Maintaining systems with heterogeneous spare parts

We consider the problem of optimally maintaining a stochastically degrading, single‐unit system using heterogeneous spares of varying quality. The system's failures are unannounced; therefore, it is inspected periodically to determine its status (functioning or failed). The system continues in operation until it is either preventively or correctively maintained. The available maintenance options include perfect repair, which restores the system to an as‐good‐as‐new condition, and replacement with a randomly selected unit from the supply of heterogeneous spares. The objective is to minimize the total expected discounted maintenance costs over an infinite time horizon. We formulate the problem using a mixed observability Markov decision process (MOMDP) model in which the system's age is observable but its quality must be inferred. We show, under suitable conditions, the monotonicity of the optimal value function in the belief about the system quality and establish conditions under which finite preventive maintenance thresholds exist. A detailed computational study reveals that the optimal policy encourages exploration when the system's quality is uncertain; the policy is more exploitive when the quality is highly certain. The study also demonstrates that substantial cost savings are achieved by utilizing our MOMDP‐based method as compared to more naïve methods of accounting for heterogeneous spares.     

舰船机电系统使用故障数据分析研究

舰船机电系统在使用维修过程中所记录的故障数据通常质量不高,信息记录不完整、不准确。针对这类不完备数据,利用图示法给出了故障趋势的判定。在此基础上,分别利用齐次泊松过程、非齐次泊松过程和几何过程,对装备的历史故障数据进行了分析。结果表明,几何过程产生的拟合误差最小,并据此预测了装备的未来故障强度。     

Minimal LST representations of MAP(n)s: Moment fittings and queueing approximations

A Markovian arrival process of order n, MAP(n), is typically described by two n × n transition rate matrices in terms of rate parameters. While it is straightforward and intuitive, the Markovian representation is redundant since the minimal number of parameters is n² for non‐redundant MAP(n). It is well known that the redundancy complicates exact moment fittings. In this article, we present a minimal and unique Laplace‐Stieltjes transform (LST) representations for MAP(n)s. Even though the LST coefficients vector itself is not a minimal representation, we show that the joint LST of stationary intervals can be represented with the minimum number of parameters. We also propose another minimal representation for MAP(3)s based on coefficients of the characteristic polynomial equations of the two transition rate matrices. An exact moment fitting procedure is presented for MAP(3)s based on two proposed minimal representations. We also discuss how MAP(3)/G/1 departure process can be approximated as a MAP(3). A simple tandem queueing network example is presented to show that the MAP(3) performs better than the MAP(2) in queueing approximations especially under moderate traffic intensities. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 549–561, 2016     

具有多类索赔到达保险风险模型的破产问题

应用Markov骨架过程的方法和补充变量技巧研究了索赔为多类一般到达的保险风险模型 ,分别得到了破产时间与破产时刻前后资产盈余的联合分布以及破产时间的分布。使得索赔为一般到达的保险风险问题的研究取得了较大的进展。     

群体可拓层次分析法在C~4ISR系统效能指标赋权中的应用

指标赋权是C4ISR系统效能评估的重要环节,提出了一种新的指标赋权方法——群体可拓层次分析法(GEAHP),较好地解决了指标赋权过程中多专家意见集结的问题,以及判断矩阵的合理构建和一致性检验问题。描述了GEAHP的基本过程,并通过实例对其正确性进行了验证。     

Dynamic policy for idling time preservation

This study aims to determine and evaluate dynamic idling policies where an agent can idle while some customers remain waiting. This type of policies can be employed in situations where the flow of urgent customers does not allow the agent to spend sufficient time on back-office tasks. We model the system as a single-agent exponential queue with abandonment. The objective is to minimize the system's congestion while ensuring a certain proportion of idling time for the agent. Using a Markov decision process approach, we prove that the optimal policy is a threshold policy according to which the agent should idle above (below) a certain threshold on the queue length if the congestion-related performance measure is concave (convex) with respect to the number of customers present. We subsequently obtain the stationary probabilities, performance measures, and idling time duration, expressed using complex integrals. We show how these integrals can be numerically computed and provide simpler expressions for fast-agent and heavy-traffic asymptotic cases. In practice, the most common way to regulate congestion is to control access to the service by rejecting some customers upon arrival. Our analysis reveals that idling policies allow high levels of idling probability that such rejection policies cannot reach. Furthermore, the greatest benefit of implementing an optimal idling policy occurs when the objective occupation rate is close to 50% in highly congested situations.     

军械保障指挥自动化系统效能评估指标体系研究

在对系统结构和功能进行详细分析的基础上,构建了某级军械指挥自动化系统效能评估指标体系模型,给出了各级指标的专家判断矩阵,对其一致性进行检验,得出了各评估指标的权重。     

反导防空导弹拦截决策分析模型

反导防空导弹在防空体系中发挥着越来越重要的作用，而拦截决策是实施拦截过程的一个重要方面。在本文中，考虑了多个进攻目标的情况以及反导防空导弹拦截能力的限制，利用０—１整数规划的方法给出了确定反导防空导弹最佳拦截方案的统一的优化决策模型。     

层次分析法在武器系统效能建模中的应用

在武器系统效能评估中 ,武器系统的战技指标 ,是评估武器系统效能的重要因素。本文利用层次分析法和矩阵摄动方法 ,对武器系统的战技指标进行分析 ,建立了武器系统效能能力指数模型 ,并把可靠性和维修性应用于效能计算之中。由此建立了武器系统效能模型并进行了评估     

Markovian models of three‐on‐one combat involving a hidden defender

In this paper, Markovian models of three‐on‐one stochastic firefights between ground‐based weapon systems are developed. These models address a common scenario of interest to the military, but one which has been much neglected in analytic combat models, that of combat between a hidden defender and an exposed attacking force. Each combatant must detect an opponent before commencing their firing cycle, a task which is considerably more difficult for the attacker. In the models developed here, the defender detects the exposed attacking group after an exponentially distributed time interval, while each attacker has a fixed probability of detecting the defender via the flash signature produced after each shot fired by him. The utility of the approach is demonstrated by investigating what impact the introduction of a coordinated gun‐laying system for the attacking force might have, a system made possible by battlefield digitization. The method used here allows models to be developed incrementally. This and other advantages of the Markovian approach are discussed. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 627–646, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10041