超精密铣削的三维微加工工艺

本研究旨在对用于获取有雕刻表面金属工件的超精密微加工工艺进行探讨。研究中使用的是车床型的超精密铣床,由分辨率为1nm的X和Z向运动工作台及分辨率为0.0001度的可定位的C轴组成。作为一种铣削工具,一种改进型的由一颗水晶钻构成的“仿球尖铣刀”被放置在X轴的高速气浮轴承之上。这样一来,X轴和C轴的协调运动就可产生三维铣削的效果。为提高表面粗糙度,通过模拟我们研究的刀具边沿和工件表面的接触情况,结果发现,刀具低速进给时切削比较有效。作为三维微加工工艺的一个例子,运用数字仪提供的扫描数据在一个直径为3mm的铜表面上制作一个传统的NOH面罩。经证明,超精密铣床有潜力加工出表面粗糙度为69nm(P—V值)的工件。     

Exact first and second order moments of order statistics from the truncated exponential distribution

Exact expressions for the first and second order moments of order statistics from the truncated exponential distribution, when the proportion 1–P of truncation is known in advance, are presented in this paper. Tables of expected values and variances-covariances are given for P = 0.5 (0.1) 0.9 and n = 1 (1) 10.     

A proportional defense model

This paper considers the problem of defending a set of point targets of differing values. The defense is proportional in that it forces the offense to pay a price, in terms of reentry vehicles expended, that is proportional to the value of the target. The objective of the defense is to balance its resources so that no matter what attack is launched, the offense will have to pay a price greater than or equal to some fixed value for every unit of damage inflicted. The analysis determines which targets should be defended and determines the optimal firing doctrine for interceptors at defended targets. A numerical example is included showing the relationship between the total target damage and the size of the interceptor force for different values of p, the interceptor single shot kill probability. Some generalizations are discussed.     

Scheduling jobs,with exponentially distributed processing times,on two machines of a flow shop

This paper treats the problem of sequencing n jobs on two machines in a “flow shop.” (That is, each job in the shop is required to flow through the same sequence of the machines.) The processing time of a given job on a given machine is assumed to be distributed exponentially, with a known mean. The objective is to minimize the expected job completion time. This paper proves an optimal ordering rule, previously conjectured by Talwar [10]. A formula is also derived through Markov Chain analysis, which evaluates the expected job completion time for any given sequence of the jobs. In addition, the performance of a heuristic rule is discussed in the light of the optimal solution.     

Numerical treatment of a class of semi-infinite programming problems

Many optimization problems occur in both theory and practice when one has to optimize an objective function while an infinite number of constraints must be satisfied. The aim of this paper in to describe methods of handling such problems numerically in an effective manner. We also indicate a number of applications.     

Sequencing many jobs on a multi-purpose facility

Suppose a given set of jobs has to be processed on a multi-purpose facility which has various settings or states. There is a choice of states in which to process a job and the cost of processing depends on the state. In addition, there is also a sequence-dependent changeover cost between states. The problem is then to schedule the jobs, and pick an optimum setting for each job, so as to minimize the overall operating costs. A dynamic programming model is developed for obtaining an optimal solution to the problem. The model is then extended using the method of successive approximations with a view to handling large-dimensioned problems. This extension yields good (but not necessarily optimal) solutions at a significant computational saving over the direct dynamic programming approach.     

Optimum quantiles for the linear estimation of the parameters of the extreme value distribution in complete and censored samples

The present study is concerned with the determination of a few observations from a sufficiently large complete or censored sample from the extreme value distribution with location and scale parameters μ and σ, respectively, such that the asymptotically best linear unbiased estimators (ABLUE) of the parameters in Ref. [24] yield high efficiencies among other choices of the same number of observations. (All efficiencies considered are relative to the Cramér-Rao lower bounds for regular unbiased estimators.) The study is on the asymptotic theory and under Type II censoring scheme. For the estimation of μ when σ is known, it has been proved that there exists a unique optimum spacing whether the sample is complete, right censored, left censored, or doubly censored. Several tables are prepared to aid in the numerical computation of the estimates as well as to furnish their efficiencies. For the estimation of σ when μ is known, it has been observed that there does not exist a unique optimum spacing. Accordingly we have obtained a spacing based on a complete sample which yields high efficiency. A similar table as above is prepared. When both μ and σ are unknown, we have considered four different spacings based on a complete sample and chosen the one yielding highest efficiency. A table of the efficiencies is also prepared. Finally we apply the above results for the estimation of the scale and/or shape parameters of the Weibull distribution.