The variance of the coverage of a randomly located area target by a salvo of weapons

We derive formulas for the variance of that proportion of the value of a randomly located, circularly symmetric area target that is destroyed by N independently fired weapons of identical type whose damage functions are circularly symmetric about the respective impact points. The probability density functions of the target center location and of the weapon impact points are also circularly symmetric. The general results are specialized to uniform and Gaussian functions. In the latter case a closed-form solution (triple integral) for the variance of the coverage is derived. Similar to some well-known results on expected coverage, this expression for the variance of the coverage can be easily evaluated by numerical quadrature. Numerical results are given which indicate the target coverage variability caused by the combined effects of random target-locating errors and weapon impact point fluctuations.     

A duel complicated by false targets and uncertainty as to opponent type

An attacker, being one of two types, initiates an attack at some time in the interval [-T, 0]. The a priori probabilities of each type are known. As time elapses the defender encounters false targets which occur according to a known Poisson process and which can be properly classified with known probability. The detection and classification probabilities for each type attacker are given. If the defender responds with a weapon at the time of attack, he survives with a probability which depends on the number of weapons in his possession and on attacker type. If he does not respond, his survival probability is smaller. These probabilities are known, as well as the current number of weapons in the defender's possession. They decrease as the number of weapons decreases. The payoff is the defender's survival probability. An iterative system of first-order differential equations is derived whose unique solution V₁(t),V₂(t),…,V_k(t) is shown to be the value of the game at time t, when the defender has 1, 2,…, k,… weapons, respectively. The optimal strategies are determined. Limiting results are obtained as t→-∞, while the ratio of the number of weapons to the expected number of false targets remaining is held constant.     

Confidence intervals in discrete event simulation: A comparison of replication and batch means

Suppose that we have enough computer time to make n observations of a stochastic process by means of simulation and would like to construct a confidence interval for the steady-state mean. We can make k independent runs of m observations each (n=k.m) or, alternatively, one run of n observations which we then divide into k batches of length m. These methods are known as replication and batch means, respectively. In this paper, using the probability of coverage and the half length of a confidence interval as criteria for comparison, we empirically show that batch means is superior to replication, but that neither method works well if n is too small. We also show that if m is chosen too small for replication, then the coverage may decrease dramatically as the total sample size n is increased.     

基于效果的舰载软硬武器近卫火力分配研究

针对水面舰艇利用软硬杀伤武器抗击近区目标作战使用问题,提出基于毁伤失能和据止等作战效果的软硬武器使用火力决策方法,建立水面舰艇近卫作战软硬武器火力分配模型,通过实例建立模型,并将建立的非线性模型转化成利用匈牙利算法进行解算的指派问题进行模型解算,研究的方法和结果对水面舰艇近卫作战火力分配决策方案的制定具有一定的指导意义。     

Estimating the accuracy of the coverages of outer β-content tolerance intervals,which control both tails of the normal distribution

Tolerance limits which control both tails of the normal distribution so that there is no more than a proportion β₁ in one tail and no more than β₂ in the other tail with probability γ may be computed for any size sample. They are computed from X? - k₁S and X? - k₂S, where X? and S are the usual sample mean and standard deviation and k₁ and k₂ are constants previously tabulated in Odeh and Owen [3]. The question addressed is, “Just how accurate are the coverages of these intervals (– Infin;, X? – k₁S) and (X? + k₂S, ∞) for various size samples?” The question is answered in terms of how widely the coverage of each tail interval differs from the corresponding required content with a given confidence γ′.     

A proportional defense model

This paper considers the problem of defending a set of point targets of differing values. The defense is proportional in that it forces the offense to pay a price, in terms of reentry vehicles expended, that is proportional to the value of the target. The objective of the defense is to balance its resources so that no matter what attack is launched, the offense will have to pay a price greater than or equal to some fixed value for every unit of damage inflicted. The analysis determines which targets should be defended and determines the optimal firing doctrine for interceptors at defended targets. A numerical example is included showing the relationship between the total target damage and the size of the interceptor force for different values of p, the interceptor single shot kill probability. Some generalizations are discussed.     

电磁脉冲武器对抗来袭目标可行性研究

针对电磁脉冲武器独特的毁伤机理,计算了杀伤覆盖区域和辐射到目标处的功率密度等作战能力指标,并以反舰导弹为例分析了强电磁脉冲的耦合途径,通过评估前后门耦合的电磁能量,在理论上论证了用电磁脉冲武器对抗来袭目标的可行性.     

防空导弹的新家族——反精导武器防空导弹

现代精确制导武器对敏感点目标的威胁,主要表现在高的击毁概率和多发协同攻击上,保卫点目标的反精确制导武器防空导弹必须具有多目标通道和高速率全向射击能力;必须具有高的可靠性和对精确制导武器的击爆能力,将构成防空导弹系列中的一个新家族。     

舰载近区防卫武器综合运用

水面舰艇近区防卫武器的作战运用研究是舰载武器作战运用研究的新课题。在分析近区防卫目标特征、武器特点、作战方法的基础上,提出近区防卫武器综合运用一般原则,基于作战时域的连续性及效果的叠加性,构建近区防卫武器使用逻辑结构,建立武器运用的对策模型,可为近区防卫武器的科学使用提供理论参考。     

Signature based analysis of m‐Consecutive‐k‐out‐of‐n: F systems with exchangeable components

In this article, we study reliability properties of m‐consecutive‐k‐out‐of‐n: F systems with exchangeable components. We deduce exact formulae and recurrence relations for the signature of the system. Closed form expressions for the survival function and the lifetime distribution as a mixture of the distribution of order statistics are established as well. These representations facilitate the computation of several reliability characteristics of the system for a given exchangeable joint distribution or survival function. Finally, we provide signature‐based stochastic ordering results for the system's lifetime and investigate the IFR preservation property under the formulation of m‐consecutive‐k‐out‐of‐n: F systems. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

On maximization of the integral of a bell-shaped function over a symmetric set

Given a target T in Euclidean n-space Rⁿ and a point bomb whose point of impact in Rⁿ is governed by a probability distribution about the aim point a, what choice of a maximizes the probability of a hit v_a(T)? Of course, only in special cases is an exact solution of this problem obtainable. This paper treats targets T which are symmetric about the origin o and demonstrates conditions on the extent of T and the impact density f, a density with respect to Lebesgue measure, sufficient for v_a(T) to be monotone in the distance from a to o and maximized at a = o. The results are applied to various tactical situations.     

要地防卫反无人机装备发展与启示

无人机技术的发展及其在现代战场的广泛应用，给机场、阵地、营地、指挥所等要地的防空体系带来新的挑战。以俄罗斯铠甲武器系统为首的弹炮结合末段防空系统代表了要地防卫装备的重要发展方向。本文从无人机技术发展对要地防空系统的新威胁出发，探讨传统防空武器系统在执行要地防卫过程中应对低、慢、小无人机目标可能存在的技术问题，并对比分析了监测控制类、直接摧毁类和干扰反制类等典型反无人机技术的特点，然后针对俄罗斯“铠甲”弹炮结合武器系统发展的过程、反无人机作战案例及其在要地防卫作战中的应用特点等进行深入探讨，最后针对要地防卫反无人机装备的发展提出若干建议。研究结果可为开展要地防卫反无人机装备的体系规划和发展论证提供参考。     

舰艇近区安全防卫系统分析

针对我国舰艇近区安全存在的问题,参照国外舰艇近区自卫装备发展情况,提出了发展具有综合利用观瞄设备和声纳,并集合各种致命和非致命武器特点的舰艇近区安全防卫系统的构想。系统配备的观瞄设备用于探测地面、水上及低空近临目标,而声纳用于探测水下目标,如蛙人,无人水下航行器等。在打击方面,系统配备了可以歼灭目标的致命武器以及用于驱逐目标的非致命武器。并对系统的关键技术进行了初步探讨。 关键词：舰艇近区安全,近区安全防卫系统,非致命武器     

Confidence intervals for ranked means

Suppose that observations from populations π₁, …, π_k (k ≥ 1) are normally distributed with unknown means μ₁., μ_k, respectively, and a common known variance σ². Let μ_[1] μ … ≤ μ_[k] denote the ranked means. We take n independent observations from each population, denote the sample mean of the n observation from π₁ by X _i (i = 1, …, k), and define the ranked sample means X _[1] ≤ … ≤ X _[k]. The problem of confidence interval estimation of μ₍₁₎, …,μ_[k] is stated and related to previous work (Section 1). The following results are obtained (Section 2). For i = 1, …, k and any γ(0 < γ < 1) an upper confidence interval for μ_[i] with minimal probability of coverage γ is (? ∞, X _[i]+ h) with h = (σ/n^1/2) Φ^?1(γ^1/k-i+1), where Φ(·) is the standard normal cdf. A lower confidence interval for μ_[i] with minimal probability of coverage γ is (X _i[i] – g, + ∞) with g = (σ/n^1/2) Φ^?1(γ^1/i). For the upper confidence interval on μ_[i] the maximal probability of coverage is 1– [1 – γ^1/k-i+1]ⁱ, while for the lower confidence interval on μ_[i] the maximal probability of coverage is 1–[1– γ^1/i] ^k-i+¹. Thus the maximal overprotection can always be calculated. The overprotection is tabled for k = 2, 3. These results extend to certain translation parameter families. It is proven that, under a bounded completeness condition, a monotone upper confidence interval h(X ₁, …, X _k) for μ_[i] with probability of coverage γ(0 < γ < 1) for all μ = (μ_[1], …,μ_[k]), does not exist.     

Component importance for linear consecutive‐ k ‐Out‐of‐ n and m ‐Consecutive‐ k ‐Out‐of‐ n systems with exchangeable components

Measuring the relative importance of components in a mechanical system is useful for various purposes. In this article, we study Birnbaum and Barlow‐Proschan importance measures for two frequently studied system designs: linear consecutive k ‐out‐of‐ n and m ‐consecutive‐ k ‐out‐of‐ n systems. We obtain explicit expressions for the component importance measures for systems consisting of exchangeable components. We illustrate the results for a system whose components have a Lomax type lifetime distribution. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Consecutive k‐within‐m‐out‐of‐n:F system with exchangeable components

As a generalization of k‐out‐of‐n:F and consecutive k‐out‐of‐n:F systems, the consecutive k‐within‐m‐out‐of‐n:F system consists of n linearly ordered components such that the system fails iff there are m consecutive components which include among them at least k failed components. In this article, the reliability properties of consecutive k‐within‐m‐out‐of‐n:F systems with exchangeable components are studied. The bounds and approximations for the survival function are provided. A Monte Carlo estimator of system signature is obtained and used to approximate survival function. The results are illustrated and numerics are provided for an exchangeable multivariate Pareto distribution. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Reliability of a 2‐dimensional k‐within‐consecutive‐r × s‐out‐of‐m × n:F system

A 2‐dimensional rectangular (cylindrical) k‐within‐consecutive‐r × s‐out‐of‐m × n:F system is the rectangular (cylindrical) m × n‐system if the system fails whenever k components in a r × s‐submatrix fail. This paper proposes a recursive algorithm for the reliability of the 2‐dimensional k‐within‐consecutive‐r × s‐out‐m × n:F system, in the rectangular case and the cylindrical case. This algorithm requires min ( O (mk^r(n?s)), O (nk^s(m?r))), and O (mk^rn) computing time in the rectangular case and the cylindrical case, respectively. The proposed algorithm will be demonstrated and some numerical examples will be shown. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 625–637, 2001.     

An absolute approximation algorithm for scheduling unrelated machines

Non‐preemptive scheduling of n independent jobs on m unrelated machines so as to minimize the maximal job completion time is considered. A polynomial algorithm with the worst‐case absolute error of min{(1 ? 1/m)p_max, p} is presented, where p_max is the largest job processing time and p is the mth element from the non‐increasing list of job processing times. This is better than the earlier known best absolute error of p_max. The algorithm is based on the rounding of acyclic multiprocessor distributions. An O(nm²) algorithm for the construction of an acyclic multiprocessor distribution is also presented. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Suboptimal decision rule for attacking targets of opportunity

A player having only a definite number of weapons is hunting targets. His total hunting time is also limited. Targets of opportunity with various values arrive at random, and as soon as a target arrives the player observes the target value and decides whether or not to shoot it down. The issue is what the decision rule is which guarantees him a maximum expected gain during the hunting time. Poisson arrival of the targets, uniform distribution of the target value, and the shoot-look-shoot scheme qre assumed. A decision rule is derived which is not optimal but has a very simple form and gives almost as good value as the optimal decision rule does.     

非致命激光武器综合效能评估

非致命激光武器是采用低能激光使目标暂时丧失战斗力的一种战术武器,通过对影响非致命激光武器综合效能关键因素的分析,建立了非致命激光武器的综合效能评价核心指标体系,提出了非致命激光武器综合效能的评估方法,采用最优传递矩阵改进层次分析方法确定各指标的相对权重,运用灰色层次分析法对非致命激光武器的综合效能进行了评估,为非致命激光武器的研发和实际应用提供了理论支持。