自动化车床最优刀具检测更换模型

本文通过对自动化车床 1 0 0次刀具故障的记录进行数理统计分析 ,研究了自动化车床连续加工单一零件时刀具的检测及更换模型 .首先利用概率大样本场合的 D检验方法证明了刀具的故障发生规律服从正态分布 [1] ,继而求出系统工序的寿命分布函数 [2 ] ,列出以合格零件单位期望损失为目标 ,关于检测间隔和刀具定期更换间隔为变量的多目标函数方程 ,最后利用计算机进行列举比较求解 ,从而得出取得最大经济效益的系统工序的最优检测间隔以及最优刀具更换策略 .由于刀具的故障发生服从正态分布 ,我们对模型进行了改进 ,采取有规律的不等间隔的检查方式 ,结果取得了相对于等检查间隔的更优解 .本文利用算法较好地解决了问题 ,得到了问题的优化解 .对于问题 1 ,解得换刀间隔和检查间隔分别为369和 1 8,单位合格零件损失 4 .61 5元 ,采用不等间隔的损失为 4 .4 0 5元 ;对于问题 2 ,由于情况复杂 ,解得换刀间隔和检查间隔分别为 30 6和 2 8,单位合格零件损失 9.2 68元 ,采用不等间隔的损失为 9.0 4 7元 ,从而验证了本文提出的不等间隔检查方式的更优性     

刀具问题的仿真及灵敏度分析

本文通过计算机模拟仿真 ,搜索到了 CMCM-99A题中换刀间隔与检查间隔的近似最优解及单位正品最小费用 ,并对 p1(好刀生产正品的概率 ) ,p2 (坏刀生产正品的概率 ) ,k,f,d进行了灵敏度分析 ,得出 u(换刀间隔 )是最重要的优化参数的结论     

关于“截断切割”的最优设计

针对 1 997年全国大学生数学建模竟赛 B题 ,对于换刀费用 e=0的情况 ,本文设计了一种异常简捷的切割厚度排序法来寻找最优切割方案 ,同时在数学上给出了严格的证明 .对于换刀费用 e≠ 0的情况 ,以 e=0时得到的最优切割方案为基础 ,先通过简单的调整原则寻找出限定不同换刀次数时各自的最优切割方案 ,再通过费用比较便可简捷地得到随 e值的大小而变化的最优切割方案 .本文构造的模型在求解时无须用计算机编程 ,只用手算即可简捷地得到答案     

例谈数学期望在效益、利润等经济问题中的应用

设离散型随机变量 ξ的概率分布为Ｐ(ξ =ｘｉ) =ｐｉ,ｉ =1 ,2 ,3,… ,则Ｅξ =ｘ1ｐ2+ｘ2 ｐ2 +ｘ3ｐ3+…叫做随机变量 ξ的数学期望 (简称期望 ) .数学期望是随机变量的一个重要数学特征 ,它代表了随机变量总体取值的平均水平 .下面举例谈谈数学期望在效益、利润等经济问题中的应用 .例 1　某人用 1 0万元进行为期一年的投资 ,有两种投资方案 :一是购买股票 ,二是存入银行获取利息 .买股票的收益取决于经济形势 ,若形势好可获利 4万元 ,形势中等可获利 1万元 ,形势不好要损失 2万元 .如果存入银行 ,假设年利率为 8% ,可得利息 80 0 0元 .…     

车床管理优化模型

本文讨论了自动化车床连续加工零件工序定期检查和刀具更换的最优策略 .针对问题一 ,应用管理成本理论结合概率统计方法 ,建立定期检查调节零件的平均管理成本的优化设计模型 ,通过计算机求解、模拟 ,得到工序设计效益最好的检查间隔和刀具更换间隔 .针对问题二 ,在问题一的基础上 ,利用概率知识调整了检查间隔中的不合格品数带来的平均损失 ,同时加上了因工序正常而误认为有故障停机产生的平均损失 ,然后建立起目标函数 ,得到工序设计效益最好的检查间隔和刀具更换策略 .对于工序故障采用自动检查装置 ,设计出了自动检查调节系统 ,并给出了算法框图 ,有效地避免工序正常而误认为有故障停机损失 ,提高工序效益     

自动化车床最优刀具检测模型研究

针对自动化车床工序最优检测和刀具更换问题进行了探讨.将定期检测和将刀具更换作用于同一工序流程,在只考虑刀具故障条件下,通过概率论和更新过程理论建立了以单位时间内期望费用为目标函数的数学模型,以检测间隔和刀具更换间隔为策略,确定最优的策略使得目标函数达到最小,并求出了经长期运行单位时间内期望费用的明显表达式.最后还对结果进行了讨论.     

奇数阶边值问题正解的存在性与多重性

利用锥拉伸锥压缩不动点定理,证明了在一定条件下,下列非线性奇数阶方程(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,u(0)=u′(τ)=u″(1)=0u(2j+1)(0)=u(2j+1)(1)=0,j=1,2,…,q-1.单个和多个正解的存在性,其中λ>0,12<τ<1,q∈N.得到了λ的区间Λ,对一切λ∈Λ,该问题至少有一个正解,同样也得到了该问题至少有两个正解λ相应的区间.     

关于C*-代数Mn(A)上矩阵迹的一些不等式

C*-代数Mn(A)上矩阵迹是一个正线性映射τ∶Mn(A)→A且满足τ(u*au)=τ(a)(a∈Mn(A),u∈U(Mn(A)))及τ(a2)≤(τ(a))2(a≥0).论文讨论这种矩阵迹的一些性质,给出了若干不等式性质,并且证明:对Mn(A)中的H erm itian元a,b,当m=2k(k∈N)时,τ((ab)m)≤τ(ambm)成立.同时还证明了当m=2k(k∈N)时,对Mn(A)中任一元a,不等式τ(am(a*)m)≤τ((aa*)m)成立.     

此题的结论应予修正

有这样一道题:在△.4刀C中,1匕tg.4+1马tgC== 21gtgB,求汀一2‘证:号成”此题在给学生练习时,一般都能证出要‘ J.然而,我们同时有一同学在求丑的范国时得到了异于题中的刀的范围,他的解答咬。下:o咬刀《忍了 j解:依题意tg.4、tgB、tgC>0,即0<才、几c<号.又由题设条件知to.4tgC=tgZB,z一tg乞刀=1一tg‘峨tgC即‘1一tg乞B=t叮.理+t.艺C_tg通+tgCtg(_4+C)一tg刀》坦重红丝够二 一tg刀:.. fg,B成3,又坛刀)仍,,...:.。<刀‘导·Zt仁刀一tg刀一2一心了毛tg刀书了不o相似文献   

Richard模型最佳控制的存在性及其费用的函数结构

§0.导言.Richard 提出的是一个以一维齐次扩散过程为状态模型的最佳控制问题——有折扣费用的无限水平线问题,具体描述如下:设 W_t,t≥0为概率空间(Q,(?),p)上的一维 Wiener 过程,(?)=σ(W_(?),(?)≤t).0=τ_0≤τ_1≤…为一列上升的(?)停时.(?)表τ_n 前σ-域.对每个τi     

A time delay model for the diffusion of a new technology

In this paper, we propose a mathematical model with time delay to describe the process of diffusion of a new technology. This model is suitable for modeling diffusion processes of all those technologies that require great initial investments and public subsidies, such as technologies used for producing renewable energy. We consider external factors, such as the government policy and the production costs, that influence the decision of adoption of the new technology. We also consider the internal influence from adopters. The adoption process is described by a delay differential equation. The time delay represents the evaluation stage at which the potential consumers decide whether to adopt the new technology or not. A qualitative analysis is carried out in order to assess the stability of the equilibrium for certain parameters and to find the final level of adopters.     

TOWARD CONTROLLING NONPOINT SOURCE POLLUTION OF GROUNDWATER: A HIERARCHICAL POLICY FORMULATION GAME

An integrative approach to formulating agricultural policy instrument levels is suggested for controlling groundwater quality deterioration from agricultural chemical-use, while reconciling the conflicting goals of primary interest groups in the farm policy process. The paper develops a Stackelberg game-theoretic model of public policy formation that simultaneously determines endogenous price supports and nitrogen-use quota, as well as the optimal permissible water contamination. The analysis distinguishes between the private and social opportunity costs of producing agricultural crops and using groundwater as a repository for nitrate leachate from agricultural sources. It is recognized that the social benefit of using nitrogen in agriculture is less than the private benefit to producers. Private and social benefits, as well as optimal production and pollution solutions, will vary as the relative weights which policymakers attach to different social constituents change. The method developed in this paper may be applicable to any policy process in which policymakers exercise indirect influence over industrial production decisions through economic instruments.     

Timing order fulfillment of capital goods under a constrained capacity

This paper studies the order-fulfillment process of a supplier producing multiple customized capital goods. The times when orders are confirmed by customers are random. The supplier can only work on one product at any time due to capacity constraints. The supplier must determine the optimal time to start the process for each order so that the total expected cost of having the goods ready before or after their orders are confirmed is minimized. We formulate this problem as a discrete time Markov decision process. The optimal policy is complex in general. It has a threshold-type structure and can be fully characterized only for some special cases. Based on our formulation, we compute the optimal policy and quantify the value of jointly managing the order fulfillment processes of multiple orders and the value of taking into account demand arrival time uncertainty.     

A new risk model based on policy entrance process and its weak convergence properties

In this paper, we construct a new risk model based on the policy entrance process. The model is concerned with n kinds of independent policies, and each policy is allowed to claim more than once before it expires. As each kind of policy is issued according to a non‐homogeneous Poisson process, the long run behaviour of the new risk process is investigated. When the tail of the claim size distribution is regularly varying, the standardized risk process is proved to converge to a stable law. When each kind of policy is issued according to a homogeneous Poisson process, we also give a diffusion approximation of the new risk process. Copyright © 2007 John Wiley & Sons, Ltd.     

Optimal maintenance strategy under renewable warranty with repair time threshold

In this paper, we consider a periodic preventive maintenance model, from the manufacturer's perspective, which can be implemented to reduce the maintenance cost of a repairable product during a given warranty period. The product is assumed to deteriorate with age and the warranty policy we adopt in this paper takes into account the two factors of failure time and repair time of the product when the product failure occurs. Under the proposed two-factor warranty, a repair time threshold is pre-determined and if the repair takes more time than that of the threshold, the failed product is replaced with a renewed warranty policy. Otherwise, the product is only minimally repaired to return to the operating state. During such a renewable warranty period, preventive maintenance is conducted to reduce the rate of degradation periodically while the product is in operation. By assuming certain cost structures, we formulate the expected warranty cost during the warranty period from the manufacturer's perspective when a periodic preventive maintenance strategy is adapted. Although more frequent preventive maintenance increases the warranty cost, the chance of product failures would be reduced. The main aim of this paper is to accomplish the optimal trade-off between the warranty cost and the preventive maintenance period by determining the optimal preventive maintenance period that minimizes the total expected warranty cost during the warranty period. Assuming the power law process for the product failures, we illustrate our proposed maintenance model numerically and study the impact of relevant parameters on the optimal preventive maintenance policy.     

An optimal replacement policy for a multistate degenerative simple system

In this paper, a degenerative simple system (i.e. a degenerative one-component system with one repairman) with k + 1 states, including k failure states and one working state, is studied. Assume that the system after repair is not “as good as new”, and the degeneration of the system is stochastic. Under these assumptions, we consider a new replacement policy T based on the system age. Our problem is to determine an optimal replacement policy T^∗ such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression of the average cost rate is derived, the corresponding optimal replacement policy can be determined, the explicit expression of the minimum of the average cost rate can be found and under some mild conditions the existence and uniqueness of the optimal policy T^∗ can be proved, too. Further, we can show that the repair model for the multistate system in this paper forms a general monotone process repair model which includes the geometric process repair model as a special case. We can also show that the repair model in the paper is equivalent to a geometric process repair model for a two-state degenerative simple system in the sense that they have the same average cost rate and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results of this model.     

Stackelberg strategy solution for optimal software release policies

We present a software release policy which is based on the Stackelberg strategy solution concept. The model formulated assumes the existence of two type of producers in the market, the leader and follower. The resulting release policy combines both cost factors and a loss of opportunity factor which is the result of competition between the rival producers. We define a Stackelberg strategy pair in the context of our model and, through a series of preliminary results, show that an optimal strategy pair exists. We also present a numerical example which utilizes a software reliability growth model based on the nonhomogeneous Poisson process. Finally, we explore the relative leadership property of the optimal strategies.This work was supported in part by a FOAS Research Grant provided by RMIT. The author would like to thank the referees for constructive suggestions which helped to improve a previous version of this paper.     

Repeated Downsian electoral competition

We analyze an infinitely repeated version of the Downsian model of elections. The folk theorem suggests that a wide range of policy paths can be supported by subgame perfect equilibria when parties and voters are sufficiently patient. We go beyond this result by imposing several suitable refinements and by giving separate weak conditions on the patience of voters and the patience of parties under which every policy path can be supported. On the other hand, we show that only majority undominated policy paths can be supported in equilibrium for arbitrarily low voter discount factors: if the core is empty, the generic case in multiple dimensions, then voter impatience leads us back to the problem of non-existence of equilibrium. We extend this result to give conditions under which core equivalence holds for a non-trivial range of voter and party discount factors, providing a game-theoretic version of the Median Voter Theorem in a model of repeated Downsian elections. J. Duggan was supported by the National Science Foundation, grant number 0213738, is gratefully acknowledged.     

On the modelling of finite growth considering the mechanics of cell division

Mitotic cells grow in volume and divide themselves into two identical cells producing at macroscopic scale a volume expansion in living bodies. Due to inhomogeneous distributions of the growth factors, growth occurs at different rates and directions. Focusing into the direction of growth, some living bodies alter their growing behaviour influenced by mechanical loads. If loads appear during the growth process, cell division is reorientated following the main direction of the elastic deformations. Therefore, new cells will be created in this direction while relaxing the stress state of the body at the same time. In this work, we present a modelling approach for growing bodies which change their growth direction depending on mechanical loads. The model is implemented into a finite element framework to be an useful tool for predicting morphological changes in growing bodies. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Joint Determination of Production Cycle and Inspection Intervals in a Deteriorating Production System

This paper considers production-maintenance policy for the deteriorating production system which can go ‘out of control’ while producing items. Once out of control, the production process produces some proportion of defective items. The defective items are reworked at some cost before being shipped, or, if passed to the customer, incur much larger warranty cost. Thus, to operate this system economically, periodic inspection and restoration of the process are needed. A mathematical model representing the expected annual cost is developed to determine the production cycle and process inspection intervals jointly. A case of equally spaced inspection intervals is solved by using an approximation to the cost function.