysis for parallel and series systems using Type-II progressive censoring

Abstract

Recently, the study of the lifetime of systems in reliability and survival analysis in the presence of several causes of failure (competing risks) has attracted attention in the literature. In this paper, series and parallel systems with exponential lifetime for each item of the system are considered. Several causes of failure independently affect lifetime distributions and observations of failure times of the systems are considered under progressive Type-II censored scheme. For series systems, the maximum likelihood estimates of parameters are computed and confidence intervals for parameters of the model are obtained using Fisher information matrix. For parallel systems, the generalized EM algorithm which uses the Newton-Raphson algorithm inside the EM algorithm is used to compute the maximum likelihood estimates of parameters. Also, the standard errors of the maximum likelihood estimates are computed by using the supplemented EM algorithm. The simulation study confirms the good performance of the introduced approach.     

工程质量政府监督多层次利益分配与激励协同机制探究

The implementation of the government supervision of the quality of the project is an international practice. The basic form of government supervision of engineering quality is government supervision on the quality behavior of the engineering main bodies and its results by the competent government department entrusted. Its essence is a dual principal-agent process. The frequent accidents of the engineering quality reflect the loss and failure of the government law enforcement supervision of the engineering quality to some extent. Its root lies in the lack of endogenous power in the law enforcement supervision of the project quality government supervisors in the law enforcement supervision. Therefore, the incentive coordination mechanism of the government supervision based on the multi-level interest distribution is worth explored. In views of the multi-level management system which is formed by the government departments, government quality supervision organizations, quality supervision team (or group) for the government supervision of engineering quality. The benefit distribution function between every party is constructed, and the game model of the multi-level incentive and coordination for the government supervision in engineering quality is built. To solve and deduce from the first stage of the cooperative game and the second stage of the non-cooperative game, the cooperative game can obtain the reward coefficient: . The coordination degree of the best effort can be obtained by the non cooperative game. The result shows that:the coordination degree of government engineering quality supervisor is related to the coordination costs, and had nothing to do with fixed costs. The benefit distribution coefficient not only depends on the efforts of the quality government monitors, but also on the efficiency of other parties' efforts. The quality supervisors of the project will also focus on the coordination with other parties when enhancing their management capabilities to improve the overall performance of project quality government supervision. The strategy of the incentive coordination mechanism for the supervision and cooperation of the project quality government is:the government quality supervision team should set up the supervisory team properly, improve the coordination efficiency and reduce the cost of supervision-coordination to maximize the value of self-motivation. Quality supervision team (or group) should establish the partnership to improve the coordination efficiency for achieving the maximization of their own incentive value.The model and conclusion of incentive synergy mechanism based on multi-level benefit allocation mechanism are researched. It can provide theoretical support and practice reference for the market governance and supervision of general public goods.     

The exponential distribution analog of the Grubbs–Weaver method

Abstract

Grubbs and Weaver (1947 Grubbs, F. E., and C. L. Weaver. 1947. The best unbiased estimate of population standard deviation based on group ranges. Journal of the American Statistical Association 42 (238):224–41. doi: 10.2307/2280652.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggest a minimum-variance unbiased estimator for the population standard deviation of a normal random variable, where a random sample is drawn and a weighted sum of the ranges of subsamples is calculated. The optimal choice involves using as many subsamples of size eight as possible. They verified their results numerically for samples of size up to 100, and conjectured that their “rule of eights” is valid for all sample sizes. Here we examine the analogous problem where the underlying distribution is exponential and find that a “rule of fours” yields optimality and prove the result rigorously.     

Multivariate normal mean–variance mixture distribution based on Birnbaum–Saunders distribution

A multivariate normal mean–variance mixture based on a Birnbaum–Saunders (NMVMBS) distribution is introduced and several properties of this new distribution are discussed. A new robust non-Gaussian ARCH-type model is proposed in which there exists a relation between the variance of the observations, and the marginal distributions are NMVMBS. A simple EM-based maximum likelihood estimation procedure to estimate the parameters of this normal mean–variance mixture distribution is given. A simulation study and some real data are used to demonstrate the modelling strength of this new model.     

黄国雄教授商品流通理论研究回顾

黄国雄教授是中国现代商品流通理论的奠基人.文章通过文献梳理和实际观察,对黄国雄教授的商品流通理论研究进行了回顾.黄国雄教授的商品流通理论主要包括三个方面:在内容方面,聚焦于商品流通理论的研究;在方法方面,多使用经验主义范式;在主要贡献方面,奠定了现代商学理论的根基,具体包括提出了“商业创造价值论”“流通产业基础论”和“商道即人道论”等三大理论,以及建立了现代商学的学科体系.     

On An Intriguing Distributional Identity

For a continuous random variable X with support equal to (a, b), with c.d.f. F, and g: Ω₁ → Ω₂ a continuous, strictly increasing function, such that Ω₁∩Ω₂?(a, b), but otherwise arbitrary, we establish that the random variables F(X) ? F(g(X)) and F(g^{? 1}(X)) ? F(X) have the same distribution. Further developments, accompanied by illustrations and observations, address as well the equidistribution identity U ? ψ(U) = ^dψ^{? 1}(U) ? U for U ～ U(0, 1), where ψ is a continuous, strictly increasing and onto function, but otherwise arbitrary. Finally, we expand on applications with connections to variance reduction techniques, the discrepancy between distributions, and a risk identity in predictive density estimation.     

Bayesian estimation of reliability using time-to-failure distribution of parametric degradation models

This paper focusses on computing the Bayesian reliability of components whose performance characteristics (degradation – fatigue and cracks) are observed during a specified period of time. Depending upon the nature of degradation data collected, we fit a monotone increasing or decreasing function for the data. Since the components are supposed to have different lifetimes, the rate of degradation is assumed to be a random variable. At a critical level of degradation, the time to failure distribution is obtained. The exponential and power degradation models are studied and exponential density function is assumed for the random variable representing the rate of degradation. The maximum likelihood estimator and Bayesian estimator of the parameter of exponential density function, predictive distribution, hierarchical Bayes approach and robustness of the posterior mean are presented. The Gibbs sampling algorithm is used to obtain the Bayesian estimates of the parameter. Illustrations are provided for the train wheel degradation data.     

Joint Modelling of Survival and Longitudinal Data with Informative Observation Times

In this paper, we consider the joint modelling of survival and longitudinal data with informative observation time points. The survival model and the longitudinal model are linked via random effects, for which no distribution assumption is required under our estimation approach. The estimator is shown to be consistent and asymptotically normal. The proposed estimator and its estimated covariance matrix can be easily calculated. Simulation studies and an application to a primary biliary cirrhosis study are also provided.     

安徽教育投资发展状况及优化路径研究

近年来，安徽省教育投资环境明显改善，大力推进教育均衡发展，教育投资总量不断增加，教育事业稳步发展，但同时也暴露出诸多问题。安徽省教育投资发展存在的主要问题是：教育投资增速放缓，多元化投资渠道尚未形成，投资结构不合理，区域分布不均衡。在“十九大”提出的教育发展精神指导下，针对安徽省教育投资发展现状与存在的主要问题，提出优化安徽省教育投资发展的主要路径。