A Lanchester-type model of combat with stochastic rates

The effects of environmental stochasticity in a Lanchester-type model of combat are investigated. The methodology is based on a study of stochastic differential equations with random parameters characterized by dichotomous Markov processes. Exact expressions for the Laplace transforms of the time evolution of the first- and second-order moments of the system are obtained. A special case when the fluctuations in the parameters occur with great rapidity in comparison with the natural time scale of the system is also analyzed. The stochastic stability in the mean-square sense is discussed by using the Routh–Hurwitz criterion and it is found that the stochastic perturbations tend to destabilize the system.     

柱壳极限分析的广义变分原理

本文提供了适用于满足简化Mises屈服条件的刚塑性体柱壳极限分析的两类变量广义变分原理,并证明了它与柱壳极限分析的全套方程和条件等价。     

A heuristic with tie breaking for certain 0–1 integer programming models

A heuristic for 0–1 integer programming is proposed that features a specific rule for breaking ties that occur when attempting to determine a variable to set to 1 during a given iteration. It is tested on a large number of small- to moderate-sized randomly generated generalized set-packing models. Solutions are compared to those obtained using an existing well-regarded heuristic and to solutions to the linear programming relaxations. Results indicate that the proposed heuristic outperforms the existing heuristic except for models in which the number of constraints is large relative to the number of variables. In this case, it performs on par with the existing heuristic. Results also indicate that use of a specific rule for tie breaking can be very effective, especially for low-density models in which the number of variables is large relative to the number of constraints.     

An analysis of constrained robust regression estimators

Multicollinearity and nonnormal errors are problems often encountered in the application of linear regression. Estimators are proposed for dealing with the simultaneous occurrence of both multicollinearity and nonnormality. These estimators are developed by combining biased estimation techniques with certain robust criteria. An iteratively reweighted least-squares procedure is used to compute the estimates. The performance of the combined estimators is studied empirically through Monte Carlo experiments structured according to factorial designs. With respect to a mean-squared-error criterion, the combined estimators are superior to ordinary least-squares, pure biased estimators, and pure robust estimators when multicollinearity and nonnormality are present. The loss in efficiency for the combined estimators relative to least squares is small when these problems do not occur. Some guidelines for the use of these combined estimators are given.     

Optimal replacement policies for multistate deteriorating systems

We consider state-age-dependent replacement policies for a multistate deteriorating system. We assume that operating cost rates and replacement costs are both functions of the underlying states. Replacement times and sojourn times in different states are all state-dependent random variables. The optimization criterion is to minimize the expected long-run cost rate. A policy-improvement algorithm to derive the optimal policy is presented. We show that under reasonable assumptions, the optimal replacement policies have monotonic properties. In particular, when the failure-rate functions are nonincreasing, or when all the replacement costs and the expected replacement times are independent of state, we show that the optimal policies are only state dependent. Examples are given to illustrate the structure of the optimal policies in the special case when the sojourntime distributions are Weibull. © 1994 John Wiley & Sons, Inc.     

考虑载荷作用次数的多失效模式扭力轴灵敏度分析

机械构件的不同的失效模式之间具有一定的相关性,而且随机载荷作用次数对机械构件的可靠性有一定程度的影响。因此对机械构件进行可靠性灵敏度分析时,需要充分考虑其不同失效模式和载荷作用次数的影响。通过运用顺序统计量理论考虑载荷多次作用以及多种失效模式条件下机械构件可靠性及可靠性灵敏度的变化规律,运用随机摄动理论和四阶矩技术,建立一种考虑载荷作用次数的多失效模式机械构件可靠性灵敏度分析数值方法的应力强度干涉模型。在随机变量前四阶矩已知的情况下,结合灵敏度分析的梯度算法,推导出关于随机变量均值和方差的灵敏度计算公式。以某履带车辆底盘扭力轴为例进行计算,得到其可靠度随载荷作用次数、随机变量均值和方差而改变的可靠性灵敏度变化曲线,为扭力轴的可靠性优化提供一定的理论依据。研究成果可以推广到相关机械可靠性灵敏度设计和结构优化领域,具有非常重要的实用意义。     

Measuring information in right-censored models

The theory of majorization is used to develop measures of information in the randomly right-censored model when the lifetime and censoring variables are discrete. Majorization also enables us to prove some basic theorems about the measures in a simple and unified fashion. These measures include Shannon's information as a special case. The measures are inadequate in the continuous case and some alternative measures, based on the variance of the lifetime random variable, are proposed.     

Reliability acceptance testing for new series systems

The mean time between failures (MTBF) of a newly minted series system, all of whose components exhibit wear, will tend to be much larger than the MTBF of the same system after it has become fully aged. When fully aged systems are used for the testing, acceptance tests with a criterion regarding the MTBF of a well-aged system can be based on the assumption that times between system failures are independent, with identical exponential distributions. However, these tests are shown to offer essentially no consumer protection when applied to new systems. Tests are derived which are correct when new systems are under test but the acceptance criterion refers to the MTBF of a well-aged system. The derivation uses an approximate Poisson distribution which is valid if the total number of systems on test is sufficiently large.     

The determination of optimal base-stock inventory policy when the costs of under- and oversupply are uncertain

This article considers the determination of the optimal base-stock inventory policy for the newsboy inventory model when there is uncertainty about either or both of its basic cost inputs: either C_u, the marginal cost of an undersupply mistake, or C_o, the marginal cost of an oversupply mistake. Such uncertainties often arise in implementing the newsboy model, especially with respect to C_u, whose value depends mostly on the often-imponderable economic consequences of a lost sale or backorder. Given this uncertainty, we use decision theory to propose and analyze two measures of policy “goodness” and two base-stock selection criteria, which in combination provide four alternative “optimal” base-stock policies. Formulas and/or conditions defining each alternative policy are provided. Our empirical study indicates that the recommended policy can be quite sensitive to the measure/criterion chosen, and that the consequences of the wrong choice can be quite considerable.     

The Demand for Turkish Defence Expenditure

Although a number of studies concerning Turkish defence-growth relation have been published in recent years, little attention is given the demand for Turkish defence expenditure. This is an important issue for understanding which variables contribute to the determination of the demand for military expenditure. However, it is difficult to develop a general theory or a standard empirical approach for the determination of the demand military expenditure. This study models and estimates the demand for Turkish defence expenditure for the period 1951-1998 using autoregressive distributed lag approach to cointegration (ARDL) following the methodology outlined in Pesaran and Shin (1999). This procedure can be applied regardless of the stationary properties of the variables in the sample and allows for inferences on long-run estimates, which is not possible under alternative cointegration procedures. The findings suggest that Turkish defence spending is determined by NATO's defence spending, Greece's defence spending and some security considerations.     

Refined prediction for linear regression models

Adequate prediction of a response variable using a multiple linear regression model is shown in this article to be related to the presence of multicollinearities among the predictor variables. If strong multicollinearities are present in the data, this information can be used to determine when prediction is likely to be accurate. A region of prediction, R, is proposed as a guide for prediction purposes. This region is related to a prediction interval when the matrix of predictor variables is of full column rank, but it can also be used when the sample is undersized. The Gorman-Toman ten-variable data is used to illustrate the effectiveness of the region R.     

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     

Technical note – operational statistics: Properties and the risk‐averse case

Consider a repeated newsvendor problem for managing the inventory of perishable products. When the parameter of the demand distribution is unknown, it has been shown that the traditional separated estimation and optimization (SEO) approach could lead to suboptimality. To address this issue, an integrated approach called operational statistics (OS) was developed by Chu et al., Oper Res Lett 36 (2008) 110–116. In this note, we first study the properties of this approach and compare its performance with that of the traditional SEO approach. It is shown that OS is consistent and superior to SEO. The benefit of using OS is larger when the demand variability is higher. We then generalize OS to the risk‐averse case under the conditional value‐at‐risk (CVaR) criterion. To model risk from both demand sampling and future demand uncertainty, we introduce a new criterion, called the total CVaR, and find the optimal OS under this new criterion. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 206–214, 2015     

基于交叉熵最小化的 Turbo 码迭代译码停止准则

根据Turbo码最优译码算法及迭代译码的基本原理 ,在保证迭代收敛的条件下 ,利用交叉熵最小化原则推导出Turbo码译码过程中停止迭代的准则 ,并给出了一种降低计算复杂性和减少存贮空间的简化算法 ,最后通过仿真证明了此迭代停止准则及其简化算法的有效性。     

钢球侵彻不同靶标的相似性分析

为研究相同弹丸侵彻不同靶标所造成损伤之间的相似性,以钢球侵彻明胶造成的瞬时空腔的最大直径为研究对象,基于相似理论推导出瞬时空腔最大直径的相似准则方程,利用钢球侵彻明胶的实验数据求解出准则方程的系数和指数,最后通过钢球侵彻猪后腿实验验证了所得到的准则方程可用于不同靶标之间的相似性分析,并具有准确性和合理性。     

Demand estimation in lost sales inventory systems

This article considers the problem of estimating parameters of the demand distribution in lost sales inventory systems. In periods when lost sales occur demand is not observed; one knows only that demand is larger than sales. We assume that demands form a sequence of IID normal random variables, which could be a residual demand process after filtering out seasonality and promotional nonstationarities. We examine three estimators for the mean and standard deviation: maximum likelihood estimator, BLUE (best linear unbiased estimator), and a new estimator derived here. Extensive simulations are reported to compare the performance of the estimators for small and large samples and a variety of parameter settings. In addition, I show how all three estimators can be incorporated into sequential updating routines. © 1994 John Wiley & Sons, Inc.     

改进的Fisher准则及其在语音聚类中的应用

针对传统的Fisher准则在聚类分析方面的不足,提出了一种新的修正的Fisher准则。通过重新定义类内方差,得出最大Fisher值与最佳聚类数目的对应关系,从而预测出最佳聚类数目。通过对语音库中语音段落的说话者组成结构进行分析,证明了修正后的Fisher准则能有效地优化聚类分析,并显著提高了说话者组成结构分析结果的精度。应用基于修正后的Fisher准则的LBG聚类算法,能为语音操控系统中无监督的说话人自适应提供更可靠的说话人模板库。     

CON/SLK due date assignment and scheduling on a single machine with two agents

We consider scheduling problems involving two agents (agents A and B), each having a set of jobs that compete for the use of a common machine to process their respective jobs. The due dates of the A‐jobs are decision variables, which are determined by using the common (CON) or slack (SLK) due date assignment methods. Each agent wants to minimize a certain performance criterion depending on the completion times of its jobs only. Under each due date assignment method, the criterion of agent A is always the same, namely an integrated criterion consisting of the due date assignment cost and the weighted number of tardy jobs. Several different criteria are considered for agent B, including the maxima of regular functions (associated with each job), the total (weighted) completion time, and the weighted number of tardy jobs. The overall objective is to minimize the performance criterion of agent A, while keeping the objective value of agent B no greater than a given limit. We analyze the computational complexity, and devise polynomial or pseudo‐polynomial dynamic programming algorithms for the considered problems. We also convert, if viable, any of the devised pseudopolynomial dynamic programming algorithms into a fully polynomial‐time approximation scheme. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 416–429, 2016     

The initial provisioning decision for insurance type items

Initial provisioning decisions (inventory stocking requirements) for low demand items often have to be made without much knowledge of what future demand rates will be. When the nature of an item is such that little demand for it is expected, the problem of whether to stock initially or risk not stocking the item is most critical. This report discusses this problem and presents decision procedures which can be used to handle this aspect of initial provisioning. The procedures relate an item's provisioning desirability to its provisioning characteristics, such as expected cost, expected resupply time, current information on its likely demand rate, and to an overall operating policy or criterion. The criterion function measures the total system degredation as a function of the events of having items out of stock when demand occurs. Several different policy functions are discussed and the provisioning decision rules which apply to each are presented. Demand rate information is handled through a Bayesian type approach. The decision rules presented in this report can be utilized to either determine stocking requirements within a budgetary constraint, or determine the relative stocking desirability on an item-by-item basis.     

基于遗传算法的战时维修保障系统优化研究

分析了战时维修保障系统的结构功能,给出了维修保障系统的解析模型,提出了维修保障系统的可控参数及指标;为了使维修保障系统发挥最佳效能,以最小二乘准则作为系统的优化准则,建立了维修保障系统的优化模型,采用遗传算法对优化模型进行求解,给出了计算方法,并以计算实例验证了方法的可行性。