Linear programming and the reliability of multicomponent systems

Several problems in the assignment of parallel redundant components to systems composed of elements subject to failure are considered. In each case the problem is to make an assignment which maximizes the system reliability subject to system constraints. Three distinct problems; are treated. The first is the classical problem of maximizing system reliability under total cost or weight constraints when components are subject to a single type of failure. The second problem deals with components which are subject to two types of failure and minimizes the probability of one mode of system failure subject to a constraint on the probability of the other mode of system failure. The third problem deals with components which may either fail to operate or may operate prematurely. System reliability is maximized subject to a constraint ori system safety. In each case the problem is formulated as an integer linear program. This has an advantage over alternative dynamic programming formulations in that standard algorithms may be employed to obtain numerical results.     

Sequential determination of inspection epochs for reliability systems with general lifetime distributions

The problem of determining the optimal inspection epoch is studied for reliability systems in which N components operate in parallel. Lifetime distribution is arbitrary, but known. The optimization is carried with respect to two cost factors: the cost of inspecting a component and the cost of failure. The inspection epochs are determined so that the expected cost of the whole system per time unit per cycle will be minimized. The optimization process depends in the general case on the whole failure history of the system. This dependence is characterized. The cases of Weibull lifetime distributions are elaborated and illustrated numerically. The characteristics of the optimal inspection intervals are studied theoretically.     

Some comparisons of residual life of coherent systems with exchangeable components

Most of the research, on the study of the reliability properties of technical systems, assume that the components of the system operate independently. However, in real life situation, it is more reasonable to assume that there is dependency among the components of the system. In this article, we give sufficient conditions based on the signature and the joint distribution of component lifetimes to obtain stochastic ordering results for coherent and mixed systems with exchangeable components. Some stochastic orders on dynamic (or conditional) signature of coherent systems are also provided. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 549–556, 2014     

A load-sharing model: The linear breakdown rule

An n-component parallel system is subjected to a known load program. As time passes, components fail in a random manner, which depends on their individual load histories. At any time, the surviving components share the total load according to some rule. The system's life distribution is studied under the linear breakdown rule and it is shown that if the load program is increasing, the system lifetime is IFR. Using the notion of Schur convexity, a stochastic comparison of different systems is obtained. It is also shown that the system failure time is asymptotically normally distributed as the number of components grows large. All these results hold under various load-sharing rules; in fact, we show that the system lifetime distribution is invariant under different load-sharing rules.     

云模型和混合Petri网相结合的系统可靠性评价

针对复杂系统可靠性评价中工作环境可变的情形,提出基于云模型和混合Petri网相结合的可靠性评价方法。首先采用云模型描述系统的环境适应能力指数,并将其作为混合Petri模型中连续库所的托肯值来控制该模型中变迁的变迁率,然后采用基于Petri网的蒙特卡罗方法对不同环境下的系统可靠性进行仿真求解,得到系统在不同时刻下的失效率。最后以一个C4ISR系统为例,验证了该方法在解决可变工作环境下的系统可靠性评估是可行的。     

On a class of multiple failure mode systems

The primary objective of this work is to introduce and perform a detailed study of a class of multistate reliability structures in which no ordering in the levels of components' performances is necessary. In particular, the present paper develops the basic theory (exact reliability formulae, reliability bounds, asymptotic results) that will make it feasible to investigate systems whose components are allowed to experience m ≥ 2 kinds of failure (failure modes), and their breakdown is described by different families of cut sets in each mode. For illustration purposes, two classical (binary) systems are extended to analogous multiple failure mode structures, and their reliability performance (bounds and asymptotic behavior) is investigated by numerical experimentation. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 167–185, 2002; DOI 10.1002/nav.10007     

Reliability control for mission-critical items

Reliability control for mission-critical items is studied. The purpose of the control is to ensure the attainment during mission time of a required performance level which is based on suitably defined measures. This is achieved by replacing the item during normal operation time as soon as the reliability requirement is violated. We first consider the case of a known life distribution, but the main focus of the work is on the case where the life distribution is not completely specified. A Bayesian approach is taken and a replacement procedure is constructed on the basis of the overall uncertainty we face, namely, the stochastic failure process and our (continuously revised) probabilistic assessment of the underlying life distribution. The resulting replacement policy is investigated and detailed results are obtained for some common life distributions.     

军用车辆行动部分疲劳寿命随机有限元分析

阐述了基于随机有限元的车辆行动部分可靠性原理及基本过程,将结构件的弹性模量、泊松比和几何尺寸等因素定义为随机场,并对其进行离散,同时分析了车辆行驶的典型路面的路面谱,利用随机有限元求解在不同的路面状况下车辆行动零部件的受力情况,得到了零部件危险点应力的随机分布和不同路面状况下疲劳可靠性,并对相关的实例进行分析。     

Stochastic framework for partially degradation systems with continuous component degradation‐rate‐interactions

Many conventional models that characterize the reliability of multicomponent systems are developed on the premise that for a given system, the failures of its components are independent. Although this facilitates mathematical tractability, it may constitute a significant departure from what really takes place. In many real‐world applications, system components exhibit various degrees of interdependencies, which present significant challenges in predicting degradation performance and the remaining lifetimes of the individual components as well as the system at large. We focus on modeling the performance of interdependent components of networked systems that exhibit interactive degradation processes. Specifically, we focus on how the performance level of one component affects the degradation rates of other dependent components. This is achieved by using stochastic models to characterize how degradation‐based sensor signals associated with the components evolve over time. We consider “Continuous‐Type” component interactions that occur continuously over time. This type of degradation interaction exists in many applications, in which interdependencies occur on a continuum. We use a system of stochastic differential equations to capture such “Continuous‐Type” interaction. In addition, we utilize a Bayesian approach to update the proposed model using real‐time sensor signals observed in the field and provide more accurate estimation of component residual lifetimes. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 286–303, 2014     

Inspection policies and processes for deteriorating systems subject to catastrophic failure

Deteriorating reliability systems that are subject to catastrophic failure are analyzed in order to propose and evaluate some deterministic and stochastic inspection models. The underlying deterioration process is assumed to be an increasing Markov renewal process where the true state of the system can not be determined by simple observations. Instead, some tests can be done in order to detect if the system has positive deterioration or not. The results of the tests, however, are not perfect so that the probability of true and false detections depend on the unobserved state of the system. The system is inspected either deterministically at prespecified points in time, or stochastically at random points in time. Both types of models are considered to present explicit computational expressions for various performance measures like the expected number of inspections with different results and the probability of detection. Some practical applications of the results are also included.     

Optimal replacement rules based on different information levels

We consider the following replacement model in reliability theory. A technical system with random lifetime is replaced upon failure. Preventive replacements can be carried out before failure. The time for such a replacement depends on the observation of a random state parameter and is therefore in general a random time. Different costs for preventive and failure replacements are introduced which may depend on the age of the working system. The optimization criterion followed here to find an optimal replacement time is to minimize the total expected discounted costs. The optimal replacement policy depends on the observation of the state of the system. Results of the theory of stochastic processes are used to obtain the optimal strategy for different information levels. Several examples based on a two-component parallel system with possibly dependent component lifetimes show how the optimal replacement policy depends on the different information levels and on the degree of dependence of the components. © 1992 John Wiley & Sons, Inc.     

系统部件在储存状态下最佳检测周期的确定

由于储存时间长,导弹等航空系统的备件存在一定的失效,而且可靠性也会逐渐降低。为了使可靠性保持在一定的水平之上,就要定期进行检验或修理。在费用最小条件下对如何确定检验周期进行了分析,并结合具体分布举例作了计算分析。     

Probability inequalities via negative dependence for random variables conditioned on order statistics

Distributions are studied which arise by considering independent and identically distributed random variables conditioned on events involving order statistics. It is shown that these distributions are negatively dependent in a very strong sense. Furthermore, bounds are found on the distribution functions. The conditioning events considered occur naturally in reliability theory as the time to system failure for k-out-of-n systems. An application to systems formed with “second-hand” components is given.     

屏蔽数据在新型截尾样本下系统的可靠性分析

当系统含有屏蔽数据时,在具有随机移走逐步增加型截尾模型下,讨论了部件寿命服从双参数指数分布的串联系统可靠性估计问题。设随机移走系统数服从二项分布,利用极大似然方法,Bayes理论及方法,推导出双参数指数部件参数、系统可靠性函数、失效率函数及移走概率的极大似然估计和Bayes估计。并利用Monte Carlo方法对两种估计结果进行了比较,表明Bayes估计较极大似然估计效果更优。     

加权随机模拟的时变可靠性分析方法

针对结构时变可靠性的随机模拟分析方法计算代价大的问题,在极值方法的基础上提出基于加权随机模拟的时变可靠性分析策略。时变可靠性分析需要计算在不同时间处的失效概率,通常需要进行多次可靠性分析,计算代价巨大。所提方法通过对常规静态可靠性的随机模拟方法进行改进拓展,运用加权策略分别发展了加权蒙特卡洛法和加权重要抽样法,使之能够高效分析计算时变可靠性问题。所提方法仅需一次常规可靠性分析模拟,即可得到时变失效概率函数估计。采用管状悬臂梁和十杆桁架两个算例进行验证。结果表明,基于加权思想的分析方法在能确保精确度的前提下能够大幅度减小计算量,提高计算效率。     

A note on necessary and sufficient conditions for ordering properties of coherent systems with exchangeable components

We give necessary and sufficient conditions based on signatures to obtain distribution‐free stochastic ordering properties for coherent systems with exchangeable components. Specifically, we consider the stochastic, the hazard (failure) rate, the reversed hazard rate, and the likelihood ratio orders. We apply these results to obtain stochastic ordering properties for all the coherent systems with five or less exchangeable components. Our results extend some preceding results. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

软件构件可靠性与费用分配最优模型

针对软件构件可靠性和费用分配问题,给出一种可靠性和费用分配最优模型。文中将软件系统可靠性定义为软件构件失效密度、操作剖面、构件使用矩阵以及软件无失效运行时间的函数,描述了费用最优模型的建立和利用非线性规划理论求解模型的步骤,有效地处理了带有复杂计算的目标函数和约束条件的可靠性和费用最优分配问题。计算实例表明,利用该模型进行可靠性和费用分配是可行的。     

Two novel critical shock models based on Markov renewal processes

In this paper, we investigate systems subject to random shocks that are classified into critical and noncritical categories, and develop two novel critical shock models. Classical extreme shock models and run shock models are special cases of our developed models. The system fails when the total number of critical shocks reaches a predetermined threshold, or when the system stays in an environment that induces critical shocks for a preset threshold time, corresponding to failure mechanisms of the developed two critical shock models respectively. Markov renewal processes are employed to capture the magnitude and interarrival time dependency of environment-induced shocks. Explicit formulas for systems under the two critical shock models are derived, including the reliability function, the mean time to failure and so on. Furthermore, the two critical shock models are extended to the random threshold case and the integrated case where formulas of the reliability indexes of the systems are provided. Finally, a case study of a lithium-ion battery system is conducted to illustrate the proposed models and the obtained results.     

Probabilistic models of decreasing failure rate processes

The “infant mortality” effect observed in the statistical treatment of reliability consists of a decreasing with age of the conditional probability of equipment failure (failure rate). One widely applicable explanatory hypothesis is that of population heterogeneity. This is developed here as a basis for several specific models of decreasing failure rate processes. Since, in the case of repairable devices, decreasing failure rate is often observed after the occurrence of failure and repair, consideration is extended to include repair in an explicit way. This union of failure and repair models is a fruitful one in view of the interaction between the two processes and gives a complete picture of the life of the device in terms of a stochastic process, usually with non-independent interfailure times. Four models, of particular significance due to their plausibility, mathematical tractability, and frugality of parameterization, are presented.     

Coherent systems based on sequential order statistics

The sequential order statistics (SOS) are a good way to model the lifetimes of the components in a system when the failure of a component at time t affects the performance of the working components at this age t. In this article, we study properties of the lifetimes of the coherent systems obtained using SOS. Specifically, we obtain a mixture representation based on the signature of the system. This representation is used to obtain stochastic comparisons. To get these comparisons, we obtain some ordering properties for the SOS, which in this context represent the lifetimes of k‐out‐of‐n systems. In particular, we show that they are not necessarily hazard rate ordered. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011