Minimizing the false alarm rate in systems with transient abnormality

We consider a stochastic partially observable system that can switch between a normal state and a transient abnormal state before entering a persistent abnormal state. Only the persistent abnormal state requires alarms. The transient and persistent abnormal states may be similar in appearance, which can result in excess false alarms. We propose a partially observable Markov decision process model to minimize the false alarm rate, subject to a given upper bound on the expected alarm delay time. The cost parameter is treated as the Lagrange multiplier, which can be estimated from the bound of the alarm delay. We show that the optimal policy has a control‐limit structure on the probability of persistent abnormality, and derive closed‐form bounds for the control limit and present an algorithm to specify the Lagrange multiplier. We also study a specialized model where the transient and persistent abnormal states have the same observation distribution, in which case an intuitive “watchful‐waiting” policy is optimal. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 320–334, 2016     

Analysis of a machine repair problem with an unreliable server and phase type repairs and services

In this paper we study a machine repair problem in which a single unreliable server maintains N identical machines. The breakdown times of the machines are assumed to follow an exponential distribution. The server is subject to failure and the failure times are exponentially distributed. The repair times of the machine and the service times of the repairman are assumed to be of phase type. Using matrix‐analytic methods, we perform steady state analysis of this model. The time spent by a failed machine in service and the total time in the repair facility are shown to be of phase type. Several performance measures are evaluated. An optimization problem to determine the number of machines to be assigned to the server that will maximize the expected total profit per unit time is discussed. An illustrative numerical example is presented. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 462–480, 2003     

AHP及其在潜艇作战指挥上的应用

层次分析法(AHP)是一种简便的、实用的多准则决策分析方法.在对传统的AHP进行概述的基础上,针对其在实际应用中存在的问题,介绍了国内外几种经典的综合及改进的层次分析法,并建立了较为完备的潜艇作战指挥效能的评价体系和模糊综合评价模型,对潜艇的作战指挥效能进行了综合的定量分析和计算.最后展望了AHP在潜艇作战指挥上的应用前景,并对各种AHP进行了比较.     

浅谈培养解题能力

从深刻理解数学概念内涵、熟悉数学公式及变式和注重解题过程分析三个方面谈如何有效培养学生的解题能力 ,进而促进学生数学能力的发展     

基于马尔柯夫过程的武器系统目标分配问题决策分析

将防空作战中武器系统目标分配决策作为一个在动态随机系统中实现最优化的问题,并用马尔柯夫过程理论进行建模分析,提出新的算法并运用Matlab编程;通过对实行不同策略时武器系统长期平均效能的分析比较,指出在目标分配问题上仅靠原有的静态线性规划决策方法是不够的,还必须考虑动态随机对抗过程本身的特性.     

停产雷达装备维修器材持续保障风险评估方法

针对停产雷达装备维修器材持续保障过程中存在的筹措断供问题,提出基于改进风险矩阵法和层次分析法相结合的风险评估方法。首先建立保障风险评估指标体系,然后采用改进的风险矩阵进行风险评估,利用采用层次分析法解决存在递归层次时风险因素的评估问题,最后得出装备器材持续保障风险的综合量化值,为提出保障风险规避策略提供数据依据。利用某型雷达器材保障风险评估案例进行数据分析,验证了该方法的有效性。     

Bayesian enhanced decision making for deteriorating repairable systems with preventive maintenance

Since a system and its components usually deteriorate with age, preventive maintenance (PM) is often performed to restore or keep the function of a system in a good state. Furthermore, PM is capable of improving the health condition of the system and thus prolongs its effective age. There has been a vast amount of research to find optimal PM policies for deteriorating repairable systems. However, such decisions involve numerous uncertainties and the analyses are typically difficult to perform because of the scarcity of data. It is therefore important to make use of all information in an efficient way. In this article, a Bayesian decision model is developed to determine the optimal number of PM actions for systems which are maintained according to a periodic PM policy. A non‐homogeneous Poisson process with a power law failure intensity is used to describe the deteriorating behavior of the repairable system. It is assumed that the status of the system after a PM is somewhere between as good as new for a perfect repair and as good as old for a minimal repair, and for failures between two preventive maintenances, the system undergoes minimal repairs. Finally, a numerical example is given and the results of the proposed approach are discussed after performing sensitivity analysis. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

基于ARIS的战时修理业务流程仿真研究

利用ARIS建模方法与工具，对战时装备修理业务流程进行了仿真研究。以陆军某机步师某型装备为例，给出了战时修理业务的主流程模型以及各分支模型，通过仿真运行及结果分析，得出了制约该流程的瓶颈和需要进一步优化的对象，为装备维修保障过程仿真提供了一个很好的思路和方法。该方法对于开发战时维修保障效能仿真评估系统，实现维修保障系统的动态仿真和全要素评估具有重要的支撑作用。     

基于区间数的DS证据合成方法研究

在DS证据理论的应用过程中,命题的基本概率赋值函数起到了关键的作用,传统DS证据理论中基本概率赋值函数的取值为[0,1]中的单点值.在很难准确将证据所支持命题的基本概率赋值表示为[0,1]之间的单点值时,可以用区间数形式来表示命题的基本概率赋值.在建立符合运算封闭性的区间数广义求和与广义乘积算子的基础上,定义了基于区间数的基本概率赋值函数、信任函数以及似然函数等重要概念,给出了证据合成规则,进而提出了基于区间数的DS证据合成方法.计算实例表明,与传统DS证据合成方法相比,基于区间数的DS证据合成方法具有更灵活的应用特性和更小的计算复杂度.     

基于资源平衡的分布式星群网络连接接入策略

针对现有卫星网络接入策略未能充分考虑卫星资源以及合理确定卫星资源权重问题,提出了一种基于资源平衡的星群网络连接接入策略。该策略充分考虑卫星的多种资源建立卫星资源评价模型,利用移动代理技术,采用层次分析法和熵值法计算各卫星资源的主观和客观权重,并通过Kullback散度权重优化方法对主客观权重进行平衡处理,判决过程兼顾了卫星的综合性能水平和用户偏好,提高了接入的准确性和合理性。仿真结果表明,采用该接入策略,有效改善了新呼叫阻塞率和强制中断率。