十硬币集中四坏硬币的最优测试方法

在前人研究成果的基础上,给出用无砝码天平从10个硬币中搜索4枚坏硬币的最优搜索方法.     

搜索四个坏硬币的最优化方法

给出了用天平从ｎ个硬币的集合中搜索出４个坏硬币的最少测试次数的一个估计。     

一装置搜索四个坏硬币的分组测试过程

从n个硬币的集合中搜索d(d≥2)个坏硬币是一个相当困难且至今尚未完全解决的问题,本文研究了d=4的一装置分组测试模型,令tk为用测试（搜索）过程t经k次测试所能鉴别的最大硬币数,nk=maxtk,我们给出了一个相当好 的测试过程使tk/nk=0.85。     

R台装置搜索两个坏硬币的一个最优过程

通过对测试集的巧妙选取,给出了用ｒ台装置搜索两个坏硬币的本性理想模型Ｂｒｅ的一个最优测试过程。     

巧分硬币

贝卡有3个杯子和4枚硬币,老叔让贝卡把硬币全放进杯子里,还要保证每个杯子里的硬币的个数是奇数,到底应该怎样放呢？     

硬币探测仪的数字破绽

这几天小镇上发生了一件热门事儿,人们都在讨论一件神秘的机器——硬币探测仪.这是一家外来公司推出的新产品,宣传语很是让人动心: 你可曾掉落过零碎的硬币?你可知道你家中的角落、道路的两侧、树林的杂草中隐藏着多少被遗忘的硬币?这些无主硬币正是一条发财致富的好道路!我们最新型的硬币探测仪能够自动地寻找并收集这些硬币,让你坐在家中就能轻松发财!     

溶解的硬币

我有一枚硬币,还有一块魔法手绢。     

“硬币”滚动随谈

两枚同样大小的硬币,其中一个固定,另一个沿其周围滚动,滚动时,两枚硬币始终保持有一点接触,则滚动硬币再回到原来位置时,它自转的周数为( ).     

由硬币自转几周引发的思考

一、实验明辨是非题目有两个大小相同的硬币,其中一个硬币固定不动,另一个硬币在其外侧相切滚动一周,且不发生滑动,则这个滚动的硬币自转几周? (江西省2003年中考样卷试题) 很多同学首次解答这道题时,都认为这个     

关于两个伪硬币问题的一些新结果

下面的问题被称为n个外观不可区分硬币的分组测试问题,每个硬币可以是伪硬币或是标准硬币.本文所涉及的问题是:已知一个由n个硬币组成的集合中有两个伪(较重的)硬币,用一台天平以最小的称重次数,从这n个硬币组成的集合中探测出两个伪(较重的)硬币. 我们构造了找出两个伪(较重的)硬币的两个算法,并且这两个算法是最优的.     

A Simple Inspection Scheme for Two Types of Defect

The paper examines a problem in quality inspection for two independent defects, A and B. For defect A, process control is at least as important as product screening. Low-cost, rapid sequential inspection takes place for a run of k consecutive type-A defectives. When this occurs, the production process is halted and, if necessary, adjusted, and the run of k defectives is discarded. The entire pre-run sequence is retained, forming the production run. No type-B defectives are permitted; testing for this type of defect is expensive, so detection is by Dorfman screening of the production run. Features of interest are the choice of k in relation to the average length of a production run and the outgoing proportion defective, the average cost per production run of testing for attribute B, and the average number of items finally accepted per production run.     

An efficient randomized group testing procedure to determine the number of defectives

In many fault detection problems, we want to detect or identify defective items in a sample set by using the minimum number of tests. Group testing is for the scenario where each test is on a subset of items, and tells whether the subset contains at least one defective item or not. In this paper, we present an efficient randomized group testing procedure that determines the exact number of defectives in a sample set with high success probability.     

Group testing with two defectives

Recently the problem of determining the minimax number of group tests for finding two defectives separately contained in two disjoint sets has been completely solved. However, the closely related problem of determining the minimax number of groups tests for finding two defectives contained in one set remains open. This is a surprisingly difficult combinatorial problem with very little known. In this paper we give a partial solution to this problem.     

Optimal tool replacement for processes with low fraction defective

Tool wear is a frequent and natural part in many machining processes and is a systematic assignable cause. The fraction of defectives would rise as the tool deteriorates. When the fraction defective reaches a certain level, the tool must be replaced. To minimize the defective parts and the overall tool costs, the optimal tool replacement time needs to be determined. Process capability indices (PCIs) have been effectively used in the manufacturing industry to measure the fraction of defectives. Conventional methods of capability measurement become inaccurate since the process data is contaminated by the assignable cause variation. In order to determine the optimal tool replacement time to maintain maximum product quality, conventional capability calculation must be modified. Considering process capability changes dynamically, an estimator of C_pmk is investigated. We obtain an exact form of the sampling distribution in the presence of a systematic assignable cause. This study provides an effective management policy for optimal tool replacement under low fraction of defectives. To illustrate the application of this procedure, a case study involving the tool wear problem is presented.     

Dominated error correcting codes with distance two

We study the hamiltonicity of certain graphs obtained from the hypercube as a means of producing a binary code of distance two and length n, whose codewords are ordered so that for each two consecutive codewords, one dominates the other. One vector dominates the other, if and only if, in all the positions where one of them has a zero, the other has a zero too. These dominated codes have applications in group testing for consecutive defectives. We also determine when the vectors can be ordered so that every two consecutive vectors have the domination property, and are at distance two; this is a natural generalization of Gray codes. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 294–302, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10012     

Comparison of quality control plans using the average proportion of defectives in the uninspected part

Two quality control plans with zero admissible defects are compared, using additional information for the second plan. The second plan ensures fewer defectives in the uninspected batch.Translated from Statisticheskie Metody, pp. 169–182, 1982.     

The Optimal Scheme of Defective Coin Problem for Model P

ＴｈｅＯｐｔｉｍａｌＳｃｈｅｍｅｏｆＤｅｆｅｃｔｉｖｅＣｏｉｎＰｒｏｂｌｅｍｆｏｒＭｏｄｅｌＰ￥ＬｉｕＷｅｎａｎ；ＤｉｎｇＣｈｅｎｇｊｉｅ（Ｘｉｎｘｉａｎｇ，ＨｅｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｒｅｃｅｎｔｌｙｔｈｅｐｒｏｂ...     

Variables sampling plans with PPM fraction of defectives and process loss consideration

Acceptance sampling plans provide the vendor and the buyer decision rules for lot sentencing to meet their product quality needs. A problem the quality practitioners have to deal with is the determination of the critical acceptance values and inspection sample sizes that provide the desired levels of protection to both vendors and buyers. As today's modern quality improvement philosophy, reduction of variation from the target value is the guiding principle as well as reducing the fraction of defectives. The C_pm index adopts the concept of product loss, which distinguishes the product quality by setting increased penalty to products deviating from the target. In this paper, a variables sampling plan based on C_pm index is proposed to handle processes requiring very low parts per million (PPM) fraction of defectives with process loss consideration. We develop an effective method for obtaining the required sample sizes n and the critical acceptance value C₀ by solving simultaneously two nonlinear equations. Based on the designed sampling plan, the practitioners can determine the number of production items to be sampled for inspection and the corresponding critical acceptance value for lot sentencing.     

A dynamic programming approach for batch sizing in a multi-stage production process with random yields

This paper proposes a dynamic programming approach to modeling and determining batch sizes in a single period, multi-stage production process with random yields for each stage. To improve the computational performance of the proposed approach, a statistical bound is developed. A key decision incorporated into the model is whether to continue onto the next stage of processing or to scrap the entire current batch of product. This decision is based on the expected total profit from the remaining items for processing following the removal of all defectives. The decisions involving the locations of test stations after stages are also incorporated into the modeling approach.