线性不对称损失时非正态分布过程均值优化

针对常见的两种非正态分布———梯形分布和三角分布，研究线性不对称质量损失时其过程均值的优化问题，建立了梯形分布在五种不同情况下线性不对称质量损失的数学模型，基于以上模型给出了线性不对称质量损失时梯形分布最优过程均值的确定方法；研究三角分布在四种不同情况下线性不对称质量损失的数学模型，并给出了线性不对称质量损失时三角分布最优过程均值的确定方法。最后，用实例验证本过程均值优化模型的有效性。实例表明，应用线性不对称损失函数，适当的改变过程均值，可以有效地降低产品的质量损失，通过调整工艺过程将获得最佳经济效益。     

最优过程均值和生产运行长度的确定

实际生产中,过程均值由于受到随机振荡的影响,经常从受控状态逐渐漂移到失控状态,从而导致大量不合格品的出现.针对这种情况,本文假定随机振荡次数服从泊松过程,每次振荡引起过程均值漂移相互独立且服从同一指数分布,结合不对称田口质量损失函数,建立了最佳初始过程均值的经济模型,并讨论了最优生产运行长度的确定.通过与初始过程均值设置在目标值处的情形比较,说明本文模型对降低生产成本的有效性。灵敏度分析表明了各参数对最优过程均值和生产运行长度的影响.     

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.     

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。     

关于田口参数设计的专家评论(Ⅱ)

4.数据分析.信噪比,数据变换,广义线性模型Madhav Phadke 与某些统计文献中提出的数据变换不同,选择信噪比是为了确定信号因子和质量特性间的理想关系,并估价噪声因子对选择理想函数的灵敏度,不是确定稳定方差的数据变换.由于它允许估价噪声因子对理想函数的灵敏度,采取合适的调节也是重要的. 以下我将证明常见类型望目特性信噪比的合理性.令 为目标值,与 有关的二次损失为. Q=(μ-t)2+σ2(4.1)其中μ和σ表示响应变量的均值和标准差.假设两种不同工艺的均值和标准差已知,如何判别哪个工艺条件更合适?如何估价它们对噪声因子的灵敏性?为了…     

连续时间Markov决策过程的均值-方差优化问题

本文考虑连续时间Markov决策过程折扣模型的均值-方差优化问题.假设状态空间和行动空间均为Polish空间,转移率和报酬率函数均无界.本文的优化目标是在折扣最优平稳策略类里,选取相应方差最小的策略.本文致力于寻找Polish空间下Markov决策过程均值-方差最优策略存在的条件.利用首次进入分解方法,本文证明均值-方差优化问题可以转化为"等价"的期望折扣优化问题,进而得到关于均值-方差优化问题的"最优方程"和均值-方差最优策略的存在性以及它相应的特征.最后,本文给出若干例子说明折扣最优策略的不唯一性和均值-方差最优策略的存在性.     

跳-扩散模型下相对收益过程带停时的均值-方差随机控制

针对跳扩散模型下鞅测度不唯一的问题,利用识别定理和Riccati方程研究了跳扩散模型下带停时的均值-方差随机控制问题,得到了相对收益过程最优投资策略的显式解及相应的最优停时,并且给出了在最优停止时间的均值方差有效边界.     

Markov调节中基于时滞和相依风险模型的最优再保险与投资

本文研究保险公司在Markov调节下基于时滞及相依风险模型的最优再保险与最优投资问题,其中市场被划分为有限个状态,一些重要的参数随着市场状态的转换而变化.假设保险公司的盈余过程由复合Poisson过程描述,而风险资产的价格过程由几何跳扩散模型刻画,并且假设这两个跳过程是相依的.以最大化终端财富值的均值-方差效用为目标,...     

基于Hurwicz准则的不确定养老金最优投资策略问题

本文提出一种新的养老金最优投资策略模型,研究了带有不确定工资过程的DC型养老金最优投资策略问题.以二次损失函数的Hurwicz加权平均值最小化为目标,针对两类相对财富过程,给出了养老金最优投资策略的显式表达式.最后,通过数值分析,研究了模型参数对最优投资策略的影响.     

道德风险影响下的保险最优投资研究

在考虑道德风险的情况下,以均值方差准则为目标研究保险人最优投资问题.假设保险盈余过程服从C-L模型,金融市场上存在一种无风险资产和一种风险资产可供投资,其中风险资产的价格过程服从几何布朗运动.在纯道德风险保险契约设计中,借鉴相关研究对努力水平和效用化努力成本的假设,量化道德风险对盈余过程的影响.在均值方差目标下,建立保险人最优投资问题的广义Hamilton-Jacobi-Bellman(HJB)方程,给出保险人时间一致的均衡投资策略和价值函数.结果显示累计索赔比例参数越大,公司对最优努力水平越敏感,采取措施降低道德风险有利于公司收益提升;努力成本参数越大,公司会降低努力水平减少支出,避免损失.     

Joint optimization of process target mean and tolerance limits with measurement errors under multi-decision alternatives

Determining the optimal target mean for a process has been identified as an important research area and a number of models have been proposed in the literature. This paper differs from previous studies of this problem in two ways. First, most previous studies address the process target problem through models seeking the optimal process mean using fixed tolerance settings of a process. Second, in real-world industrial settings, there are several markets often available with different price/cost structures. In this paper, we develop a model for jointly determining both the optimal process target mean and the optimal tolerance limits under the situation where there are several markets available with different price/cost structures. We then investigate the effects of measurement errors on the optimum process target and tolerance limits with multi-decision alternatives. A numerical example is given, and sensitivity analyses are also performed to study the effects of measurement errors on this model.     

Reverse programming the optimal process mean problem to identify a factor space profile

For the manufacturer that intends to reduce the processing costs without sacrificing product quality, the identification of the optimal process mean is a problem frequently revisited. The traditional method to solving this problem involves making assumptions on the process parameter values and then determining the ideal location of the mean based upon various constraints such as cost or the degree of quality loss when a product characteristic deviates from its desired target value. The optimal process mean, however, is affected not only by these settings but also by any shift in the variability of a process, thus making it extremely difficult to predict with any accuracy. In contrast, this paper proposes the use of a reverse programming scheme to determine the relationship between the optimal process mean and the settings within an experimental factor space. By doing so, one may gain increased awareness of the sensitivity and robustness of a process, as well as greater predictive capability in the setting of the optimal process mean. Non-linear optimization programming routines are used from both a univariate and multivariate perspective in order to illustrate the proposed methodology.     

An iterative scheme for solving the optimal transportation problem

We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of iterations necessary for the scheme to terminate, in terms of the error tolerance and number of points in the support of the discrete target measure.     

Perfect simulation and inference for point processes given noisy observations

Summary  The paper is concerned with the exact simulation of an unobserved true point process conditional on a noisy observation. We use dominated coupling from the past (CFTP) on an augmented state space to produce perfect samples of the target marked point process. An optimized coupling of the target chains makes the algorithm considerable faster than with the standard coupling used in dominated CFTP for point processes. The perfect simulations are used for inference and the results are compared to an ordinary Metropolis-Hastings sampler.     

The effect of testing errors on a repetitive testing process

Repetitive testing is a fairly common practice in the final testing stage of a chip manufacturing. Decisions on setting initial lot size and the number of testing repetitions are crucial to the effectiveness of the testing process. The task of setting optimal parameters for a testing process is often difficult in practical situations due to uncertainties in both incoming product yield and testing equipment condition during the testing process. In this paper, we investigate a repetitive testing process where the testing equipment may shift randomly from an in-control state to an inferior state during the testing process which, correspondingly, results in different testing errors. We develop a quantitative model that helps us to find optimal test parameters that maximizes system performance. Based on the model, we performed extensive numerical experiments to test the effects of incoming product defective rate, testing equipment shift rate, especially, type II testing errors on decision and system performance. We find that test equipment condition may significantly affect the optimal decisions on the number of test repetitive and initial testing batch size. Further, we find that, while a small type II testing error may have negligible negative effect of system performance, the effect increases as the error or the incoming product yield increases. The results of this research may potentially provide practitioners with insights and a quantitative tool for designing an efficient repetitive testing process.     

含有信用风险的跳扩散市场的最优组合选择

假定投资者将其财富分配在这样两种风险资产中,一种是股票,价格服从跳跃扩散过程;一种是有信用风险的债券,其价格服从复合泊松过程.在均值-方差准则下通过最优控制原理来研究投资者的最优投资策略选择问题,得到了最优投资策略及有效边界,最后通过数值例子分析了违约强度、债券预期收益率以及目标财富对最优投资策略的影响.     

允许投资组合条件下概率准则

概率准则具有一定的现实意义，其投资决策是以期望贴现资产为导向的．本文讨论了完备标准动态金融市场中在允许投资组合条件下的概率准则问题，得到了准则函数，贴现资产过程以及最优允许投资组合过程的解析表达式．期望贴现资产越大，准则函数越小。     

Optimal solution of ordinary differential equations

We survey some recent optimality results for the numerical solution of initial value problems for ODE. We assume that information used by an algorithm about a right-hand-side function is partial. Two settings of information-based complexity are considered: the worst case and asymptotic. Upper and lower bounds on the error are presented for three types of information: standard, linear, and nonlinear continuous. In both settings, minimum error algorithms are exhibited.     

参数未知的多变量设置调整问题研究

针对存在起始设置偏差过程参数未知的多变量过程,考虑不同质量特性对总体的质量损失影响不同,研究了在调整费用恒定下的统计过程调整问题.基于过程的状态空间方程模型,利用贝叶斯方法对过程的未知参数和设置偏差进行估计,结合过程的费用结构给出了过程的调整策略.通过仿真与其他的调整策略进行了对比分析,仿真结果表明,提出的调整策略能够更为有效地减少过程的质量损失.