不忽略一次项损失且补偿量恒定时望大望小特性质量损益函数设计

因望大质量特性在实践中无法达到无穷大,望小质量特性在实践中也无法达到0值,当补偿量恒定时,质量损益函数仅采用补偿量及二次项损失表达,直接删除一次项损失是不合理的.在不忽略一次项损失且补偿量恒定时,研究了望大与望小特性质量损益函数的表达形式及二次式损益函数中一次项损失系数和二次项损失系数确定的方法,比较分析了二次式损益函数中一次项损失和二次项损失的大小.研究结果显示,二次项损益函数是二次式损益函数的一种形式.     

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。     

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.     

基于测量质量损失函数的控制图控制界限的优化

控制界限和抽样间隔是控制图的两个基本参数。常规控制图是基于3σ原理确定的控制界限,该控制界限是在大量试验基础上依据经验确定的,并没有精确的公式推导.对于抽样间隔,常规控制图也没有明确的规定。田口博士的质量损失函数可以很好的解决质量经济性方面的一些问题.利用田口博士的理论,通过确定适宜的二次测量质量损失函数,可以确定控制图的最佳控制界限和最佳抽样间隔.文章简要介绍了常规控制图原理和田口博士的质量损失函数,重点叙述了田口博士反馈控制系统的测量质量损失函数,在此基础上,研究了控制图最佳控制界限和最佳抽样间隔,并且通过具体实例验证了该控制图良好的经济性.     

二次损失下Guass-Markov非线性模型系数的Minimax随机优化模型

本文借用线性模型系数的Minimax估计方法,在二次损失函数下运用随机优化理论对Gua.ss-Markov非线性模型的系数进行了研究,建立了非线性模型系数Minimax估计的随机优化模型.     

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。     

产品设计与质量控制的动态因素模型(下)

(续上期)5·5产品动态质量损失和产品技术损失田口的质量损失函数L(y)已被人们所熟知,它不考虑跟时间的关系,其自变量为产品的特性y,其函数形式为L(y)=K(y-y0)2,其中K为常数。质量损失函数的期望值E[L(y)}=K·E(y-y0)2称之为产品质量损失,它表示在统计意义下单位产品的平均质量     

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.     

平衡损失函数下具有共同效应的信度保费(英文)

在经典的信度理论中,一个保单组合的各风险之间是相互独立的,同时从二次损失函数中推导出信度保费.(Wen et al.,2009)给出了风险间具有共同效应的特殊的相关结构的信度保费表达式.本文在平衡损失函数下考虑此种风险结构的信度理论,特别地得到了Bühlmann和Bühlmann-Straub模型的信度保费表达式.     

平衡损失下有限总体回归系数的线性可容许预测

本文研究了平衡损失函数下正态总体和非正态总体中有限回归系数的可容许预测.利用统计决策理论,获得了非正态总体中齐次线性预测为可容许预测的充分必要条件和在正态总体中齐次线性预测在一切预测类中可容许性的充要条件,推广了二次损失下的若干相关结果.     

二次损失下G-M模型中可估函数的条件Minimax估计与性质

在二次损失下关于任意矩阵V对G-M模型讨论了齐次线性估计类中可估函数的条件Mimimax估计与性质。     

Some modifications of improved estimators of a normal variance

Consider the problem of estimating a normal variance based on a random sample when the mean is unknown. Scale equivariant estimators which improve upon the best scale and translation equivariant one have been proposed by several authors for various loss functions including quadratic loss. However, at least for quadratic loss function, improvement is not much. Herein, some methods are proposed to construct improving estimators which are not scale equivariant and are expected to be considerably better when the true variance value is close to the specified one. The idea behind the methods is to modify improving equivariant shrinkage estimators, so that the resulting ones shrink little when the usual estimate is less than the specified value and shrink much more otherwise. Sufficient conditions are given for the estimators to dominate the best scale and translation equivariant rule under the quadratic loss and the entropy loss. Further, some results of a Monte Carlo experiment are reported which show the significant improvements by the proposed estimators.     

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.     

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A Kind of direct methods is presented for the solution of optimal control problems with state constraints.These methods are sequential quadratic programming methods.At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and Linear approximations to constraints is solved to get a search direction for a merit function.The merit function is formulated by augmenting the Lagrangian funetion with a penalty term.A line search is carried out along the search direction to determine a step length such that the merit function is decreased.The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadrade programming methods.     

二次损失下增长曲线模型参数阵的线性Minimax可容许估计

本文在二次损失函数下,给出了增长曲线模型参数阵的线性估计在给定的线性估计类中是Minimax可容许估计的充要条件.     

二次损失下随机回归系数和参数的线性Minimax估计

对带有随机效应的一般线性模型,本文提出了随机回归系数和参数线性组合的Minimax估计问题. 在二次损失下,研究了线性估计的极小极大性.关于适当的假设,得到了可估函数的唯一线性Mjnimax 估计.     

The Minimax Estimator of Stochastic Regression Coefficients and Parameters in the Class of All Estimators

In this paper, the authors address the problem of the minimax estimator of linear combinations of stochastic regression coefficients and parameters in the general normal linear model with random effects. Under a quadratic loss function, the minimax property of linear estimators is investigated. In the class of all estimators, the minimax estimator of estimable functions, which is unique with probability 1, is obtained under a multivariate normal distribution.     

An improved enumerative algorithm for solving quadratic zero-one programming

An improved algorithm is proposed for the minimization of a quadratic function in zero-one variables under quadratic constraints which is based on the idea of additive penalties proposed by P. Hansen. At first, the quadratic function in which all the coefficients except the constant term are nonnegative is obtained by the introduction of the negative variables, and the constant term is a tighter bound of the function. Starting from the tighter bound, some properties are obtained and some efficient tests are established. To obtain a much tighter bound, a simple heuristic method is suggested instead of solving a linear programming problem. Furthermore, the flexibility dealing with some tests is discussed and it is also helpful to the algorithm.