屏蔽数据在新型截尾样本下系统的可靠性分析

当系统含有屏蔽数据时,在具有随机移走逐步增加型截尾模型下,讨论了部件寿命服从双参数指数分布的串联系统可靠性估计问题。设随机移走系统数服从二项分布,利用极大似然方法,Bayes理论及方法,推导出双参数指数部件参数、系统可靠性函数、失效率函数及移走概率的极大似然估计和Bayes估计。并利用Monte Carlo方法对两种估计结果进行了比较,表明Bayes估计较极大似然估计效果更优。     

On models for business failure data

It is pointed out in this paper that Lomax's hyperbolic function is a special case of both Compound Gamma and Compound Weibull distributions, and both of these distributions provide better models for Lomax's business failure data than his hyperbolic and exponential functions. Since his exponential function fails to yield a valid distribution function, a necessary condition is established to remedy this drawback. In the light of this result, his exponential function is modified in several ways. It is further shown that a natural complement of Lomax's exponential function does not suffer from this drawback.     

Likelihood estimation for generalized mixed exponential distributions

The class of functions expressed as linear (not necessarily convex) combinations of negative exponential functions is dense in the set of all square integrable functions on the nonnegative reals. Because of this and resultant mathematical properties, linear combinations of exponential densities have excellent potential for wide application in stochastic modeling. This work documents the development and testing of a practical procedure for maximum-likelihood estimation for these generalized exponential mixtures. The algorithm offered for the problem is of the Jacobi type and guarantees that the result will provide a legitimate probability function of the prescribed type. Extensive testing has been performed and results are very favorable: convergence is rapid and the use of computer resources rather limited.     

无源雷达截获概率建模与窗口变量影响仿真

在截获概率概念和截获条件的基础上,综合时域、空域、频域等窗口函数构建截获概率模型,分别建立截获过程的4个窗口函数子模型,研究截获概率与窗口函数变量的影响关系。以SPS-48雷达为辐射源,仿真分析各窗口函数变量对截获概率的影响程度,讨论分区策略下无源雷达参数优化对截获概率的影响并总结截获概率提高方法,为无源雷达设计、研制、试验以及使用提供技术支撑。     

Designing acceptance sampling schemes for life testing with mixed censoring

Mixed censoring is useful extension of Type I and Type II censoring and combines some advantages of both types of censoring. This paper proposes a general Bayesian framework for designing a variable acceptance sampling scheme with mixed censoring. A general loss function which includes the sampling cost, the time‐consuming cost, the salvage value, and the decision loss is employed to determine the Bayes risk and the corresponding optimal sampling plan. An explicit expression of the Bayes risk is derived. The new model can easily be adapted to create life testing models for different distributions. Specifically, two commonly used distributions including the exponential distribution and the Weibull distribution are considered with a special decision loss function. We demonstrate that the proposed model is superior to models with Type I or Type II censoring. Numerical examples are reported to illustrate the effectiveness of the method proposed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

线性模型的海基制导系统误差分离方法性能分析

利用传统制导工具系统误差线性回归模型,对Bayes估计、主成分分析以及正则化分析三种改进的分离方法进行了比较,分析了它们在工程应用上的优缺点,给出了实际应用时的限制因素;同时结合海基导弹特有的初始状态误差,设计了整体估计、分段估计以及迭代估计三种估计策略,给出了相应的分离步骤。仿真结果表明,文中给出的三种误差分离方法在不同的评价标准下具有不同的实际应用意义;而在弹道差评价标准以及方差评价标准下,分段估计和迭代估计策略下的误差分离结果要明显好于传统整体估计结果。     

如何估计软件的MTBF

软件剩余初始故障个数No、平均无故障时间MTBF、故障暴露率λ和软件运行的成功率θ等是衡量软件可靠性的重要参数.其中对高可靠性软件(包括军用软件等)MTBF是最重要的.传统的MTBF计算方法有2种一是计算发生故障的平均时间间隔二是通过软件可靠性模型进行估计.前者代价较大,后者不太准确.本文从软件的失败率入手研究软件的MTBF,这是一个比较贴近实际的方法.     

注意力机制量化剪枝优化方法

面向基于注意力机制模型的巨大计算和访存开销问题,研究量化和剪枝协同优化的模型压缩技术,提出针对注意力机制中查询、键、值、概率共四个激活值矩阵的对称线性定点量化方法。同时,提出概率矩阵剪枝方法和渐进式剪枝策略,有效降低剪枝精度损失。在不同数据集上的实验结果表明,针对典型基于注意力机制模型BERT,在较低或者没有精度损失的情况下该优化方法可达到4位或8位定点量化、0.93～0.98的稀疏度,大幅度降低模型计算量,为加速量化稀疏模型的推理奠定良好的基础。     

声自导雷平行齐射发现概率解析计算模型

为了准确快速地评估声自导鱼雷平行齐射的作战效能（发现概率）,从鱼雷、目标的相对运动入手,将目标位置及运动随机误差转移到鱼雷航向上;如此建立了计算声自导鱼雷平行齐射发现概率的一重积分解析模型（不考虑鱼雷航行性能误差）和四重积分解析计算模型（考虑鱼雷航行性能误差）。最后以统计模型为标准来验证两个解析模型的正确性。仿真结果显示,对于90%左右的考察态势,解析模型与统计模型的结果差的绝对值在1%之内,另外10%左右的考察态势,也在1%-3%之间。从而验证了所建解析模型的正确性和可行性。     

基于最大后验概率候选集更换法的多故障诊断策略研究

给出了一种基于最大后验概率候选集更换法的多故障诊断策略,并深入阐述了基于最大后验概率候选集更换法的形式化描述,分析了对单故障诊断和多故障诊断的计算模型,提出了基本的故障诊断算法——改进二进制粒子群算法,并对抽象实例进行验证,结果表明,采用改进BPSO算法能有效地求解基于最大后验概率候选集更换法的多故障诊断问题。     

混合指数分布模型的Bayes分析

针对截尾试验数据的情况,给出了二元混合指数分布模型的平均寿命和可靠性函数的严格的Ｂａｙｅｓ点估计,并运用最大熵准则给出了可靠性函数的近似的Ｂａｙｅｓ置信下限估计。     

Damage functions and estimates of fratricide and collateral damage

There are multiple damage functions in the literature to estimate the probability that a single weapon detonation destroys a point target. This paper addresses differences in the tails of four of the more popular damage functions. These four cover the asymptotic tail behaviors of all monotonically decreasing damage functions with well‐behaved hazard functions. The differences in estimates of probability of kill are quite dramatic for large aim‐point offsets. This is particularly important when balancing the number of threats that can be engaged with the chances of fratricide and collateral damage. In general, analysts substituting one damage function for another may badly estimate kill probabilities in offset‐aiming, which could result in poor doctrine. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 306–321, 2003.     

基于贝叶斯方法的指数寿命型产品可靠度评估方法

以经典法为推理基础,利用无验前信息时验前分布密度的假设方式及共轭分布函数的传递性,推导出指数寿命型产品在不同试验方案下可靠度R的多层贝叶斯评估方法。使得在利用贝叶斯方法对指数寿命型产品进行评估时,更具科学性和合理性。     

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.     

假目标配置数量模型及其效费比分析

在现代战争中,示假伪装的地位越来越重要。引入了真假目标的发现识别概率的指数分布模型,综合考虑作战时间、真假目标价格比等因素,确定战场生存能力和配置假目标成本两个目标函数,并以最小加权偏差法确定两者权重,建立基于多目标决策的假目标配置数量模型。最后结合实际问题,将各参数条件带入模型计算出假目标的最佳配置数量,同时利用假目标的效费比模型进行检验分析,从而为战时假目标配置数量的确定提供参考依据。     

幂函数型完全非线性函数原像分布的特征

完全非线性函数是特征为奇数的有限域上抗差分密码攻击最优的函数,目前已有的六类完全非线性函数都是2-1的。当Π(x)为Fqm上的Dembowski-Ostrom函数或者Coulter-Matthews函数时,从Fqm到Fq的完全非线性函数tr(aΠ(x))的原像分布恰有两种取值,其中一种取值对应Fqm所有平方剩余元,另一种取值对应Fqm所有非平方剩余元。该结论在文中得到了证明。     

An integral equation for the second moment function of a geometric process and its numerical solution

In this article, an integral equation satisfied by the second moment function M₂(t) of a geometric process is obtained. The numerical method based on the trapezoidal integration rule proposed by Tang and Lam for the geometric function M(t) is adapted to solve this integral equation. To illustrate the numerical method, the first interarrival time is assumed to be one of four common lifetime distributions, namely, exponential, gamma, Weibull, and lognormal. In addition to this method, a power series expansion is derived using the integral equation for the second moment function M₂(t), when the first interarrival time has an exponential distribution.     

Estimation of the survival function of a repairable standby series system

This article deals with the statistical analysis of an N-component series system supported by an active standby and one repair facility. Assuming that the life and repair times of the components are independent exponential random variables, the probability distribution of the first passage to the system failure time is shown to be a convolution of two independent exponential distributions. Three observation schemes are considered to obtain the maximum likelihood estimates of the survival function. Information matrices are supplied. Numerical results based on Monte Carlo simulation are presented. It is noted that component level information (failure rate, repair rate) is not necessary for estimating the survival function of the system.     

方差全局灵敏度求解的空间分割结合无迹变换方法

为有效计算基于方差的全局灵敏度指标尤其是非线性程度较高的响应函数的,将积分空间的可加性以及无迹变换结合起来,利用函数在子空间内非线性程度会降低以及无迹变换方法在概率空间内对低非线性函数性质具有强捕捉能力的特点,提出计算基于方差的全局灵敏度指标的高效方法。该方法只需产生一组无迹变换样本就可以近似求得各阶灵敏度指标,并且该近似解随空间分割个数的增加而收敛于真值。通过非线性程度较高的验证算例及工程算例验证了所提方法在处理非线性功能函数上的高效性和准确性。     

A game theoretic approach to a two firm bidding problem

In this paper a model is developed for determining optimal strategies for two competing firms which are about to submit sealed tender bids on K contracts. A contract calls for the winning firm to supply a specific amount of a commodity at the bid price. By the same token, the production of that commodity involves various amounts of N different resources which each firm possesses in limited quantities. It is assumed that the same two firms bid on each contract and that each wants to determine a bidding strategy which will maximize its profits subject to the constraint that the firm must be able to produce the amount of products required to meet the contracts it wins. This bidding model is formulated as a sequence of bimatrix games coupled together by N resource constraints. Since the firms' strategy spaces are intertwined, the usual quadratic programming methods cannot be used to determine equilibrium strategies. In lieu of this a number of theorems are given which partially characterize such strategies. For the single resource problem techniques are developed for determining equilibrium strategies. In the multiple resource problem similar methods yield subequilibrium strategies or strategies that are equilibrium from at least one firm's point of view.