Response model analysis for robust design experiments

Taguchi's robust design technique, also known as parameter design, focuses on making product and process designs insensitive (i.e., robust) to hard to control variations. In some applications, however, his approach of modeling expected loss and the resulting “product array” experimental format leads to unnecessarily expensive and less informative experiments. The response model approach to robust design proposed by Welch, Ku, Yang, and Sacks (1990), Box and Jones (1990), Lucas (1989), and Shoemaker, Tsui and Wu (1991) offers more flexibility and economy in experiment planning and more informative modeling. This paper develops a formal basis for the graphical data-analytic approach presented in Shoemaker et al. In particular, we decompose overall response variation into components representing the variability contributed by each noise factor, and show when this decomposition allows us to use individual control-by-noise interaction plots to minimize response variation. We then generalize the control-by-noise interaction plots to extend their usefulness, and develop a formal analysis strategy using these plots to minimize response variation.     

A Simple Method for Obtaining Minimum Aberration Designs

Minimum aberration designs are preferred in practice, especially when it is desired to carry out a multi-factor experiment using less number of runs. Several authors considered constructions of minimum aberration designs. Some used computer algorithms and some listed good designs from the exhausted search. We propose a simple method to obtain minimum aberration designs for experiments of size less than or equal to thirty-two. Here, we use an ordered sequence of columns from an orthogonal array to design experiments and blocked experiments. When the method is implemented in MS Excel, minimum aberration designs can be easily achieved.     

Trend-Free Designs in Blocked Factorial Experiments

Appropriate run orders can make all estimable effects free of some trends in blocked fractional factorial experiments. We need to design blocked experiments with effects free of trends in blocks. The generalized foldover scheme given by Coster (1993 Coster , D. C. ( 1993 ). Trend-free run orders of mixed-level fractional factorial designs . Ann. Statist. 21 : 2072 – 2086 .[Crossref], [Web of Science ®] , [Google Scholar]) can be used to obtain such designs. In this article, we propose an easy and better approach to deal with this issue when the same trends appear in blocks. We investigate block trend property of columns in the orthogonal plans in s ^k runs for assigning factors to obtain block-trend free designs in a trend-free order. We illustrate our approach with three examples.     

Projection array based designs for computer experiments

In this paper we define a new class of designs for computer experiments. A projection array based design defines sets of simulation runs with properties that extend the conceptual properties of orthogonal array based Latin hypercube sampling, particularly to underlying design structures other than orthogonal arrays. Additionally, we illustrate how these designs can be sequentially augmented to improve the overall projection properties of the initial design or focus on interesting regions of the design space that need further exploration to improve the overall fit of the underlying response surface. We also illustrate how an initial Latin hypercube sample can be expressed as a projection array based design and show how one can augment these designs to improve higher dimensional space filling properties.     

Some new classes of orthogonal Latin hypercube designs

Orthogonal Latin hypercube (OLH) is a good design choice in a polynomial function model for computer experiments, because it ensures uncorrelated estimation of linear effects when a first-order model is fitted. However, when a second-order model is adopted, an OLH also needs to satisfy the additional property that each column is orthogonal to the elementwise square of all columns and orthogonal to the elementwise product of every pair of columns. Such class of OLHs is called OLHs of order two while the former class just possessing two-dimensional orthogonality is called OLHs of order one. In this paper we present a general method for constructing OLHs of orders one and two for n=s^m$n=s^m$ runs, where s and m may be any positive integers greater than one, by rotating a grouped orthogonal array with a column-orthogonal rotation matrix. The Kronecker product and the stacking methods are revisited and combined to construct some new classes of OLHs of orders one and two with other flexible numbers of runs. Some useful OLHs of order one or two with larger factor-to-run ratio and moderate runs are tabulated and discussed.     

对角优势化的实現

对角优势化是INA法的关键。本文对对角优势化问題进行了直接研究。给出了可实现条件和关于计算特征值的降阶方程的定理。最后,讨论了一种简便而有效的局部补偿方法。     

分解、拟合和对角优势

本文提出一种有有事分式阵作为预补偿阵以实现对角优势的新方法,先将对象传递阵和预补偿阵进行适当的分解,使待解方程的结构变得简单,再分别用极小化方法和最小二乘法术预补偿阵。通过实例计算证明本文所迷方法是成功的。     

三峡石崇拜的文化内蕴及文化特征阐论

在人类历史上,由石而生成的文化现象丰富多采。本文对发现于三峡地区的“八阵图”、“阴阳石”、“悬棺葬”的本来面貌及文化内蕴进行了历史的考察和阐论,认为这三种文化事象,从石崇拜的一隅,体现了三峡文化的某些典型特征。     

Space-filling orthogonal arrays of strength two

This paper considers the use of orthogonal arrays of strength two as experimental designs for fitting a surrogate model. Contrary to standard space-filling designs or Latin hypercube designs, the points of an orthogonal array of strength two are well distributed when they are projected on the two-dimensional faces of the unit cube. The aim is to determine if this property allows one to fit an accurate surrogate model when the computer response is governed by second-order interactions of some input variables. The first part of the paper is devoted to the construction of orthogonal arrays with space-filling properties. In the second part, orthogonal arrays are compared with standard designs for fitting a Gaussian process model.