Algorithms for the design of finite-capacity service units

Finite-capacity queues arise naturally in many practical situations, notably in communications and manufacturing engineering. In this article, the matrix formalism of probability distributions of phase type is used to develop fast algorithms to compute various steady-state distributions for the finite-capacity PH/PH/1 queue. This algorithm is an important ingredient in solving nontraditional but significant design problems. Some of these are described as illustrative examples.     

Log‐concave and concave distributions in reliability

Nonparametric classes of life distributions are usually based on the pattern of aging in some sense. The common parametric families of life distributions also feature monotone aging. In this paper we consider the class of log‐concave distributions and the subclass of concave distributions. The work is motivated by the fact that most of the common parametric models of life distributions (including Weibull, Gamma, log‐normal, Pareto, and Gompertz distributions) are log‐concave, while the remaining life of maintained and old units tend to have a concave distribution. The classes of concave and log‐concave distributions do not feature monotone aging. Nevertheless, these two classes are shown to have several interesting and useful properties. We examine the closure of these classes under a number of reliability operations, and provide sharp reliability bounds for nonmaintained and maintained units having life distribution belonging to these classes. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 419–433, 1999     

Bounds on the availability function

This paper gives bounds on the availability function for an alternating renewal process with exponential failure and general repair times. A bound on the error is also given. Several of the bounds with greatest practical consequence are worked out and illustrated. Repair distributions for which a lower bound on availability is easily computed are gamma (integer shape parameter), log normal, and Weibull. Finally, some simulation results for log normal repair versus gamma repair are given.     

Annealing adaptive search,cross‐entropy,and stochastic approximation in global optimization

The Annealing Adaptive Search (AAS) algorithm for global optimization searches the solution space by sampling from a sequence of Boltzmann distributions. For a class of optimization problems, it has been shown that the complexity of AAS increases at most linearly in the problem dimension. However, despite its desirable property, sampling from a Boltzmann distribution at each iteration of the algorithm remains a practical challenge. Prior work to address this issue has focused on embedding Markov chain‐based sampling techniques within the AAS framework. In this article, based on ideas from the recent Cross‐Entropy method and Model Reference Adaptive Search, we propose an algorithm, called Model‐based Annealing Random Search (MARS), that complements prior work by sampling solutions from a sequence of surrogate distributions that iteratively approximate the target Boltzmann distributions. We establish a novel connection between MARS and the well‐known Stochastic Approximation method. By exploiting this connection, we prove the global convergence of MARS and characterize its asymptotic convergence rate behavior. Our empirical results indicate promising performance of the algorithm in comparison with some of the existing methods. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

A markov chain version of the secretary problem

This paper deals with the Secretary Problem where n secretaries are interviewed sequentially and the best k must be hired. The values of the secretaries are observed as they are interviewed, but beforehand only the distributions of these values are known. Furthermore, the distributions of two successive secretaries' values are governed by a Markov chain. Optimal hiring policies for finite n and limiting optimal policies as k and n approach infinity are obtained.     

Some test functions for the parameters of the weibull distributions

Test functions, based on various types of censored and noncensored data, for testing several hypotheses about the location, the scale, and the shape parameters of the Weibull distributions are proposed. The exact sampling distributions of these test statistics are derived and their properties in special cases are discussed. A numerical example is considered to illustrate the application of the test functions. The results of this paper possess good possibility of wide application in view of the fact that hosts of real data arising from diverse fields of human endeavor are adequately described by the Weibull distribution.     

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     

The error in the normal approximation to the multinomial with an increasing number of classes

In an earlier paper, it was shown that under certain conditions, if the number of classes in a multinomial distribution increases as the number of trials increases, the probabilities assigned to arbitrary regions by the multinomial distribution are close to the probabilities assigned by the distribution of slightly rounded-off normal random variables. A different method of studying the approximation of the multinomial distribution by a normal distribution is to use the multivariate Berry-Esseen bound. In this paper, these two methods are compared, particularly with respect to the class of multinomial distributions for which the bounds on the error remain useful.     

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     

Shock models with phase type survival and shock resistance

New closure theorems for shock models in reliability theory are presented. If the number of shocks to failure and the times between the arrivals of shocks have probability distributions of phase type, then so has the time to failure. PH-distributions are highly versatile and may be used to model many qualitative features of practical interest. They are also well-suited for algorithmic implementation. The computational aspects of our results are discussed in some detail.     

Interrelationships between performance measures for the machine-repairman problem

The machine-repairman problem with heterogeneous machines and multiple repairmen is considered. It is assumed that machine up times and repair times have general distributions, and a work-conserving service discipline is employed. Under these general assumptions, steady-state relationships between performance measures are examined for the individual machines. Also, various performance measures are defined for the aggregate system and interrelationships between these measures are established.     

地铁站台防排烟设计方案探讨

以双层岛式站台为研究对象,建立了物理模型,采用FDS模拟软件对地铁站台进行了火灾模拟。重点研究了岛式站台在现阶段机械通风条件下,火灾发生在站台一端的几种通风模式,掌握在机械排烟情况下烟气的扩散形式,并对多种烟气控制方式进行了分析比较,在此基础上分别给出了相对最优化的结果。     

On the use of standard tables to obtain Dodge-Romig LTPD sampling inspection plans

Procedures are described which yield single and double sample Dodge-Romig [1] lot tolerance percent defective (LTPD) rectifying inspection plans. For the determination of such plans only a desk calculator and standard tables of the discrete probability distributions are required. Some advantages gained by using these procedures rather than the Dodge-Romig table include: (a) The Consumer's Risk is not limited to 0.10. (b) More choices of LTPD are available. (c) Smaller average total inspection is achieved by using a plan designed for specific “process average” and lot size rather than a compromise plan designed to cover intervals on these two parameters.     

Properties of a source location estimator in the plane

The statistical properties of an estimator of a source location were established by simulation for the case in which the source location is estimated—using transformation of lines to points—from the angles in which different observers see the source, and both the assumed locations of the observer points and the observed angles are subject to error. It was found that for normal error distributions the estimator is unbiased, and the resulting estimates are approximately normally distributed with a small standard deviation. An easy-to-use and reliable forecasting formula was suggested to forecast the parameters of the distributions of the estimates for different observer-source relationships. © 1993 John Wiley & Sons, Inc.     

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.     

Linear search with bounded resources

A point is placed at random on the real line according to some known distribution F, and a search is made for this point, beginning at some starting points s on the line, and moving along the line according to some function x(t). The objective of this article is to maximize the probability of finding the point while traveling at most d units. Characterizations of simple optimal searches are found for arbitrary distributions, for continuous distributions with continuous density everywhere (e.g., normal, Cauchy, triangular), and for continuous distributions with density which is continuous on its support (e.g., exponential, uniform). These optimal searches are also shown to be optimal for maximization of the expected number of points found if the points are placed on the line independently from a known distribution F.     

论以实战为中心的法律文书课程教学模式

法律文书是公安部门执法工作的文字载体,是执法规范化的重要体现。法律文书课程由于自身的实践性、操作性、判断标准独特性等方面的特点使得传统的讲授式教学模式难以取得良好的教学效果。法律文书课程应建立以实战为中心的教学模式,可通过视觉实战、听觉实战、制作实战、应用实战及实战化考核等不同的方式进行。实战模式是法律文书课程教学水平提高的最有力措施,信息资源建设和物资支撑在该模式中具有重要地位,而课程间的横向联系则是建立在实战化基础上的法律文书课程教学模式的发展方向。     

爆炸复合接头剪切强度测试方法研究

参照正交各向异性层压复合板层间剪切强度的测试方法,提出了用于测试爆炸复合接头复合界面剪切强度的3种方法;并建立三维有限元模型,分别对3种测试方法进行模拟;最后分别对3种方法进行了测试试验.结果表明,3种试验方法均能有效测试爆炸复合接头的剪切强度,其中对称试件双切口拉伸法最适合实际应用.     

Some recent findings in bayesian attribute single and double sampling

This article deals with several items, including theoretical and applied results. Specific topics include (1) a discrete, economically based, attributes acceptance sampling model and its adaptations, (2) relevant costs, (3) relevant prior distributions, (4) comparison of single- and double-sampling results, and (5) reasons for marginal implementation success following excellent implementation efforts. The basic model used is one developed by Guthrie and Johns; adaptations include provisions for fixed costs as well as modifications to permit double sampling. Optimization is exact, rather than approximate. Costs incorporated into the model are for sampling inspection, lot acceptance, and lot rejection. For each of these three categories a fixed cost is included as well as two variable costs, one for each item and the other for each defective item. Discrete prior distributions for the number of defectives in a lot are used exclusively. These include the mixed binomial and Polya distributions. Single- and double-sampling results are compared. Double sampling regularly performs at only slightly lower cost per lot than single sampling. Also, some cost and prior distribution sensitivity results are presented. Comments are provided regarding actual implementation experiences in industry. Practical deficiencies with the Bayesian approach are described, and a recommendation for future research is offered.     

On a shape estimator of weiss

The problem of estimating the shape-parameter of a distribution is considered. We introduce a class of estimators the distributions of which are independent of location and scale. An estimator proposed by Weiss [1] is a member of this class. We find the asymptotically most efficient estimator in this class which differs from that proposed by Weiss.