A note on the relationship between correlation and circular error probability (CEP)

This note investigates the effects of ignoring correlation (p) as is sometimes done when estimating or placing confidence intervals on circular error probability (CEP). It is shown that better estimates of CEP can be made if the axis is rotated [5] so that the estimate of p is zero. It is also shown that ignoring variability in estimating correlation can affect the confidence intervals on CEP or the placing of a lower bound on the probability content of a circle.     

On the reliability,availability and bayes confidence intervals for multicomponent systems

The problem of computing reliability and availability and their associated confidence limits for multi-component systems has appeared often in the literature. This problem arises where some or all of the component reliabilities and availabilities are statistical estimates (random variables) from test and other data. The problem of computing confidence limits has generally been considered difficult and treated only on a case-by-case basis. This paper deals with Bayes confidence limits on reliability and availability for a more general class of systems than previously considered including, as special cases, series-parallel and standby systems applications. The posterior distributions obtained are exact in theory and their numerical evaluation is limited only by computing resources, data representation and round-off in calculations. This paper collects and generalizes previous results of the authors and others. The methods presented in this paper apply both to reliability and availability analysis. The conceptual development requires only that system reliability or availability be probabilities defined in terms acceptable for a particular application. The emphasis is on Bayes Analysis and the determination of the posterior distribution functions. Having these, the calculation of point estimates and confidence limits is routine. This paper includes several examples of estimating system reliability and confidence limits based on observed component test data. Also included is an example of the numerical procedure for computing Bayes confidence limits for the reliability of a system consisting of N failure independent components connected in series. Both an exact and a new approximate numerical procedure for computing point and interval estimates of reliability are presented. A comparison is made of the results obtained from the two procedures. It is shown that the approximation is entirely sufficient for most reliability engineering analysis.     

Statistical variability and fragility assessment of ballistic perforation of steel plates for 7.62 mm AP ammunition

The paper describes field test results of 7.62 × 51 mm M61 AP (armour piercing) ammunition fired into mild steel targets at an outdoor range. The targets varied from 10 mm to 32 mm in thickness. The tests recorded penetration depth, probability of perforation (i.e., complete penetration), muzzle and impact velocities, bullet mass, and plate yield strength and hardness. The measured penetration depth exhibited a variability of approximately ±12%. The paper then compared ballistic test results with predictive models of steel penetration depth and thickness to prevent perforation. Statistical parameters were derived for muzzle and impact velocity, bullet mass, plate thickness, plate hardness, and model error. A Monte-Carlo probabilistic analysis was then developed to estimate the probability of plate perforation of 7.62 mm M61 AP ammunition for a range of impact velocities, and for mild steels, and High Hardness Armour (HHA) plates. This perforation fragility analysis considered the random variability of impact velocity, bullet mass, plate thickness, plate hardness, and model error. Such a probabilistic analysis allows for reliability-based design, where, for example, the plate thickness with 95% reliability (i.e. only 1 in 20 shots will penetrate the wall) can be estimated knowing the probabilistic distribution of perforation. Hence, it was found that the plate thickness to ensure a low 5% probability of perforation needs to be 11–15% thicker than required to have a 50/50 chance of perforation for mild steel plates. Plates would need to be 20–30% thicker if probability of perforation is reduced to zero.     

Monitoring poisson count data with probability control limits when sample sizes are time varying

This article considers the problem of monitoring Poisson count data when sample sizes are time varying without assuming a priori knowledge of sample sizes. Traditional control charts, whose control limits are often determined before the control charts are activated, are constructed based on perfect knowledge of sample sizes. In practice, however, future sample sizes are often unknown. Making an inappropriate assumption of the distribution function could lead to unexpected performance of the control charts, for example, excessive false alarms in the early runs of the control charts, which would in turn hurt an operator's confidence in valid alarms. To overcome this problem, we propose the use of probability control limits, which are determined based on the realization of sample sizes online. The conditional probability that the charting statistic exceeds the control limit at present given that there has not been a single alarm before can be guaranteed to meet a specified false alarm rate. Simulation studies show that our proposed control chart is able to deliver satisfactory run length performance for any time‐varying sample sizes. The idea presented in this article can be applied to any effective control charts such as the exponentially weighted moving average or cumulative sum chart. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 625–636, 2013     

On the discrete-time queue length distribution under markov-dependent phases

The technique of probability generating functions has been applied to solve the steady state behavior of a discrete-time, single-channel, queueing problem wherein the arrivals to the queue at consecutive time-marks are statistically independent, but the service is accomplished in phases which are Markov-dependent. Special cases of importance have been discussed. In the end, mean number of phases, its special cases, the mean queue lengths, and the variances have been ascertained.     

保证率点值区间估计的Monte-Carlo方法

提出了一种根据实测样本系列对保证率点值进行区间估计的Ｍｏｎｔｅ─Ｃａｒｌｏ方法。对于具有正态分布或对数正态分布的样本,首先推出总体参数的分布,然后用Ｍｏｎｔｅ─Ｃａｒｌｏ法生成总体参数系列,据此求得相应的保证率点值系列,最后通过经验分布推得在给定置信度下保证率点值的区间估计,本文还给出了一个算例。     

基于雷达波束篱笆的空间碎片数量的置信区间估计

针对雷达波束篱笆空间碎片探测模式,提出了一种估计碎片数量置信区间的方法.对于给定的轨道高度范围,将轨道倾角和雷达散射截面足够大的碎片是否真正穿越波束篱笆这一事件用(0-1)分布来建模,根据所获取的轨道高度数据,得到该轨道高度范围内碎片穿越波束篱笆的平均概率,进而采用中心极限定理估计出该范围内碎片总数量的置信区间.仿真实验验证了方法的有效性.     

Scheduling stochastic jobs with asymmetric earliness and tardiness penalties

We consider a stochastic counterpart of the well-known earliness-tardiness scheduling problem with a common due date, in which n stochastic jobs are to be processed on a single machine. The processing times of the jobs are independent and normally distributed random variables with known means and known variances that are proportional to the means. The due dates of the jobs are random variables following a common probability distribution. The objective is to minimize the expectation of a weighted combination of the earliness penalty, the tardiness penalty, and the flow-time penalty. One of our main results is that an optimal sequence for the problem must be V-shaped with respect to the mean processing times. Other characterizations of the optimal solution are also established. Two algorithms are proposed, which can generate optimal or near-optimal solutions in pseudopolynomial time. The proposed algorithms are also extended to problems where processing times do not satisfy the assumption in the model above, and are evaluated when processing times follow different probability distributions, including general normal (without the proportional relation between variances and means), uniform, Laplace, and exponential. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44, 531–557, 1997.     

再入弹头滚速过零与落点散布

滚转弹头的再入过程中,滚速过零对落点精度影响最大。本文分析了滚速过零的机理,推导了考虑滚动阻尼影响的过零高度公式,以及滚速过零影响下的落点散布公式。最后用六自由度弹道数字仿真结果同近似计算结果作了比较,比较结果表明了近似分析的可行性。     

Sample sizes for β-expectation tolerance limits which control both tails of the normal distribution

Sample sizes for tolerance limits are given on a normal distribution. β-Expectation tolerance intervals are defined and constructed to control the proportion in each tail of the normal distribution. We also require with a high probability that the proportion in each tail is close to its corresponding expected coverage. Under these conditions. we dctcrniine a minimum sample size and its accompanying tolerance limits. Graphs of minimum sample sizes for the tolerance limits are provided. The computation for minimum samplc sizes is based on the bivariate noncentral t distribution. Examples are given to illustrate the use of the graphs.     

备件库存限量分析及决策模型

分析了备件库存管理所对应的库存控制策略及其有关的因素,以费用为目标函数、不缺备件概率为约束条件,运用概率论及库存论原理建立了备件库存限量的决策摸型。     

Estimating the point availability with right‐censored data

The point availability of a one‐unit system at a specified time is defined as the probability that the component is operating at that time. When both operating time and repair time are subject to random (right) censorship, we propose an asymptotic nonparametric approach for constructing confidence intervals for the point availability of the system. The technique is based on the fact that a product limit estimator converges to a Gaussian process. The method is also extended to finding confidence intervals for the point availability of a complex system using the δ‐Method. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 119–127, 1999     

航天遥感监测信息态势感知能力分析

针对遥感监测信息的效用评估问题,提出了一种态势感知能力定量分析的新方法。首先利用NIIRS等级尺度和GIQE模型建立了遥感图像与地面目标检测率之间的联系,由此得到这些目标在监视区域出现的概率分布。然后,以地面目标在监视区域的实际分布表示使用者信息需求,并利用信息理论中的Kullback Leibler距离来度量不确定性分布和信息需求之间的差异,从而得到不同遥感侦察与监视系统态势感知能力曲线,给出了传输处理时延对态势感知能力曲线的影响。     

Replicated batch means for steady‐state simulations

This paper studies a new steady‐state simulation output analysis method called replicated batch means in which a small number of replications are conducted and the observations in these replications are grouped into batches. This paper also introduces and compares methods for selecting the initial state of each replication. More specifically, we show that confidence intervals constructed by the replicated batch means method are valid for large batch sizes and derive expressions for the expected values and variances of the steady‐state mean and variance estimators for stationary processes and large sample sizes. We then use these expressions, analytical examples, and numerical experiments to compare the replicated batch means method with the standard batch means and multiple replications methods. The numerical results, which are obtained from an AR(1) process and a small, nearly‐decomposable Markov chain, show that the multiple replications method often gives confidence intervals with poorer coverage than the standard and replicated batch means methods and that the replicated batch means method, implemented with good choices of initialization method and number of replications, provides confidence interval coverages that range from being comparable with to being noticeably better than coverages obtained by the standard batch means method. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

连续波强激光武器动态毁伤概率的非毁检测法

给出一种强激光武器与目标存在相对运动时的毁伤概率(动态毁伤概率)在非致毁条件下的检测方法。该方法是在已知强激光对目标的致毁时间、一次发射时间的基础上,在武器的跟瞄子系统对目标无毁的跟踪试验中,通过检测跟踪误差在射击门内外交替出现的时间间隔,给出动态毁伤概率的点估计,以及在既定置信度下,动态毁伤概率的置信区间,同时还能判断所测毁伤概率是否处于最佳状态,为进一步优化动态毁伤概率提供依据。     

The search for an intelligent evader: Strategies for searcher and evader in the two-region problem

This paper considers the search for an evader concealed in one of two regions, each of which is characterized by its detection probability. The single-sided problem, in which the searcher is told the probability of the evader being located in a particular region, has been examined previously. We shall be concerned with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move: his optimal strategy consists of that probability distribution which maximizes the expected time to detection, while the searcher's optimal strategy is the sequence of searches which limits the evader to this expected time. It transpires for this problem that optimal strategies for both searcher and evader may generally be obtained to a surprisingly good degree of approximation by using the optimal strategies for the closely related (but far more easily solved) problem in which the evader is completely free to move between searches.     

电视制导无人攻击机垂直命中目标毁伤概率分析

综合考虑电视指令制导无人攻击机的攻击作战过程,将其末制导设定为满足落角约束的目标跟踪问题,设计了一种基于自动驾驶仪能保持无人攻击机垂直命中目标末制导律,并提出了一种电视制导无人攻击机垂直命中目标的毁伤概率的计算方法.通过仿真计算.结果比较符合实际,为提高和评估无人攻击机的作战效能.提供了简单有效的方法.     

舰载雷达对水面目标发现概率研究

为了提高舰载雷达的作战效能,研究了舰载雷达发现水面目标的概率模型,采用了数学建模方法,结合舰载雷达发现目标接收机输入端的信噪比,利用发现距离与发现概率之间的关系,建立了舰载雷达发现水面目标的概率模型,对于提高舰载雷达信息作战能力具有实践意义。     

Chance-constrained linear programming with location scale distributions

M. Kress, in 1984, studied the chance-constrained critical path problem. The author proved that if the project time random variables follow a class of location-scale probability distributions, then there exists a specific threshold confidence level, such that the critical path for the system remains the same for all higher confidence levels. The purpose of this article is to study the similar properties for a general chance-constrained linear programming (C²LP) problems with location-scale probability distributions. We present results for chance-constrained linear programming which parallel those in Kress's article. © 1992 John Wiley & Sons, Inc.     

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′.