An empirical bayes estimator for the scale parameter of the two-parameter weibull distribution

An empirical Bayes estimator is given for the scale parameter in the two-parameter Weibull distribution. The scale parameter is assumed to vary randomly throughout a sequence of experiments according to a common, but unknown, prior distribution. The shape parameter is assumed to be known, however, it may be different in each experiment. The estimator is obtained by means of a continuous approximation to the unknown prior density function. Results from Monte Carlo simulation are reported which show that the estimator has smaller mean-squared errors than the usual maximum-likelihood estimator.     

复合材料层合板疲劳寿命形状参数与门槛值分析方法

复合材料性能具有较大的分散性,在表征复合材料疲劳寿命时,必须考虑分散性的影响。以M21C复合材料开孔层合板为研究对象,采用Sendeckyj等效静强度模型和随机变量函数的概率分布方法推导了复合材料层合板疲劳寿命形状参数和剩余强度形状参数的关系,通过试验和统计的方法获得了M21C复合材料开孔层合板的疲劳寿命形状参数和疲劳门槛值,对载荷放大系数以及低载截除水平的确定提供了数据支持。     

Simulation of natural fragmentation of rings cut from warheads

Natural fragmentation of warheads that detonates causes the casing of the warhead to split into various sized fragments through shear or radial fractures depending on the toughness,density,and grain size of the material.The best known formula for the prediction of the size distribution is the Mott formulae,which is further examined by Grady and Kipp by investigating more carefully the statistical most random way of portioning a given area into a number of entities.We examine the fragmentation behavior of radially expanding steel rings cut from a 25 mm warhead by using an in house smooth particle hydrodynamic(SPH) simulation code called REGULUS.Experimental results were compared with numerical results applying varying particle size and stochastic fracture strain.The numerically obtained number of fragments was consistent with experimental results.Increasing expansion velocity of the rings increases the number of fragments.Statistical variation of the material parameters influences the fragment characteristics,especially for low expansion velocities.A least square regression fit to the cumulative number of fragments by applying a generalized Mott distribution shows that the shape parameter is around 4 for the rings,which is in contrast to the Mott distribution with a shape parameter of 1/2.For initially polar distributed particles,we see signs of a bimodal cumulative fragment distribution.Adding statistical variation in material parameters of the fracture model causes the velocity numerical solutions to become less sensitive to changes in resolution for Cartesian distributed particles.     

A good simple percentile estimator of the weibull shape parameter for use when all three parameters are unknown

In this paper we consider a simple three-order-statistic asymptotically unbiased estimator of the Weibull shape parameter c for the case in which all three parameters are unknown. Optimal quantiles that minimize the asymptotic variance of this estimator, c? are determined and shown to depend only on the true (unknown) shape parameter value c and in a rather insensitive way. Monte Carlo studies further verified that, in practice where the true shape parameter c is unknown, using always c? with the optimal quantities that correspond to c = 2.0 produces estimates, c?, remarkably close to the theoretical optimal. A second stage estimation procedure, namely recalculating c? based on the optimal quantiles corresponding to c?, was not worth the additional effort. Benchmark simulation comparisons were also made with the best percentile estimator of Zanakis [20] and with a new estimator of Wyckoff, Bain and Engelhardt [18], one that appears to be the best of proposed closed-form estimators but uses all sample observations. The proposed estimator, c?, should be of interest to practitioners having limited resources and to researchers as a starting point for more accurate iterative estimation procedures. Its form is independent of all three Weibull parameters and, for not too large sample sizes, it requires the first, last and only one other (early) ordered observation. Practical guidelines are provided for choosing the best anticipated estimator of shape for a three-parameter Weibull distribution under different circumstances.     

基于局部双参数估计的SAR图像CFAR目标检测技术

提出了在背景杂波呈现Weibull分布条件下的SAR图像恒虚警目标检测方法.从统计分析观点,推导了基于局部窗口的Weibull分布参数估计和自适应CFAR目标检测阈值的计算公式;对检测后的图像进行形态滤波处理以消除检测中的虚假目标;最后提出了应适当选择恒虚警率.仿真结果表明该方法的有效性.     

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.     

The logistic–exponential survival distribution

For various parameter combinations, the logistic–exponential survival distribution belongs to four common classes of survival distributions: increasing failure rate, decreasing failure rate, bathtub‐shaped failure rate, and upside‐down bathtub‐shaped failure rate. Graphical comparison of this new distribution with other common survival distributions is seen in a plot of the skewness versus the coefficient of variation. The distribution can be used as a survival model or as a device to determine the distribution class from which a particular data set is drawn. As the three‐parameter version is less mathematically tractable, our major results concern the two‐parameter version. Boundaries for the maximum likelihood estimators of the parameters are derived in this article. Also, a fixed‐point method to find the maximum likelihood estimators for complete and censored data sets has been developed. The two‐parameter and the three‐parameter versions of the logistic–exponential distribution are applied to two real‐life data sets. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

车辆悬挂系统扭杆弹簧疲劳寿命的统计分析

本文对车辆悬挂系统扭杆弹簧的寿命作了统计分析,得到服从形状参数m=1.5～2.0的威布尔分布.论证了把可靠度R(t)=0.9的工作寿命作为规范中所规定的额定寿命值的合理性,同时对影响其寿命的若干因素进行了讨论.     

The effect of nonnormality on variables sampling plans

Acceptance sampling plans based on variables have been in use for many years. Recently, there has been a renewal of interest in these plans, because of the relative efficiencies that they offer with respect to attributes sampling regarding sample size. Furthermore, in situations where acceptable quality levels are very small, and a high level of protection is desired, variables sampling is often much more efficient than attributes sampling. An important disadvantage of variables sampling is that the distribution of the parameter being inspected must be known. Most standard variables sampling plans assume that the distribution of this parameter is normal. This article examines the effect of the normality assumption in variables sampling. Methods to detect departures from normality are reviewed.     

3种不同形状电枢对线圈炮发射性能影响的仿真分析

分析电磁线圈炮基本原理，建立单级感应线圈炮数学模型，并借助Matlab仿真软件，对3种不同形状（锥体、半球体和圆柱体）电枢的线圈炮进行仿真。分别得到电枢与驱动线圈之间互感与互感梯度的相对位置变化曲线、电枢内涡流分布及随时间变化曲线，3种发射器在同一坐标下的射弹电磁力-时间和速度-时间变化曲线。通过对比分析，确定了线圈炮合理的电枢形状，为线圈炮的系统结构设计奠定了基础。     

Estimation for a weibull accelerated life testing model

It is sometimes reasonable to assume that the lifetime distribution of an item belongs to a certain parametric family, and that actual parameter values depend upon the testing environment of the item. In the two-parameter Weibull family setting, suppose both the shape and scale parameters are expressible as functions of the testing environment. For various models of functional dependency on environment, maximum likelihood methods are used to estimate characteristics of interest at specified environmental levels. The methodology presented handles exact, censored, and grouped data. A detailed accelerated life testing analysis of stress-rupture data for Kevlar/epoxy composites is given.     

空间绳网系统展开动力学特性分析

空间绳网系统是一种新型轻质空间柔性结构,具有很大的应用价值。针对地面环境和太空环境下的不同受力特性,推导空间绳网动力学模型;通过地面试验验证仿真模型的可信度;基于展开面积、飞行距离等性能参数,仿真分析空间绳网展开过程中的绳网位形、应力分布以及能量变化等动力学特性,分析轨道高度、捕获方向和发射参数对展开效果的影响。     

Bayesian estimation: A sensitivity analysis

The robustness of the assigned prior distribution in a Bayesian estimation problem is examined. A Bayesian analysis for a stochastic intensity parameter of a Poisson distribution is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by assuming the existence of a true prior which is different in form from that of the assigned prior distribution. By using mean-squared error as a measure of performance, the ensuing Bayes decision function is compared to the corresponding minimum variance unbiased estimator. Results indicate that the Bayes estimator is largely robust to deviations from the assigned prior and remains squared-error superior to the MVU type within a broad region.     

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     

基于权值的NURBS曲线形状修改

针对基于控制顶点的NURBS曲线形状修改的不足,讨论了如何通过修改控制顶点的权值进行NURBS曲线的形状修改问题。NURBS曲线可以看作是高一维空间非有理B样条曲线的中心投影,该B样条的控制顶点为原NURBS曲线的带权控制顶点,并且这样的B样条曲线有无数多条。根据这个性质,以实例的方式通过特定自由参数确定B样条曲线,实现了基于权值的NURBS曲线形状修改。该方法不仅能够较好地确定新的带权控制顶点,还解决了修改后曲线在给定点的切矢问题,具有更好的灵活性。     

Warranty policies and burn-in

Warranty is an important factor for consumer durable products in the marketplace. However, the warranty cost may drastically reduce profitability. Burn in is a common procedure to improve the quality of products after they have been produced, but it is also costly. By taking both the burn-in procedure and warranty policy into consideration, several cost functions can be formulated and optimized. Assuming that the failure-rate function of the product has a bathtub shape, it is shown that the optimal burn-in times that minimize the considered cost functions never exceed the first change point of the failure-rate function. The continuous dependence of the optimal burn-in times on the model parameters and the underlying distribution is also established. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 199–209, 1997     

正态总体下分布参数的Bayes序贯估计

论述正态总体分布参数的序贯估计和Bayes序贯估计问题。在Stein的双子样序贯估计的基础上 ,构造了Bayes双子样序贯估计 ,并作了剖析。此外 ,为了适应当前试验场地“试试看看 ,看看试试”的试验分析和鉴定的需要 ,给出了以序贯Bayes检验为基本出发点 ,使检验和序贯估计相联合的分析方法     

基于均匀实验设计的温压战斗部爆炸冲击波毁伤仿真研究

以温压战斗部爆炸冲击波对地下目标的毁伤为背景,设计毁伤仿真模拟的基本方案,在对影响冲击波毁伤因素合理分析的基础上,利用均匀试验设计方法设计以装药密度、空气温度、大气压强以及混凝土密度为影响因素的均匀试验方案,最后通过正态分布检验图和Bootstrap法等方法对毁伤参数的统计特性进行研究。结果表明,固定条件下温压战斗部爆炸冲击波对地下目标的毁伤中,毁伤参数值具有明显的正态分布特性,对后续结合现场试验数据确定毁伤参数真值和毁伤试验鉴定提供了一定的指导和借鉴作用。     

基于预报误差分布拟合的卫星历史机动检测方法

轨道机动会引起在轨卫星的轨道异常，是空间态势感知的重点关注对象之一。为此，提出一种从卫星的两行轨道要素编目数据中检测历史机动的方法。通过分析预报误差检测轨道参数的异常编目值，进而获得相应的历史机动信息。对卫星的两行轨道要素编目数据两两预报求差得到预报误差的样本数据后，利用期望最大化算法可以拟合得到以高斯混合模型表达的预报误差的概率分布模型；以此为基础，可以确定利用预报误差检测轨道参数异常编目值的门限；利用轨道机动与异常编目值之间的对应关系，最终实现机动检测。对典型活动卫星的机动检测结果表明，所提方法能够在准确检出历史机动事件的同时保持较低的误检率。     

再生冷却通道结构参数对碳氢燃料流量分配影响

以液体火箭发动机再生冷却技术为背景,采用数值模拟方法对Z-type型并联通道流量分配特性进行研究,分析了通道数、通道截面形状及入口汇流结构对流量分配特性的影响。研究结果表明:在冷却通道总流通面积相同的情况下,随着再生冷却系统通道数的增加,流量分配不均匀度系数从2.59%降低至0.5%,相同流通面积下增加通道数可以有效提高流量分配的均匀程度。通道截面形状对流量分配不均匀度系数影响不大,其影响主要表现在通道内部流体速度分布及换热面积上。从换热效果看,梯形截面构型要优于矩形构型。入口汇流结构倾斜角有利于流量的均匀性分布。该研究对于再生冷却通道结构设计具有一定参考价值。