Product moments of order statistics from the doubly truncated exponential distribution

Recurrence relations for the product moments of order statistics from a doubly truncated exponential distribution are obtained. These relations allow us to evaluate the product moments for all sample sizes.     

On the moments of gamma order statistics

A recurrence relation between the moments of order statistics from the gamma distribution having an integer parameter r is obtained. It is shown that if the negative moments of orders -(r?1), …, ?1 of the smallest order statistic in random samples of size n are known, then one can obtain all the moments. Tables of negative moments for r = 2 (1) 5 are also given.     

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew (PFGS) plates. The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate. A nonlinear finite element (FE) formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory (FSDT) in conjunction with von Karman’s nonlinear strain displacement relations. The governing equations of the PFGS plate are derived using the principle of virtual work. The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations. The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters. The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.     

Poisson分布与正态分布参数的Γ—极小极大估计

对于Poisson分布及正态分布,本文在其参数θ的先验一阶矩和二阶矩的部分信息已知的情况下,给出了θ的极小极大估计,同时也给出了最不利先验分布。     

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.     

仿射不变轮廓矩及其稳定性分析

针对区域矩需要计算全图像素的统计分布、计算量大的问题,构造了基于目标形状的仿射不变轮廓矩。首先采用PDE方法推导得到了6个仿射不变矩的数学模型,然后将积分区间变为目标区域的边界,计算得到基于目标形状的仿射不变轮廓矩,最后通过三类舰船不同姿态下的图像进行了实验验证并对其稳定性进行了分析。研究结果表明:仿射不变轮廓矩具有较好的稳健性及区分度,可将其作为不变特征用于舰船目标识别。     

Tests for homogeneity of distributions of component lifetimes from system lifetime data with known system signatures

In this article, we discuss the problem of testing the homogeneity of distributions of component lifetimes based on system lifetime data when the system signatures are known. Both parametric and nonparametric procedures are developed for this problem. For nonparametric testing, the Mann–Whitney‐type statistic is used, and its performance and limitations are discussed. Next, we assume the component lifetimes to follow exponential distributions and then develop different parametric tests. Exact and asymptotic methods are developed based on the method of moments estimators. A Monte Carlo simulation study is used to compare the performance of different parametric procedures with that of the nonparametric procedure. Based on the results of the simulation study, discussions and practical recommendations are made and finally some concluding remarks are provided. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 550–563, 2015     

On the output of parallel exponential service channels

The paper treats the output process of a service center that has a large number of independent exponential channels in parallel. Initially all channels are working and there is a fixed backlog of items awaiting service. The moments are derived and central limit theorems are developed. Problems of computation are discussed and suitable formulae are developed. The joint distribution of the output of the center with the center's total busy time and total idle time are derived. Normal approximations to these distributions are presented.     

Quadratic forms in spherical random variables: Generalized noncentral x2 distribution

Let X denote a random vector with a spherically symmetric distribution. The density of U = X'X, called a “generalized chi-square,” is derived for the noncentral case, when μ = E(X) ≠ 0. Explicit series representations are found in certain special cases including the “generalized spherical gamma,” the “generalized” Laplace and the Pearson type VII distributions. A simple geometrical representation of U is shown to be useful in generating random U variates. Expressions for moments and characteristic functions are also given. These densities occur in offset hitting probabilities.     

An approximation for the waiting time distribution in single server queues

Single server queues with general interarrival and service times are approximated by queues with two-point (Bernoulli) interarrival times and exponential service times. The parameters are chosen such that the first four moments of the difference of the service times and interarrival times in the approximating system equal those of the original system. The aptness of the approximation is discussed and some examples are presented comparing the exact and approximate waiting time distributions. A more complicated approximation is presented using the dual system (exponential arrivals, Bernoulli service) for those cases where the original approximation cannot be used.     

考虑摩擦时Diesel循环功率效率特性新析

对有摩擦时Diesel循环进行了有限时间热力学分析 .导出功率和压缩比、效率和压缩比的新关系式 ,进而得到功率效率关系 ,并进行了计算和讨论 ,给出一些有益的结论     

Discriminating between the Weibull and log‐normal distributions

Log‐normal and Weibull distributions are the most popular distributions for modeling skewed data. In this paper, we consider the ratio of the maximized likelihood in choosing between the two distributions. The asymptotic distribution of the logarithm of the maximized likelihood ratio has been obtained. It is observed that the asymptotic distribution is independent of the unknown parameters. The asymptotic distribution has been used to determine the minimum sample size required to discriminate between two families of distributions for a user specified probability of correct selection. We perform some numerical experiments to observe how the asymptotic methods work for different sample sizes. It is observed that the asymptotic results work quite well even for small samples also. Two real data sets have been analyzed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

正反向量子斯特林循环有限时间热力学性能界限和优化准则

研究了正反向量子斯特林循环的最优性能.在经典极限下,导出了循环的有限时间热力学性能界限和优化准则.得到了斯特林热机、制冷机和热泵特性参数之间的优化关系.     

各向异性材料的有效弹性模量

在夹杂理论的基础上,采用用自洽法导出了含分布夹杂的各向异性弹性体的本构关系和有效弹性模量的细观力学表达式。本文得到的公式不仅可以处理含缺陷和损伤的材料的有效弹性模量,而且还可处理诸于纤维复合材料等各向异性材料的理论及有效弹性模量,从而为建立材料细观结构与宏观性能之间的关系提供了理论基础。     

具有等熵压缩、膨胀过程的回热式布雷顿热泵循环有限时间热力学性能

研究恒温和变温热源条件下具有等熵压缩、膨胀过程的闭式回热式布雷顿热泵循环有限时间热力学性能,导出循环供热率和供热系数与循环压比间的解析关系,由此可得最佳供热率、供热系数关系。分析中计入了工质与高、低温热源间换热器和回热器的热阻损失。     

Parametric inference for component distributions from lifetimes of systems with dependent components

In system reliability analysis, for an n ‐component system, the estimation of the performance of the components in the system is not straightforward in practice, especially when the components are dependent. Here, by assuming the n components in the system to be identically distributed with a common distribution belonging to a scale‐family and the dependence structure between the components being known, we discuss the estimation of the lifetime distributions of the components in the system based on the lifetimes of systems with the same structure. We develop a general framework for inference on the scale parameter of the component lifetime distribution. Specifically, the method of moments estimator (MME) and the maximum likelihood estimator (MLE) are derived for the scale parameter, and the conditions for the existence of the MLE are also discussed. The asymptotic confidence intervals for the scale parameter are also developed based on the MME and the MLE. General simulation procedures for the system lifetime under this model are described. Finally, some examples of two‐ and three‐component systems are presented to illustrate all the inferential procedures developed here. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

A queuing model for due date control in a multiserver repair shop

This paper deals with a repair shop with multiple parallel servers, which has to carry out planned overhauls. Each overhaul consists of a large number of maintenance jobs. The overhaul process is interrupted by randomly arriving emergency jobs. To control the delivery performance of the overhauls, knowledge about the overhaul makespan distribution should be available. Using a 2‐dimensional Markov model, we derive the first and second moment of the overhaul makespan analytically for the case that the repair times of all overhaul jobs are identically and exponentially distributed. For the case of nonidentical repair time distributions, an approximation is presented. Simulation shows that the makespan distribution fitted on these moments gives an excellent approximation. © John Wiley & Sons, Inc. Naval Research Logistics 48: 281–282, 2001     

Reliability of a single unit with k spares in case of the hyper-exponential and the erlang failure distribution

In this paper formulas are derived for the reliability of a single unit to which identical spares in standby are allocated, with all of these units having a hyper-exponential or Erlang distributed lifetime. Two advantages are obtained by using these distributions. First, the general procedure for calculating the effect of redundancy is applicable, in contrast with most of the common life distributions, such as Weibull. Moreover, both distributions are suitable for matching to observed curves and practical data by varying the values of the parameters, covering together most of the cases of practical interest.     

Analysis on Stochastic Passage Characteristics for Gun Barrel in Shooting Domain

Aiming at some weapon systems with shooting domain,the stochastic passage characteristics of the barrel were studied.On the basis of the exact definition of the stochastic passage characteristics,its opportunity-awaiting time,residence time and stochastic passage period were given by using the transition probability matrix,and they all obeyed the geometry distributions.Their means and variances were also derived,and the relations between the time indexes and the structure and parameters of weapon control system were established.Finally,the creditability of the conclusions was verified by the test data of weapon system in proving ground.     

一类具有脉冲效应的害虫综合管理模型的分析

基于害虫综合管理（IPM）策略,研究一类具有脉冲效应和非线性发生率的害虫染病的生态一流行病模型,分别在不同的固定时刻喷洒农药、释放染病害虫及天敌。利用Floquet乘子理论、脉冲微分比较定理,证明了易感类害虫灭绝周期解的全局渐近稳定性,给出了系统持续生存的充分条件。