考虑调整随机误差的设置调整问题研究

针对存在设置偏差的小批量离散制造过程,研究了每次调整成本固定且调整存在随机误差情形下的质量控制问题。在建立过程状态空间方程模型的基础上,通过贝叶斯方法估计过程的未知参数,利用动态规划的方法得到了边界形式的过程最优调整策略。通过算例验证了所提出调整策略的有效性,并利用仿真对本文提出的调整策略与其他调整策略进行了比较分析,结果表明,本文提出的方法能够更好地减少过程总体质量损失。     

基于非对称损失函数的参数设计

本文针对望目特性的正态指标,在非对称的二次质量损失函数下,讨论了参数设计的可行性, 证明田口方法的稳健性设计和灵敏度设计依然行之有效.定义了调整参数,求出了使质量损失最小的数值解,并给出了参数设计的具体步骤.     

基于非对称损失函数指数分布总体的参数设计

田口玄一的参数设计思想只是针对对称的损失函数所做,有一定的局限性.讨论了非对称的损失函数,定义了损失系数比,并在指标服从指数分布的情形下定义了调整参数,并指出了调整参数在参数设计中的特殊位置和重要特性,给出了参数设计的方法和步骤.     

基于截尾正态分布的最优过程均值的确定

过程均值的选择对生产率的提高以及产品质量改进非常重要,因为它直接影响到过程的缺陷率、材料费用、重加工费及产品性能偏离目标值对顾客造成的损失等.本文讨论了在不对称田口质量损失函数下截尾正态分布的最优过程均值的确定问题.通过灵敏度分析,研究了过程参数对过程均值选择的影响.     

右删失数据下非线性回归模型的经验似然推断

考虑随机右删失数据下非线性回归模型,提出了模型中未知参数的调整的经验对数似然比统计量.在一定的条件下,证明了.所提出的的统计量具有渐近χ~2分布,由此结果构造了兴趣参数的置信域.通过模拟研究,对经典的经验似然、调整的经验似然和非线性最小二乘方法在有限样本下进行了比较,并对氯离子浓度试验数据进行了分析.     

基于未知分布的均值和方差的稳健EWMA图

研究了当待监控质量特性所服从的分布类型和分布参数未知时的EWMA控制图的构建问题。通过仿真分析对几种分别用于监控过程均值和过程方差的EWMA控制图方法的运行长度进行比对,用以评价控制图的效率以及对未知分布的稳健性,根据效率评价的结果获得了适用于分布未知情况下的均值和方差的稳健EWMA控制图。最后分别提出了这两种均值和方差的稳健EWMA图的优化设计方法.     

基于追溯保费原理的最优再保险策略

追溯保费是一种依赖于保单期保险人实际损失的保费厘定计划,是对过去已经发生的损失进行承保的保险方式.本文将追溯保费应用于再保险模型中,当最优准则选为最小化风险调整值而风险资本用TVaR来度量时,得到的最优分保函数形式为停止损失再保险.进而,研究了最优停止损失再保险中最优自留额的求解算法.最后,假设损失服从指数分布、Pareto分布和Gamma分布等情形,利用数值举例的方法研究了税租乘数T和安全负荷系数ρ对最优自留额和最小风险调整值的影响.结果表明,当其他参数一定时, T增大,最优自留额增大而最小风险调整值减小;而其他参数一定时,最优自留额和最小风险调整值都会随着ρ的增大而增大.     

基于性能的直流电机系统未知推力波动的自适应补偿控制

针对一类直流电机系统,设计基于性能的未知推力波动的自适应补偿控制器.由于推力波动中含有非线性化的未知参数,因此无法利用常规的自适应方法,通过直接估计这些参数对其影响进行补偿.根据未知推力波动的结构特性,基于Lipshitz条件引入推力波动项的放大技术,设计其内部非线性化未知参数的自适应估计律,精确补偿其影响,从而避免了简单的把波动看作未知扰动所造成的系统性能的损失.有别于现有模型,在模型变换中并未忽略微小等效电感的影响,使得系统模型更具一般性.仿真结果表明该自适应控制器可有效补偿推力波动的影响,实现对指令信号的高精度快速跟踪且具有较强的抗干扰性和鲁棒性.     

基于收益及收益偏差平方和多期组合投资

本文在分析Markowitz组合投资的基础上,建立考虑交易费用的收益偏差平方和极小化和收益率极大化的动态资产的投资组合模型.通过调整多期投资组合各期的投资数量,保障投资者根据股票市场变化进行易于操作的、相对合理的投资调整策略,为投资者进行风险管理提供决策依据.最后通过释例进行了说明.     

需求变化的多阶段EOQ订购策略

多阶段库存管理是供应链研究的重要课题,其中独立需求的订购策略问题,现有文献一般设定计划期内各阶段需求且计划执行过程中需求不再变化,给出了相应的算法.本文选择EOQ模型作为基本订购策略,研究下面一类需求变化的多阶段订购策略问题：给定费用参数（物资单价、一次订货费用、单位库存保管费用）的情况下,在订购计划执行过程中,在阶段i（1＜i＜m）需要调整阶段m的需求,而其它阶段的需求不变,订购策略如何调整,使得库存总费用最低.     

Adaptive deadband control of a drifting process with unknown parameters

Adjusting a drifting process to minimize the expected sum of quadratic off-target and fixed adjustment costs is considered under unknown process parameters. A Bayesian approach based on sequential Monte Carlo methods is presented. The benefits of the resulting “deadband” adjustment policy are studied.     

基于非对称损失的过程均值设计研究

在损失非对称的情况下，使工序加工出的产品均值等于目标值，并不会使期望损失最小，优化过程均值，使其接近目标值，尤为重要。本研究了三种典型的非对称损失的过程均值设计问题，探讨了非对称比率与质量损失率之间的关系，提出了有效偏移的概念，给出了具体的调整措施，最后给出一个实例。     

Sequential Fixed-Width Confidence Interval for the Product of Two Means

For the product of two population means, the problem of constructing a fixed-width confidence interval with preassigned coverage probability is considered. It is shown that the optimal sample sizes which minimize the total sample size and at the same time guarantee a fixed-width confidence interval of desired coverage depend on the unknown parameters. In order to overcome this, a fully sequential procedure consisting of a sampling scheme and a stopping rule are proposed. It is then shown that the sequential confidence interval is asymptotically consistent and the stopping rule is asymptotically efficient, as the width goes to zero. Furthermore, a second order result for the difference between the expected stopping time and the (total) optimal fixed sample size is established. The theoretical results are supported by appropriate simulations.     

考虑机器能耗的绿色作业车间调度问题

针对传统作业车间调度,在保证交货期的前提下,以机器能耗最小为目标研究带有关机/重启策略的绿色车间调度问题。首先建立数学规划模型,然后在遗传算法的框架下,根据问题特点提出了一种局部调整的解码方式,在排产时进行工序的移动并确定其开始加工时刻。最后进行小规模算例运算,验证数学规划模型的有效性,再利用算例对基于局部调整解码和顺序解码的遗传算法进行对比测试,结果表明提出的局部调整解码可以在降低机器能耗的同时提高求解效率。     

基于效用比的多工序并联制造过程能力分析

多工序制造过程通常包含串联和并联两种结构,具有串并联混合结构的多工序制造过程是实践中最为常见的形式,而不同模式的并联结构其上游工序质量波动对下游工序及总过程能力的影响不同。针对多工序制造过程并联结构特点,本文从波动减少的角度重点对多工序并联制造过程中并行、分散和收敛三种基本模式进行过程能力分析,研究多工序制造过程中各子过程波动对整体过程能力的影响,并根据各子过程质量波动减少的“困难度”和“效用比”评价质量改进的效果,给出多工序并联过程能力改进策略选择依据。通过实例表明,本方法能较好地识别各工序质量波动减少对本工序过程能力和总过程能力的不同影响,确定质量改进的优先顺序,实现多工序制造过程的经济性质量改进和优化。     

Joint economic design of EWMA control charts for mean and variance

Control charts with exponentially weighted moving average (EWMA) statistics (mean and variance) are used to jointly monitor the mean and variance of a process. An EWMA cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria. The pure economic model is extended to the economic-statistical design by adding constraints associated with in-control and out-of-control average run lengths. The quality related production costs are calculated using Taguchi’s quadratic loss function. The optimal values of smoothing constants, sampling interval, sample size, and control chart limits are determined by using a numerical search method. The average run length of the control scheme is computed by using the Markov chain approach. Computational study indicates that optimal sample sizes decrease as the magnitudes of shifts in mean and/or variance increase, and higher values of quality loss coefficient lead to shorter sampling intervals. The sensitivity analysis results regarding the effects of various inputs on the chart parameters provide useful guidelines for designing an EWMA-based process control scheme when there exists an assignable cause generating concurrent changes in process mean and variance.     

On the existence and computation of an equilibrium in an economy with constant returns to scale production

In this paper we consider the problem of finding an equilibrium in an economy with non-linear constant returns to scale production activities. To find an equilibrium we propose an adjustment process in which the prices of the commodities and the activity levels of production adjust simultaneously. The process starts at a price vector at which each production activity has non-positive profit. We show that the process follows a path which connects the starting point with an equilibrium of the economy. From this it follows that the existence of a price vector at which each production activity has non-positive profit implies the existence of an equilibrium. The equilibrium can be computed by using a simplicial algorithm or by solving a sequence of Linear Variational Inequality Problems.This research is part of the VF-program Competition and Cooperation. The authors are very grateful to Dolf Talman and two unknown referees for their valuable comments and suggestions.     

Robust cutting parameters optimization for production time via computer experiment

This study intends to determine the optimal cutting parameters required to minimize the cutting time while maintaining an acceptable quality level. Usually, the equation for predicting cutting time is unknown during the early stages of cutting operations. This equation can be determined by studying the output cutting times vs. input cutting parameters through CATIA software, with assistance from the statistical method, response surface methodology (RSM). Then, the equation is formulated as an objective function in the form of mathematical programming (MP) to determine the optimal cutting parameters so that the cutting time is minimized. The formulation in MP also includes the constraints of feasible ranges for process capability consideration and surface roughness for quality concerns. The important ranking obtained from the statistical method in cooperation with the optimal solutions found from MP can also be used as references for the possibility of robust design improvements.