Bayesian inference for a Lanchester type combat model

We undertake inference for a stochastic form of the Lanchester combat model. In particular, given battle data, we assess the type of battle that occurred and whether or not it makes any difference to the number of casualties if an army is attacking or defending. Our approach is Bayesian and we use modern computational techniques to fit the model. We illustrate our method using data from the Ardennes campaign. We compare our results with previous analyses of these data by Bracken and Fricker. Our conclusions are somewhat different to those of Bracken. Where he suggests that a linear law is appropriate, we show that the logarithmic or linear‐logarithmic laws fit better. We note however that the basic Lanchester modeling assumptions do not hold for the Ardennes data. Using Fricker's modified data, we show that although his “super‐logarithmic” law fits best, the linear, linear‐logarithmic, and logarithmic laws cannot be ruled out. We suggest that Bayesian methods can be used to make inference for battles in progress. We point out a number of advantages: Prior information from experts or previous battles can be incorporated; predictions of future casualties are easily made; more complex models can be analysed using stochastic simulation techniques. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 541–558, 2000     

基于Rough集理论的数据库推理通道动态消除

提出了一种基于Rough集理论的数据库推理泄漏通道消除方法。在由数据库中所有数据生成的不完备决策表上,该方法应用Rough集理论,分析提取出敏感和非敏感数据之间的确定性推理关系,以此产生推理控制规则。利用这些规则对数据库系统返回给普通用户的数据动态地做最小修改,防止推理通道的产生。实验结果表明,该方法可扩展性强,在保证较高的数据库安全性的同时提高了数据可用性。     

A nonparametric approach to accelerated life testing under multiple stresses

Accelerated life testing (ALT) is concerned with subjecting items to a series of stresses at several levels higher than those experienced under normal conditions so as to obtain the lifetime distribution of items under normal levels. A parametric approach to this problem requires two assumptions. First, the lifetime of an item is assumed to have the same distribution under all stress levels, that is, a change of stress level does not change the shape of the life distribution but changes only its scale. Second, a functional relationship is assumed between the parameters of the life distribution and the accelerating stresses. A nonparametric approach, on the other hand, assumes a functional relationship between the life distribution functions at the accelerated and nonaccelerated stress levels without making any assumptions on the forms of the distribution functions. In this paper, we treat the problem nonparametrically. In particular, we extend the methods of Shaked, Zimmer, and Ball [7] and Strelec and Viertl [8] and develop a nonparametric estimation procedure for a version of the generalized Arrhenius model with two stress variables assuming a linear acceleration function. We obtain consistent estimates as well as confidence intervals of the parameters of the life distribution under normal stress level and compare our nonparametric method with parametric methods assuming exponential, Weibull and lognormal life distributions using both real life and simulated data. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 629–644, 1998     

步进加速退化试验及其在电子产品可靠性评估中的应用

为快速评估具有高可靠、长寿命特点的电子产品的可靠性,提出了使用步进加速退化试验技术的方法。文中首先给出了步进加速退化的试验方法及基本假设,然后给出了步进退化数据向恒加退化数据的折算方法,在此基础上提出了基于伪失效寿命的步进加速退化可靠性评估算法,最后利用试验数据对该方法进行了验证。该方法与恒加退化试验相比,在保持样本量不变的基础上,可以极大地缩短试验时间,因此,具有更高的效费比。     

Bayesian analysis of queues with impatient customers: Applications to call centers

Queuing models have been extensively used in the literature for obtaining performance measures and developing staffing policies. However, most of this work has been from a pure probabilistic point of view and has not addressed issues of statistical inference. In this article, we consider Bayesian queuing models with impatient customers with particular emphasis on call center operations and discuss further extensions. We develop the details of Bayesian inference for queues with abandonment such as the M/M/s + M model (Erlang‐A). In doing so, we discuss the estimation of operating characteristics and its implications on staffing. We illustrate the implementation of the Bayesian models using actual arrival, service, and abandonment data from call centers. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Planning accelerated life tests for censored two‐parameter exponential distributions

We consider optimal test plans involving life distributions with failure‐free life, i.e., where there is an unknown threshold parameter below which no failure will occur. These distributions do not satisfy the regularity conditions and thus the usual approach of using the Fisher information matrix to obtain an optimal accelerated life testing (ALT) plan cannot be applied. In this paper, we assume that lifetime follows a two‐parameter exponential distribution and the stress‐life relationship is given by the inverse power law model. Near‐optimal test plans for constant‐stress ALT under both failure‐censoring and time‐censoring are obtained. We first obtain unbiased estimates for the parameters and give the approximate variance of these estimates for both failure‐censored and time‐censored data. Using these results, the variance for the approximate unbiased estimate of a percentile at a design stress is computed and then minimized to produce the near‐optimal plan. Finally, a numerical example is presented together with simulation results to study the accuracy of the approximate variance given by the proposed plan and show that it outperforms the equal‐allocation plan. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 169–186, 1999     

Assessment of machine tool reliability using a proportional hazards model

In this article we present a proportional hazards model for describing machine tool failures. The model enables us to describe the effect of aging as well as the effect of the machining environment on tool life. We discuss inference for the model and show that computable results can be obtained in a fully Bayesian analysis by using approximation techniques. We illustrate the usefulness of our model by applying it to some actual data on machine tool failures.     

A selective newsvendor approach to order management

Consider a supplier offering a product to several potential demand sources, each with a unique revenue, size, and probability that it will materialize. Given a long procurement lead time, the supplier must choose the orders to pursue and the total quantity to procure prior to the selling season. We model this as a selective newsvendor problem of maximizing profits where the total (random) demand is given by the set of pursued orders. Given that the dimensionality of a mixed‐integer linear programming formulation of the problem increases exponentially with the number of potential orders, we develop both a tailored exact algorithm based on the L‐shaped method for two‐stage stochastic programming as well as a heuristic method. We also extend our solution approach to account for piecewise‐linear cost and revenue functions as well as a multiperiod setting. Extensive experimentation indicates that our exact approach rapidly finds optimal solutions with three times as many orders as a state‐of‐the‐art commercial solver. In addition, our heuristic approach provides average gaps of less than 1% for the largest problems that can be solved exactly. Observing that the gaps decrease as problem size grows, we expect the heuristic approach to work well for large problem instances. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008     

A general model for accelerated life testing with time‐dependent covariates

This paper introduces a general or “distribution‐free” model to analyze the lifetime of components under accelerated life testing. Unlike the accelerated failure time (AFT) models, the proposed model shares the advantage of being “distribution‐free” with the proportional hazard (PH) model and overcomes the deficiency of the PH model not allowing survival curves corresponding to different values of a covariate to cross. In this research, we extend and modify the extended hazard regression (EHR) model using the partial likelihood function to analyze failure data with time‐dependent covariates. The new model can be easily adopted to create an accelerated life testing model with different types of stress loading. For example, stress loading in accelerated life testing can be a step function, cyclic, or linear function with time. These types of stress loadings reduce the testing time and increase the number of failures of components under test. The proposed EHR model with time‐dependent covariates which incorporates multiple stress loadings requires further verification. Therefore, we conduct an accelerated life test in the laboratory by subjecting components to time‐dependent stresses, and we compare the reliability estimation based on the developed model with that obtained from experimental results. The combination of the theoretical development of the accelerated life testing model verified by laboratory experiments offers a unique perspective to reliability model building and verification. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 303–321, 1999     

ANFIS网络在舰船维修费用预测中的应用

利用自适应模糊推理系统(ANFIS)的模糊推理能力和学习功能相结合的优点,运用于舰船维修费用预测中.分析了影响维修费用的因素,采用变量投影重要性分析方法(VIP)对影响因素进行评估和筛选,使用ANFIS网络建立模型.通过实际算例进行分析,用历史数据训练ANFIS网络,预测舰船维修费用,在数据样本量小的情况下,较一般神经网络精度有明显提高.     

A branch‐and‐price algorithm for a targeting problem

In this paper, we consider a new weapon‐target allocation problem with the objective of minimizing the overall firing cost. The problem is formulated as a nonlinear integer programming model, but it can be transformed into a linear integer programming model. We present a branch‐and‐price algorithm for the problem employing the disaggregated formulation, which has exponentially many columns denoting the feasible allocations of weapon systems to each target. A greedy‐style heuristic is used to get some initial columns to start the column generation. A branching strategy compatible with the pricing problem is also proposed. Computational results using randomly generated data show this approach is promising for the targeting problem. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

面向开放式测试环境的诊断服务系统

为了将诊断与测试分离,提高TPS与诊断推理机制的复用性,采用组件技术构建面向开放式测试环境的诊断服务系统,并详细阐述了诊断模型描述方法和诊断推理服务组件的实现技术。以XML作为诊断模型描述语言,通过数据访问接口进行诊断模型数据与知识的交互,在模型管理服务的基础上,进行高级的推理和控制服务。     

基于直接数据域自适应算法的相干信号DOA估计

利用直接数据域自适应算法的稳态权值代替噪声子空间构建空间谱,构造了一种超分辨波达方向(DOA)估计方法.为了解决谱峰搜索时的伪峰问题,采用参考阵元轮换得到多组线性无关稳态权值,逼近噪声子空间,能有效去除伪峰.针对相干信号的DOA估计,进一步提出了直接数据域取对称共轭向量的解相干方法.相比子空间分解类算法,本文算法不需估计信号源数目和协方差矩阵、不需特征分解,复杂度仅为O(MP),同时能有效完成解相干处理.     

Reliability inference for field conditions from accelerated degradation testing

Accelerated degradation testing (ADT) is usually conducted under deterministic stresses such as constant‐stress, step‐stress, and cyclic‐stress. Based on ADT data, an ADT model is developed to predict reliability under normal (field) operating conditions. In engineering applications, the “standard” approach for reliability prediction assumes that the normal operating conditions are deterministic or simply uses the mean values of the stresses while ignoring their variability. Such an approach may lead to significant prediction errors. In this paper, we extend an ADT model obtained from constant‐stress ADT experiments to predict field reliability by considering the stress variations. A case study is provided to demonstrate the proposed statistical inference procedure. The accuracy of the procedure is verified by simulation using various distributions of field stresses. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006.     

海洋环境中基于WVD的LFM信号检测方法

海洋环境中弱信号的谱与海杂波的谱相混叠 ,目标和背景的位置差异很小 ,经典的频域或空域处理对海杂波中弱信号的检测难以奏效。鉴于Wigner-Ville分布 (WVD)对线性调频信号 (LFM )具有时频聚集性这一特点 ,提出了一种海洋环境中基于WVD的LFM信号检测方法。利用雷达采集的真实海杂波数据 ,在不同信杂比的条件下 ,研究了该方法与经典频域法在信号检测中的差别。通过实验分析 ,与经典方法相比 ,该方法具有明显的优越性 ,且信杂比达到 -14 . 3dB时 ,其仍能很好地对信号进行检测。     

Satellite constellation design for forest fire monitoring via a stochastic programing approach

There is significant value in the data collected by satellites during and after a natural disaster. The current operating paradigm in practice is for satellites to passively collect data when they happen to fly over a disaster location. Conversely, this article considers the alternative approach of actively maneuvering satellites to fly directly overhead of the disaster site on a routine basis. Toward this end, we seek to compute a satellite constellation design that minimizes the expected maneuver costs for monitoring an unknown forest fire. In this article, we present a 2‐stage stochastic programing model for this problem as well as a accelerated L‐shaped decomposition approach. A comparison between our approach and the current operating paradigm indicates that our solution provides longer duration data collections and a greater number of data collections. Analysis also shows that our proposed solution is robust over a wide array of scenarios.     

Fitting Lanchester equations to the battles of Kursk and Ardennes

Lanchester equations and their extensions are widely used to calculate attrition in models of warfare. This paper examines how Lanchester models fit detailed daily data on the battles of Kursk and Ardennes. The data on Kursk, often called the greatest tank battle in history, was only recently made available. A new approach is used to find the optimal parameter values and gain an understanding of how well various parameter combinations explain the battles. It turns out that a variety of Lanchester models fit the data about as well. This explains why previous studies on Ardennes, using different minimization techniques and data formulations, have found disparate optimal fits. We also find that none of the basic Lanchester laws (i.e., square, linear, and logarithmic) fit the data particularly well or consistently perform better than the others. This means that it does not matter which of these laws you use, for with the right coefficients you will get about the same result. Furthermore, no constant attrition coefficient Lanchester law fits very well. The failure to find a good‐fitting Lanchester model suggests that it may be beneficial to look for new ways to model highly aggregated attrition. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Optimum step‐stress accelerated life test plans for log‐location‐scale distributions

This article presents new tools and methods for finding optimum step‐stress accelerated life test plans. First, we present an approach to calculate the large‐sample approximate variance of the maximum likelihood estimator of a quantile of the failure time distribution at use conditions from a step‐stress accelerated life test. The approach allows for multistep stress changes and censoring for general log‐location‐scale distributions based on a cumulative exposure model. As an application of this approach, the optimum variance is studied as a function of shape parameter for both Weibull and lognormal distributions. Graphical comparisons among test plans using step‐up, step‐down, and constant‐stress patterns are also presented. The results show that depending on the values of the model parameters and quantile of interest, each of the three test plans can be preferable in terms of optimum variance. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Choosing arrival process models for service systems: Tests of a nonhomogeneous Poisson process

Service systems such as call centers and hospital emergency rooms typically have strongly time‐varying arrival rates. Thus, a nonhomogeneous Poisson process (NHPP) is a natural model for the arrival process in a queueing model for performance analysis. Nevertheless, it is important to perform statistical tests with service system data to confirm that an NHPP is actually appropriate, as emphasized by Brown et al. [8]. They suggested a specific statistical test based on the Kolmogorov–Smirnov (KS) statistic after exploiting the conditional‐uniform (CU) property to transform the NHPP into a sequence of i.i.d. random variables uniformly distributed on [0,1] and then performing a logarithmic transformation of the data. We investigate why it is important to perform the final data transformation and consider what form it should take. We conduct extensive simulation experiments to study the power of these alternative statistical tests. We conclude that the general approach of Brown et al. [8] is excellent, but that an alternative data transformation proposed by Lewis [22], drawing upon Durbin [10], produces a test of an NHPP test with consistently greater power. We also conclude that the KS test after the CU transformation, without any additional data transformation, tends to be best to test against alternative hypotheses that primarily differ from an NHPP only through stochastic and time dependence. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 66–90, 2014     

Call center arrival modeling: A Bayesian state‐space approach

In this article, we introduce three discrete time Bayesian state‐space models with Poisson measurements, each aiming to address different issues in call center arrival modeling. We present the properties of the models and develop their Bayesian inference. In so doing, we provide sequential updating and smoothing for call arrival rates and discuss how the models can be used for intra‐day, inter‐day, and inter‐week forecasts. We illustrate the implementation of the models by using actual arrival data from a US commercial bank's call center and provide forecasting comparisons. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 28–42, 2011