Reliability Evaluation for A Class of Multi-Unit Cold Standby Systems under Poisson Shocks

The reliability evaluation for a multi-units cold standby system with a switch-over under Poisson shocks is investigated. The random value of each shock is assumed to be i.i.d. with some known distribution. Each arrival of a shock has a random effect on the operating unit and on the switch-over. When the operating unit fails while the switch-over is normal, the next cold standby unit will start to operate immediately. The system fails only when all the units have failed or both the operating unit and the switch-over have failed. The reliability function and the mean time to the failure (MTTF) of the system are obtained.     

Numerical Method for Reliability Analysis of Phased-Mission System Using Markov Chains

This article presents a numerical method for solving continuous time Markov chain (CTMC) model for reliability evaluation of phased-mission system. The method generates infinitesimal matrix based on the statistical independence of subsystem failure and repair process. The infinitesimal generator matrix is stored by the use of sparse matrix-compressed storage schemes, and the transient solution of the CTMC model is obtained by using three methods including the uniformization method, forward Euler method, and Runge-Kutta method, which take advantage of the sparseness of the infinitesimal generator matrix. An example PMS is used to compare the preconditioning methods for sparse matrix and numerical methods. Experiment results show that compressed row storage scheme (CRS) saves more storage than other storage formats, and uniformization method combined with CRS achieves the best efficiency and accuracy.     

A Poisson Limit Theorem for Reliability Models Based on Markov Chains

Abstract

In this article, we deal with a class of discrete-time reliability models. The failures are assumed to be generated by an underlying time inhomogeneous Markov chain. The multivariate point process of failures is proved to converge to a Poisson-type process when the failures are rare. As a result, we obtain a Compound Poisson approximation of the cumulative number of failures. A rate of convergence is provided.     

Reliability Evaluation of a Load-sharing Parallel System with Failure Dependence

In a parallel structure load-sharing system, the failure rate of the operating components will usually increase, due to the additional loading induced by the other components' failure. Hence failure dependency exists among components. To quantify the failure dependency, a dependence function is introduced. Under the assumptions that the repair time distributions of components are arbitrary and life times are exponential distributions whose failure rates vary with the number of operating components, a new load-sharing parallel system with failure dependency is proposed. To model the stochastic behavior of the system, the Semi-Markov process induced by it is given. The Semi-Markov kernel associated with the process is also presented. The availability and the time to the first system failure are obtained by employing Markov renewal theory. A numerical example is presented to illustrate the results obtained in the paper. The impact of the failure dependence on the system is also considered.     

Bayesian Analysis for a Redundant Repairable System with Imperfect Coverage

System characteristics of a redundant repairable system with two primary units and one standby are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the coverage factor is the same for an operating unit failure as that for a standby unit failure. Times to failure and times to repair of the operating and standby units are assumed to follow exponential distributions. When times to failure and times to repair with uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper.     

A natural conjugate prior for the nonhomogeneous poisson process with an exponential intensity function

This article presents a natural conjugate prior for the nonhomogeneous Poisson process (NHPP) with an exponential intensity function, for modeling the failure rate of repairable systems. The behavior of the conjugate prior distribution with respect to its parameters is studied, and the use of this prior in Bayesian estimation is compared to two other estimation approaches (the use of independent prior distributions, and the bivariate normal distribution). The use of the conjugate prior proposed here facilitates Bayesian statistical analysis of aging. In particular, the proposed prior allows us to explicitly account for dependence between the initial failure rate and the aging rate. This is a significant improvement over the assumptions made in most prior work (either the assumption that the aging rate is known, or the assumption that the initial failure rate and the aging rate are independent). Monte Carlo simulation shows that Bayesian estimation using the proposed prior generally performs at least as well as Bayesian estimation using independent priors for the initial failure rate and the aging rate,except in the case where the prior distribution underestimates both the initial failure rate and the aging rate.     

A Markov Chain Copula Model for Credit Default Swaps with Bilateral Counterparty Risk

Reduced-form credit risk models are widely used in pricing and hedging credit derivatives. Generating default dependency is the key element in any such model. In this article, we use Markov copulae approach to model the dependence structure of defaults between the three obligors, one is the reference entity, another is the protection seller, the other is the protection buyer(the investor), so we can consider the bilateral counterparty risk of credit default swaps(CDS). In this Markov chain copula model, we obtain the explicit formulas of the CDS premium rates C ₁(T) (with unilateral counterparty risk) and C ₂(T) (with bilateral counterparty risk). And then we perform some numerical experiments to analyze the difference of the fair spreads between the unilateral case and the bilateral case.     

Bayesian inference for generalized additive mixed models based on Markov random field priors

Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carlo simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as the usual covariates with fixed effects, metrical covariates with non-linear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates, are all treated within the same general framework by assigning appropriate Markov random field priors with different forms and degrees of smoothness. We applied the approach in several case-studies and consulting cases, showing that the methods are also computationally feasible in problems with many covariates and large data sets. In this paper, we choose two typical applications.     

A new characterization of the jump rate for piecewise-deterministic Markov processes with discrete transitions

Piecewise-deterministic Markov processes form a general class of non diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate of such a process with discrete transitions. We deduce from this result a non parametric technique for estimating this feature of interest. We state the uniform convergence in probability of the estimator. The methodology is illustrated on a numerical example.     

A natural conjugate prior for the non-homogeneous poisson process with a power law intensity function

This paper develops a natural conjugate prior for the non-homogeneous Poisson process (NHPP) with a power law intensity function. This prior allows for dependence between the scale factor and the aging rate of the NHPP. The proposed prior has relatively simple closed-form expressions for its moments, facilitating the assessment of prior parameters. The use of this prior in Bayesian estimation is compared to other estimation approaches using Monte Carlo simulation. The results show that Bayesian estimation using the proposed prior generally performs at least as well as either maximum likelihood estimation or Bayesian estimation using independent prior     

Exact Inference for the pth-Quantile and the Reliability of the Two-Parameter Exponential Distribution with Singly Type II Censoring: A Standard Approach

Starting from a standard pivot, exact inference for the pth-quantile and for the reliability of the two-parameter exponential distribution in case of singly Type II censored samples is developed in this article. Fernandez (2007 Fernandez , A. J. ( 2007 ). On calculating generalized confidence intervals for the two-parameter exponential reliability function . Statistics 41 : 129 – 135 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) first obtained some of the results proposed in this article, but, differently from what are proposed here, and developed his theory starting from a generalized pivot. An illustrative example shows that, with the expressions proposed in this article, it is also possible to overcome some shortcomings raising from the formulas by Fernandez (2007 Fernandez , A. J. ( 2007 ). On calculating generalized confidence intervals for the two-parameter exponential reliability function . Statistics 41 : 129 – 135 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Finally, a new expression for the moments of the pivot is obtained.     

宁夏荒漠化治理生态经济系统耦合效应研究

通过建立耦合度和耦合协调度模型,运用了层次分析法,分析了宁夏荒漠化治理的生态经济系统耦合状况。研究表明:宁夏荒漠化治理的生态水平有了较大幅度的提高,系统的耦合状况从最初的严重失调衰退类生态损益型过度到中级协调发展类生态滞后型,系统的耦合水平在逐年提高。但是,由于自然条件和工程实施的长期性等因素的制约,宁夏生态系统的耦合协调状况大多处于初级或者中级协调发展型,没有出现良好的状态。今后应协同推进区域经济生态化和生态经济化建设,建立高效生态经济体系,提升区域生态经济系统耦合的状态水平。     

渔业统计制度的国际比较及对我国的启示

随着全球经济一体化和信息技术的快速发展,我国的经济和贸易交往将进一步增强,社会经济现象将越来越复杂。因此,了解渔业统计制度并进行国际比较分析显得十分重要,它对国家制定渔业发展及经济管理政策有着重要意义。本文通过对各国渔业的统计制度和组织机构、统计法规和统计指标以及渔业统计管理和方法等方面的比较研究,为完善我国的渔业统计制度和运行机制提供借鉴。     

指标体系构建与优良性评价的方法研究

文章分析了传统构建指标体系中存在的问题,探讨了构建指标体系应遵循的几个主要原则。在此基础上阐述了构建指标体系定量方法的基本思路,从理论的角度构造了确定指标体系的定量方法,叙述了如何实现评价指标优良性的理论方法。该研究对建立科学的指标体系具有一定的理论指导价值,有利于建立科学的评价指标体系。     

A Markov-chain-based regression model with random effects for the analysis of 18O-labelled mass spectra

The enzymatic ¹⁸O-labelling is a useful technique for reducing the influence of the between-spectra variability on the results of mass-spectrometry experiments. A difficulty in applying the technique lies in the quantification of the corresponding peptides due to the possibility of an incomplete labelling, which may result in biased estimates of the relative peptide abundance. To address the problem, Zhu et al. [A Markov-chain-based heteroscedastic regression model for the analysis of high-resolution enzymatically ¹⁸O-labeled mass spectra, J. Proteome Res. 9(5) (2010), pp. 2669–2677] proposed a Markov-chain-based regression model with heteroscedastic residual variance, which corrects for the possible bias. In this paper, we extend the model by allowing for the estimation of the technical and/or biological variability for the mass spectra data. To this aim, we use a mixed-effects version of the model. The performance of the model is evaluated based on results of an application to real-life mass spectra data and a simulation study.     

国际服务贸易统计方法制度研究（上）

国际服务贸易是广义国际贸易的重要内容。国际服务贸易统计是社会经济统计的一个新的分支 ,在我国还处于起步阶段 ,尚无健全的方法制度。此文是对我国国际服务贸易统计方法制度的探索性研究 ,对国际服务贸易统计的重要意义、国际服务贸易的概念和统计原则、国际服务贸易的分类方法、指标体系、统计模式和实施步骤等问题提出了建设性的意见     

构建社会主义新农村指标体系研究

文章以中国当前建设社会主义新农村的科学内涵为依据,在借鉴和比较国内、外现有研究成果的基础上,按照一定的基本原则,从经济发展、管理民主、生活安康、设施改善、乡风文明、生态良好六个方面设置53项个体指标,并确定其对应目标值。通过定性与定量相结合的研究与分析,可以初步构建社会主义新农村指标体系。