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。     

基于非对称损失函数的过程均值与标准差优化设计

质量特性的过程均值与过程标准差的选定是一个重要的命题,它们是影响质量成本的重要因素.由顾客定义的特性目标均值以及初始标准差往往并不一定能使得总体的质量损失最小化。针对此问题,本文首先讨论了非对称的质量损失函数,并在此基础上构造出质量特性目标均值与标准差的优选模型,进而得到最优目标过程均值与标准差。在模型的应用中表明:其他情况不变的情况下,质量特性最优均值与最优标准差对质量损失系数具有一定的稳健性。     

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.     

排它过程的占位时函数的扩散行为

该文考虑对于非对称的排它过程的占位时函数的扩散行为, 在均值m ≠ 0和 ρ =1/2的条件下, 给出了扩散行为的一个上界.     

非对称需求扰动信息下的供应链显示机制设计

研究由一个供应商和一个零售商组成的供应链在非对称的需求扰动信息下的显示机制设计问题。假定市场需求为指数函数形式和常数柔性需求函数形式,给出了非对称的需求扰动信息下的供应链最优契约,并且分析了非对称扰动信息对于供应链性能的影响。研究表明,当市场需求为指数函数形式和常数柔性函数形式时,仍然可以设计有效的契约菜单来改善供应链的运作性能;当需求扰动满足一定条件时,初始的生产计划仍然是最优的;非对称需求扰动信息并不必然会给供应链带来利润损失,并且显式地给出了非对称的需求扰动信息不会给供应链带来利润损失的条件。     

不同模型下ES风险度量的计算

给出当金融资产遵从几何布朗运动时期望损失的计算。当金融资产价格的对数收益率服从均值方程为ARMA模型,方差方程为GARCH(s,n)模型,而均值修正后的收益率分别服从正态分布、t分布和GED分布时,给出了期望损失的计算。     

非对称绝对线性损失下正态总体的参数设计

田口玄一提出了很多损失函数,其中二次损失是应用最为广泛的一种。当实际损失函数不是二次损失函数而使用二次损失时,就会引起参数设计的不正确。在某些情况下,线性损失函数更适合工业应用。本文在非对称的线性损失下,讨论了参数设计的可行性,证明田口先生方法的稳健性设计和灵敏度设计依然行之有效。结果表明性能指标平均值必须稍微偏离目标值,才能使平均损失达到最小。     

09-0685(四次修改稿)_王亮 师义民 (逐步增加II型截尾下比例危险率模型的可靠性分析) 2010-03-05

基于逐步增加 II 型截尾样本，分别在均方损失和 Linex 损失下，利用 ML-II 方法研究了比例危险率模型的参数和可靠性指标的经验 Bayes 估计问题。为了研究估计结果的精确性，分析了一个实际应用例子，并利用 Monte-Carlo 方法给出一个数值模拟例子，结果表明在非对称 Linex 损失下，经验 Bayes 估计更具灵活性，且结果更加有效。     

一类独立随机变量均值中参数的估计

本文给出了独立随机变量均值中参数ａ＝（ａ１，…，ａｐ）′的估计量（ａ１Ｘ１，…，ａｐＸｐ）′在加权平方和损失下为可容许估计的充要条件及在一般损失Ｌｖ下为可容许估计的充分条件（在线性估计类中）。     

Economic manufacturing quantity,optimum process mean,and economic specification limits setting under the rectifying inspection plan

Economic manufacturing quantity, process mean, and specification limits setting are three important methods for the inventory and quality control problems. In the imperfect production system, we usually consider the manufacturing quantity for reducing the inventory cost, determine the process level for reducing the production cost, and select the specification limits for screening the products. In this paper, we propose the above integrated model based on the application of rectifying inspection plan for obtaining maximum expected total profit of product. The asymmetric quadratic quality loss function is adopted for measuring the product quality. The sensitivity analyses of parameters are provided for illustration.     

基于预防维修和质量损失函数的VSI EWMA控制图经济设计

为了提高过程监控效率的同时降低过程控制成本,研究可变抽样区间(VSI)指数加权移动平均(EWMA)控制图的经济设计问题。首先建立基于预防维修和质量损失函数的VSI EWMA控制图联合经济模型;使单位时间的损失成本函数最小来确定参数的最优值;其次用遗传算法来寻找联合经济模型的最优解,并给出一个算例。最后对VSI EWMA控制图联合经济模型进行灵敏度分析,得出控制图模型参数对设计参数的影响关系。     

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.     

考虑质量失误的建筑供应链质量控制协调研究

考虑内外部质量损失条件下,研究由分包商和总包商组成的两级建筑供应链中的质量控制博弈问题。根据典型的建设工程施工质量控制流程,建立了建筑供应链的三层质量控制树。基于质量控制树分别建立了集中决策条件下和协调决策条件下的收益函数模型。通过对模型求解结果的对比分析,得出在双方共同原因导致的内部质量损失由双方分摊的情况下,双方共同分担外部质量损失可使供应链质量控制决策达到协调。进一步的分析得出,内外部质量损失比率越大,总包商所承担的内部质量损失比例越大,而分担的外部质量损失比例越小。     

The total median in statistical quality control

In industry, most of the process observations are assumed to come from a normal population, but usually we merely want to control the process mean value. It is thus sensible to find control statistics, which are ‘robust’ to monitor the process mean, giving the expected rate of false alarms whenever that mean is close to the target value, although not under a normal regime. Simulation studies for a few symmetric and asymmetric distributions allow us to suggest the total median as a robust median estimator. We shall here analyse such a robustness, as well as the robustness of the total median chart comparatively to the sample mean chart, whenever we want to control the mean value of a symmetric underlying parent. Some indication is also provided on the comparative out‐of‐control behaviour of the two charts. Copyright © 2004 John Wiley & Sons, Ltd.     

Real estate price prediction under asymmetric loss

This paper deals with the problem of how to adjust a predictive mean in a practical situation of prediction where there is asymmetry in the loss function. A standard linear model is considered for predicting the price of real estate using a normal-gamma conjugate prior for the parameters. The prior of a subject real estate agent is elicited but, for comparison, a diffuse prior is also considered. Three loss functions are used: asymmetric linear, asymmetric quadratic and LINEX, and the parameters under each of these postulated forms are elicited. Theoretical developments for prediction under each loss function in the presence of normal errors are presented and useful tables of adjustment factor values given. Predictions of the dependent price variable for two properties with differing characteristics are made under each loss function and the results compared.     

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.     

Minimax confidence bound of the normal mean under an asymmetric loss function

This paper considers a minimax confidence bound of the normal mean under an asymmetric loss function. A minimax confidence bound is obtained for the case that the variance is known or unknown. The admissibility of the minimax confidence bound is also considered for the case of known variance.     

Multivariate Bayesian process control for a finite production run

Most industrial products and processes are characterized by several, typically correlated measurable variables, which jointly describe the product or process quality. Various control charts such as Hotelling’s T², EWMA and CUSUM charts have been developed for multivariate quality control, where the values of the chart parameters, namely the sample size, sampling interval and the control limits are determined to satisfy given economic and/or statistical requirements. It is well known that this traditional non-Bayesian approach to a control chart design is not optimal, but very few results regarding the form of the optimal Bayesian control policy have appeared in the literature, all limited to a univariate chart design. In this paper, we consider a multivariate Bayesian process mean control problem for a finite production run under the assumption that the observations are values of independent, normally distributed vectors of random variables. The problem is formulated in the POMDP (partially observable Markov decision process) framework and the objective is to determine a control policy minimizing the total expected cost. It is proved that under standard operating and cost assumptions the control limit policy is optimal. Cost comparisons with the benchmark chi-squared chart and the MEWMA chart show that the Bayesian chart is highly cost effective, the savings are larger for smaller values of the critical Mahalanobis distance between the in-control and out-of-control process mean.