二维正态分布不同方差小样本检验射击精度方法研究

讨论了在小样本条件下,如何检验不同方差的二维正态分布的方差问题,绘制了拒真概率α和纳伪概率β相等时的临界值曲线.模拟表明该方法对武器检验具有一定的意义.     

小样本三维正态分布整体检验射击精度方法研究

讨论了小样本三维同方差正态分布整体检验射击精度问题.给出了n=3,4,5的不同显著水平α的检验OC曲线.计算出了与第一类错误和第二类错误相联系的有关重要物理参数.模拟表明该方法检验效果良好.     

药物效用鉴定的序贯抽样检验方法和条件推导

给出了制定药物效用鉴定的序贯抽样检验方案,对未用的同类药品进行随机抽样,利用抽样结果,对剩下的N-n个样品的性能进行推断,得到判断药品是否失效的抽样方法以及有效的抽样截断方案,在减小抽样量的前提下,准确的判断药物是否有效.并对该序贯抽样性能的优劣与固定样本最优检验方法进行了比较,得到在犯同样错误的前提下,序贯抽样检验的样本量比固定样本最优检验的样本量小的多.     

环境本底统计特性研究

在研究移动物体放射性监测报警技术的背景下,对环境本底的统计特性进行了研究。阐述了检验环境本底是否符合正态分布的几种方法以及MATLAB软件中检验正态分布的工具,并利用采集的环境本底数据计算、分析了环境本底的统计分布模型,最后给出了各方法的评价。     

子母弹射击精度的仿真研究

提出了子母弹命中目标的定义,研究了子母弹射击误差的组成与概率分布,建立了计算子母弹命中概率的两种仿真计算模型--直接模拟子母弹射击误差法和射击误差模拟与数值积分相结合的方法.给出了对圆形目标和矩形目标的具体计算方法,以及正态分布随机向量和均匀分布随机向量的产生方法,根据算例的结果,讨论了子弹重迭度对子母弹首发命中概率的影响.比较了两种不同仿真方法的计算结果.     

命中概率的一致最小方差无偏估计

本文从随机落点的样本值直接估计命中概率。文中给出了一致最小方差无偏估计(UMVU估计)。首先给出命中狭长地带(区间)概率的UMVU估计。然后对于平面落点情况,在纵向和横向落点为独立的场合下,给出命中散布圆概率的UMVU估计。对于估值的精度同时进行了讨论。     

基于保障概率的装备磨损单元备件配置研究

备件在装备保障中发挥着至关重要的作用,而备件的数量则决定着装备的维修能力和保障水平.针对装备磨损部件预防性维修的研究较少,介绍了一种较为简便、实用的定时更换策略,通过对寿命服从正态分布的磨损部件的分析,导出了基于保障概率的磨损单元备件计算模型,最后给出了计算实例.结果表明,该方法在明确磨损部件故障规律的情况下,应用方便,计算简单.     

应召搜潜中已知概略航向的潜艇分布概率计算

针对应召搜潜过程中已知概略航向的潜艇分布概率计算的问题,推导了潜艇的初始位置服从正态分布、潜艇概略航向已知、潜艇航速已知或服从均匀分布或服从瑞丽分布等几种情况下,潜艇概率的分布随时间变化的计算公式,并通过蒙特卡罗方法验证了所推导公式的正确性,给出了部分时刻潜艇位置联合概率密度的计算结果。     

基于区间数的DS证据合成方法研究

在DS证据理论的应用过程中,命题的基本概率赋值函数起到了关键的作用,传统DS证据理论中基本概率赋值函数的取值为[0,1]中的单点值.在很难准确将证据所支持命题的基本概率赋值表示为[0,1]之间的单点值时,可以用区间数形式来表示命题的基本概率赋值.在建立符合运算封闭性的区间数广义求和与广义乘积算子的基础上,定义了基于区间数的基本概率赋值函数、信任函数以及似然函数等重要概念,给出了证据合成规则,进而提出了基于区间数的DS证据合成方法.计算实例表明,与传统DS证据合成方法相比,基于区间数的DS证据合成方法具有更灵活的应用特性和更小的计算复杂度.     

Weibull分布环境因子工程计算方法

目前,常用的指数型环境因子计算公式缺乏广泛的适用性,不能适用小样本失效数据或零失效数据的情况,尽管工程中有相应的处理方法,但因有人为因素的影响使其结果不够客观。针对这一问题,提出Weibull分布环境因子小概率评估法,并给出工程具体实施方法,使结果更合理,更具实用价值。     

Multivariate tests of fit using asymptotically sufficient grouping

A sample is taken from a continuous multivariate distribution. The problem is to test the hypothesis that the unknown joint cumulative distribution function is equal to a completely specified function. The observed data are transformed so that the hypothesis being tested is that the distribution is uniform over a unit hypercube. If only neighboring alternatives are considered, it is shown that the numbers of observations falling in a gradually increasing number of subcubes are asymptotically sufficient. It is shown that for all asymptotic probability calculations, we can assume that the joint distribution of the numbers of observations can be considered to be the distribution of slightly rounded off normal random variables. Tests based on these facts are constructed.     

The asymptotic sufficiency of sparse order statistics in tests of fit with nuisance parameters

In an earlier paper, it was shown that for the problem of testing that a sample comes from a completely specified distribution, a relatively small number of order statistics is asymptotically sufficient, and for all asymptotic probability calculations the joint distribution of these order statistics can be assumed to be normal. In the present paper, these results are extended to certain cases where the problem is to test the hypothesis that a sample comes from a distribution which is a member of a specified parametric family of distributions, with the parameters unspecified.     

基于截尾正态分布的最大值指标精度换算方法

提出了基于截尾正态分布的最大值指标精度换算方法,为最大值指标与常用精度指标间的精度换算,以及真值测量系统精度指标的确定提供了参考依据。该方法假设系统输出序列中各观测点的合格概率服从对数截尾正态分布;根据给定最大值指标的置信水平及序列样本量,证明并推导了截尾正态分布之截尾上限、截尾下限、均值及标准偏差的计算公式,导出了最大值精度指标与 等常用精度指标间的换算关系,最后结合精密仪器有关理论给出了最大值指标下真值测量系统精度指标的确定方法。实例应用的实验结果表明,该方法是可行的。     

Normal and weibull distributions

Numerous applications of the Weibull distribution in diverse fields of human endeavor are well known today. Nevertheless, it is not uncommon to find applications of the normal distribution in such fields of studies as agriculture, biology, chemistry, engineering, physics, sociology and others. At the present time we have at our disposal many more refined statistical techniques for analyzing the normal rather than the Weibull data. Consequently, it is important for applied statisticians to know if some of their data which can be described by the Weibull distribution can also be described by the normal distribution. The present investigation of the author reveals that the normal distri,bution can be considered to be a good approximation to the Weibull distribution as long as its shape parameter is in the open interval (3.25, 3.61). This fact enables them to perform a refined statistical analysis of their data. Conversely, they can now easily compute the desired normal cumulative probabilities from the Weibull distribution function, which would be especially helpful for those standard normal deviates whose cumulative probabilities cannot be read from the available tables of normal cumulative probability. In a similar situation they can also use the Weibull distribution to obtain an approximation to any desired normal deviate for a given normal probability which may be better than those obtained by the linear interpolation method.     

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。     

Lower confidence limits for the impact probability within a circle in the normal case

Lower confidence limits are derived for the impact probability within a circle of fixed radius. The bivariate normal distribution with zero means, unequal variances, and zero correlation is the probability model for impacts. A new representation of the impact probability function is offered. This presentation is valid also for the dependent case, where the eigenvalues of the covariance matrix replace the variances. When the ratio of variances is known the lower confidence limits are uniformly most accurate (UMA). A few alternative approaches are compared by simulation when the ratio of variances is unknown.     

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.     

Exact bayesian estimation of system reliability from component test data

System reliability is often estimated by the use of components' reliability test results when system test data are not available, or are very scarce. A method is proposed for computing the exact posterior probability density function, cumulative distribution function, and credible intervals for system reliability in a Bayesian setting, with the use of components' prior probability distributions and current test results. The method can be applied to series, parallel, and many mixed systems. Although in theory the method involves evaluating infinite series, numerical results show that a small number of terms from the infinite series are sufficient in practice to provide accurate estimates of system reliability. Furthermore, because the coefficients in the series follow some recurrence relations, our results allow us to calculate the reliability distribution of a large system from that of its subsystems. Error bounds associated with the proposed method are also given. Numerical comparisons with other existing approaches show that the proposed method is efficient and accurate. © 1997 John Wiley & Sons, Inc.     

MAD: Mathematical analysis of downtime

The MAD model presents a mathematic treatment of the relationship between aircraft reliability and maintainability, system manning and inspection policies, scheduling and sortie length, and aircraft downtime. Log normal distributions are postulated for subsystem repair times and simultaneous repair of malfunctions is assumed. The aircraft downtime for maintenance is computed with the distribution of the largest of k log normal distributions. Waiting time for maintenance men is calculated either by using a multiple-channel queuing model or by generating the distribution of the number of maintenance men required and comparing this to the number of men available to determine the probability of waiting at each inspection.