Reliability modeling for mutually dependent competing failure processes due to degradation and random shocks

Many systems are subject to two mutually dependent competing risks namely degradation and random shocks, and they can fail due to two competing modes of failure, soft and hard failure. Soft failure occurs when the total degradation performance, including continuous degradation and sudden degradation increments caused by random shocks, exceeds a certain critical threshold level. Hard failure occurs when the magnitude of any shock (extreme shock model) or the accumulated damage of shocks (cumulative shock model) is beyond some strength threshold level, which is affected by the temporal degradation performance. From viewpoints of Stress-Strength models and Cumulative damage/shock model, a realistic reliability model is developed in this article for mutually dependent competing failure processes due to degradation and random shocks. Finally, a numerical example of Micro-Electro-Mechanical System (MEMS) is conducted to illustrate the implementation and effectiveness of the proposed model.     

The transformed inverse Gaussian process as an age- and state-dependent degradation model

In this paper, a transformed inverse Gaussian (TIG) process is introduced as a new family of monotonic degradation models. Different from most state-of-the-art degradation models, which can only characterize age-dependent performance degradation, the TIG process model is mainly introduced for degradation modelling of industrial products with age- and state-dependent performance degradation. With this new model, promising properties include (1) the modelling capability for characterizing products observed at discrete time points with age- and state-dependent degradation, (2) the mathematical tractability for calculating the reliability function and remaining useful life distribution with high efficiency, and (3) the modelling flexibility of incorporating explanatory variables and random effects for investigating a product population with unit-to-unit heterogeneity. To facilitate the degradation modelling and analysis, methods for parameter estimation and model selection are developed under a coherent Bayesian framework. Simulation studies and real cases are presented to demonstrate the proposed degradation model and the Bayesian methods.     

Reliability and availability analysis of stochastic degradation systems based on bivariate Wiener processes

It is still a challenge to study the degradation mechanisms of complex systems with multiple performance characteristics. This paper develops a two-stage stochastic degradation model. The degeneration processes of two correlated performance characteristics are described by a correlated bivariate Wiener process in the first stage, in which neither of the degradation levels of performance characteristics reaches their thresholds. When one of the degradation levels of performance characteristics reaches its threshold, the system operates defectively in the second stage, and the system degradation process is described by the other performance characteristic which is modeled by a univariate Wiener process. The system fails completely when both the degradation levels of performance characteristics reach their thresholds. Explicit expressions of the system reliability and availabilities are given based on different inspection and maintenance policies. Simulation is also presented, and it shows that the analytical results and the simulation results are in good agreement. Finally, a detailed case study of the rail track geometry degradation is given to demonstrate the results obtained in the paper.     

二元性能相关多阶段退化系统可靠性建模与分析

针对具有两个相关性能指标的随机退化系统,考虑退化过程的多阶段特征,采用Copula函数描述性能指标间的相关关系,建立多阶段二元相关Wiener过程退化模型。给出系统可靠度的解析表达式,提出蒙特卡洛方法模拟系统可靠度的流程步骤,得到系统可靠度的数值解,并验证了解析解的正确性。最后,通过数值算例验证模型的有效性。     

基于马尔可夫更新过程的多阶段冲击退化系统可靠性分析

系统所遭受的冲击和退化损害过程广泛存在着多阶段特征和相互依赖关系,为了更精确建模和分析系统冲击和退化间的依赖性,论文建立了多阶段冲击和退化过程的复合模型,提出了一种更加广义的冲击和退化过程依赖关系,即二者同时对系统损害累积过程产生贡献,进而导致系统阶段的改变,而状态转移又反馈性地影响冲击和退化过程。通过构造马尔可夫更新过程,基于半马尔科夫核,得到此类冲击退化模型的可靠度解析表达。     

Nonlinear general path models for degradation data with dynamic covariates

Degradation data have been widely used to estimate product reliability. Because of technology advancement, time‐varying usage and environmental variables, which are called dynamic covariates, can be easily recorded nowadays, in addition to the traditional degradation measurements. The use of dynamic covariates is appealing because they have the potential to explain more variability in degradation paths. We propose a class of general path models to incorporate dynamic covariates for modeling of degradation paths. Physically motivated nonlinear functions are used to describe the degradation paths, and random effects are used to describe unit‐to‐unit variability. The covariate effects are modeled by shape‐restricted splines. The estimation of unknown model parameters is challenging because of the involvement of nonlinear relationships, random effects, and shaped‐restricted splines. We develop an efficient procedure for parameter estimations. The performance of the proposed method is evaluated by simulations. An outdoor coating weathering dataset is used to illustrate the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

长贮产品基于贮存可靠度的序贯检测方法

长贮产品在贮存过程中,性能会逐步退化直至失效,保持和恢复系统可靠性的一种极为有效的方法就是周期地测试贮存产品的关键性能,并且修复和更换所发现的故障产品.检测时间间隔过长,则产品贮存可靠性达不到要求;检测时间过短,不仅要耗费大量的人力、物力甚至会诱发失效.考虑到产品贮存状态变化的复杂性,论文提出了Weibull分布产品基于贮存可靠度的序贯检测方法,可以动态调整检测间隔期,并结合仿真实例给出了序贯模型和参数估计方法.     

Robust portfolio selection involving options under a “ marginal+joint ” ellipsoidal uncertainty set

In typical robust portfolio selection problems, one mainly finds portfolios with the worst-case return under a given uncertainty set, in which asset returns can be realized. A too large uncertainty set will lead to a too conservative robust portfolio. However, if the given uncertainty set is not large enough, the realized returns of resulting portfolios will be outside of the uncertainty set when an extreme event such as market crash or a large shock of asset returns occurs. The goal of this paper is to propose robust portfolio selection models under so-called “ marginal+joint” ellipsoidal uncertainty set and to test the performance of the proposed models. A robust portfolio selection model under a “marginal + joint” ellipsoidal uncertainty set is proposed at first. The model has the advantages of models under the separable uncertainty set and the joint ellipsoidal uncertainty set, and relaxes the requirements on the uncertainty set. Then, one more robust portfolio selection model with option protection is presented by combining options into the proposed robust portfolio selection model. Convex programming approximations with second-order cone and linear matrix inequalities constraints to both models are derived. The proposed robust portfolio selection model with options can hedge risks and generates robust portfolios with well wealth growth rate when an extreme event occurs. Tests on real data of the Chinese stock market and simulated options confirm the property of both the models. Test results show that (1) under the “ marginal+joint” uncertainty set, the wealth growth rate and diversification of robust portfolios generated from the first proposed robust portfolio model (without options) are better and greater than those generated from Goldfarb and Iyengar’s model, and (2) the robust portfolio selection model with options outperforms the robust portfolio selection model without options when some extreme event occurs.     

Sampled‐data reliable stabilization of T‐S fuzzy systems and its application

In this article, based on sampled‐data approach, a new robust state feedback reliable controller design for a class of Takagi–Sugeno fuzzy systems is presented. Different from the existing fault models for reliable controller, a novel generalized actuator fault model is proposed. In particular, the implemented fault model consists of both linear and nonlinear components. Consequently, by employing input‐delay approach, the sampled‐data system is equivalently transformed into a continuous‐time system with a variable time delay. The main objective is to design a suitable reliable sampled‐data state feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop fuzzy system. For this purpose, using Lyapunov stability theory together with Wirtinger‐based double integral inequality, some new delay‐dependent stabilization conditions in terms of linear matrix inequalities are established to determine the underlying system's stability and to achieve the desired control performance. Finally, to show the advantages and effectiveness of the developed control method, numerical simulations are carried out on two practical models. © 2016 Wiley Periodicals, Inc. Complexity 21: 518–529, 2016     

Non-parametric estimation from simultaneous degradation and failure time dataEstimation non-paramétrique à partir de données de dégradation et de défaillances

The paper considers degradation and failure time models with multiple failure modes. Dependence of traumatic failure intensities on the degradation level are included into the models. Non-parametric estimators of various reliability characteristics are proposed. Theorems on simultaneous asymptotic distribution of random functions characterizing degradation and intensities of traumatic events are proposed. To cite this article: V. Bagdonavi?ius et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 183–188.     

Modeling of degradation data via wiener stochastic process based on acceleration factor constant principle

This paper proposes a systematic method of modeling accelerated degradation data based on the acceleration factor constant principle. Wiener stochastic process is considered because it is the most extensively used for degradation modeling. For the Wiener stochastic processes with three different time functions, the parameter relationships, which should be satisfied under any two different stress levels, are deduced according to the acceleration factor constant principle. The deduced parameter relationships indicate the stress-related parameters, which are applied to establish accurate accelerated degradation models. In addition, the deduced parameter relationships provide a guidance to test the consistency of the degradation mechanisms under different stress levels. A hypothesis method based on Analysis of Variance is adopted to identify the accelerated stress levels with different degradation mechanism. The degradation data under these stress levels should not be used to assess the product's reliability. The methods of validating accelerated degradation models and reliability assessments are also proposed. The simulation results prove the feasibility and effectiveness of the proposed methods. From the numerical example, it is concluded that the accelerated degradation model established based on the acceleration factor constant principle is more credible and accurate.     

Improved techniques for parametric and nonparametric evaluations of the first‐passage time for degradation processes

For degradation data in reliability analysis, estimation of the first‐passage time (FPT) distribution to a threshold provides valuable information on reliability characteristics. Recently, Balakrishnan and Qin (2019; Applied Stochastic Models in Business and Industry, 35:571–590) studied a nonparametric method to approximate the FPT distribution of such degradation processes if the underlying process type is unknown. In this article, we propose some improved techniques based on saddlepoint approximation, which enhance those existing methods. Numerical examples and Monte Carlo simulation studies are used to illustrate the advantages of the proposed techniques. Limitations of the improved techniques are discussed and some possible solutions to such are proposed. Some concluding remarks and practical recommendations are provided based on the results.     

Failure probability estimation with differently sized reference products for semiconductor burn‐in studies

A burn‐in study is applied to demonstrate compliance with a targeted early life failure probability of semiconductor products. This is achieved by investigating a sample of the produced chips for reliability‐relevant failures. Usually, a burn‐in study is carried out for a specific reference product with the aim to scale the reference product's failure probability to follower products with different chip sizes. It also appears, however, that there are multiple, differently sized reference products for which burn‐in studies are performed. In this paper, we present a novel model for estimating the failure probability of a chip, which is capable of handling burn‐in studies on multiple reference products. We discuss the model from a combinatorial and a Bayesian perspective; both approaches are shown to provide more accurate estimation results in comparison with a simple area‐based approach. Moreover, we discuss the required modifications of the model if the observed failures are tackled by countermeasures implemented in the chip production process. Finally, the model is applied to the problem of determining the failure probabilities of follower products on the basis of multiple reference products.     

Epsilon‐stable quasi‐static brittle fracture evolution

We introduce a new definition of stability, ε‐stability, that implies local minimality and is robust enough for passing from discrete‐time to continuous‐time quasi‐static evolutions, even with very irregular energies. We use this to give the first existence result for quasi‐static crack evolutions that both predicts crack paths and produces states that are local minimizers at every time, but not necessarily global minimizers. The key ingredient in our model is the physically reasonable property, absent in global minimization models, that whenever there is a jump in time from one state to another, there must be a continuous path from the earlier state to the later along which the energy is almost decreasing. It follows that these evolutions are much closer to satisfying Griffith's criterion for crack growth than are solutions based on global minimization, and initiation is more physical than in global minimization models. © 2009 Wiley Periodicals, Inc.     

Bayesian inference on longitudinal-survival data with multiple features

The modeling of longitudinal and survival data is an active research area. Most of researches focus on improving the estimating efficiency but ignore many data features frequently encountered in practice. In this article, we develop a joint model that concurrently accounting for longitudinal-survival data with multiple features. Specifically, our joint model handles skewness, limit of detection, missingness and measurement errors in covariates which are typical observed in the collection of longitudinal-survival data from many studies. We employ a Bayesian approach for making inference on the joint model. The proposed model and method are applied to an AIDS study. A few alternative models under different conditions are compared. Some interesting results are reported. Simulation studies are conducted to assess the performance of the proposed methods.     

考虑失效相关性的长寿命系统可靠性置信限综合评估模型

根据高长寿命产品的试验数据特征,采用退化轨迹拟合、两点分布和区间估计思想,分位数置信限-失效阈值干涉、可靠度预估响应模拟,分别给出了小样本和大样本试样下的零部件可靠性置信限评估方法。运用Copula理论拟合零部件失效间的动态相关性,从而对应性地建立了系统级可靠性置信限综合评估模型。该模型改善了独立性系统可靠性置信限评估方法预估结果过于保守的情形。算例验证了该类模型的可行性和有效性。     

Reliability assessment for load‐sharing systems with exponential components using statistical expansion as a correction

Among recent system models, one specific type of system is generally used to model the dependence among components. Components are connected parallel in such systems as they fail one by one and are supposed to share the system work load. The model is thus referred to as the load‐sharing system model. Despite the availability of extensive reliability assessment methods for different systems, load‐sharing systems have not received enough attention from the scholars who have studied reliability assessment so far. Load‐sharing systems are generally designed for high levels of reliability. Therefore, tests for such systems can be expensive and time consuming. Limitation on resources always leads to small test sample sizes. This increases the difficulties associated with obtaining an accurate and robust system reliability assessment result. This paper proposes a novel assessment method for a certain type of load‐sharing system with components following exponential lifetime distributions. Based on the parameter estimation of the system reliability model, we introduce the Winterbottom‐Cornish‐Fisher asymptotic expansion method for implementing a correction of normal approximation. We demonstrate the accuracy of our method through a series of examples and simulation studies.     

Causes of the damage created by laser pulses in transparent polymers

The characteristics of the damage created in PMM, PS, and PC specimens by multiple irradiation are discussed. It is shown that, in addition to the growth of the damage zone, the processes of crack development that determine this zone are also important. The damage created in PMM when the laser beam is interrupted by a cylindrical cavity is considered. In this case, the cavity acts as a diverging lens and the damage beyond it is determined by the scattered flux. The damage produced in specimens of different shapes is investigated. A model is proposed for crack development in a polymer irradiated by a powerful flux. The model is consistent with most of the known experimental facts.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1035–1042, 1967     

云计算环境资源监控系统研究

为保障云计算平台的可靠性,基于Ganglia,采用Eucalyptus开源云平台,提出了云计算平台资源监控系统架构.从总体结构、监控信息处理流程等多个方面对监控系统进行了详细阐述,提出了动态更换虚拟机簇头的算法,并对算法与原型系统进行了验证和性能评测.分析与评测结果表明,所提系统能够适用于云计算环境资源信息的实时监测与预警,具备系统开销较低,用户接口友好的特点,能准确反映系统、虚拟机的负载信息,有助于云计算系统服务可靠性的提升.簇头动态更换算法能及时发现失效的簇头并更换为更健壮的虚拟机,保证了监测系统的正常运行.     

Concentrated portfolio selection models based on historical data

A new risk measure fully based on historical data is proposed, from which we can naturally derive concentrated optimal portfolios rather than imposing cardinality constraints. The new risk measure can be expressed as a quadratics of the introduced greedy matrix, which takes investors' joint behavior into account. We construct distribution‐free portfolio selection models in simple case and realistic case, respectively. The latest techniques for describing transaction cost constraints and solving nonconvex quadratic programs are utilized to obtain the optimal portfolio efficiently. In order to show the practicality, efficiency, and robustness of our new risk measure and corresponding portfolio selection models, a series of empirical studies are carried out with trading data from advanced stock markets and emerging stock markets. Different performance indicators are adopted to comprehensively compare results obtained under our new models with those obtained under the mean‐variance, mean‐semivariance, and mean‐conditional value‐at‐risk models. Out‐of‐sample results sufficiently show that our models outperform the others and provide a simple and practical approach for choosing concentrated, efficient, and robust portfolios. Copyright © 2014 John Wiley & Sons, Ltd.