At The Same Time To Estimate The Mean And Variance Of The Experimental Design

Originated by Dr. Taguchi, parameter design is always an economical and effective approach to reduce variation in products and improve product quality during the period of designing. The key idea of this approach is: classifying the factors which influence the product's performance into two classes, control factors and noise factors; employing a product array to arrange experiments to investigate the relationship between the performance measure and control factors and noise factors; and making use of the control-by-noise interactions to identify the setting of control factors, so as to improve product's robustness and its quality without the augmentation of cost. During 1970s and 1980s, the wide spread of Taguchi's parameter design in Japanese industry society played an important role in course of the development of Japanese industry and the flourish of Japanese economics after World War II. In the recent 20 years, parameter design was also extended to China, USA, Canada and other countries. In various fields, there were many successful cases which brought significant economical and social benefit.Although the idea of parameter design is of originality whether on engineering practice or on the theory of experimental design, Taguchi's approach is not perfect. A lot of studies on parameter design have been done by many statisticians from different directions and many alternatives to Taguchi's approach have been proposed. Up to now, however, most of the studies focused on data analysis or optimization methods, and a little has been done on experiment design. The theme of this thesis is on experimental design. Two issues on the experimental design are discussed in this thesis: one is the design of outer array with respect to a product array, the other is the simultaneous design for estimating both mean and variance.Taguchi employs product arrays to design experiments. Orthogonal arrays are always used to design both inner array and outer array. It is known that orthogonal arrays have some good property when used as experimental plans such as the uiformity and regularlity. Unlike an inner array, it is inappropriate to employ an orthogonal arrays to design an outer array because it is unsuitable for estimating variance that the points of an experimental design are scattered uniformly and regularly. We think that the points of an outer array should sufficiently reflect the characteristics of the noise factors' probability distribution. Essentially, the design of an outer array is to select the representative points of a probability distribution. Based on the measurement of the goodness of an outer array on the moments of a distribution, this thesis proposes some methods to construct outer arrays for noise factors which are normally or uniformly distributed in a unit sphere. Some concrete designs for outer arrays are also given under the four-moment criterion.To achieve the goal of parameter design by modeling the performance is one of important alternatives to Taguchi's approach. One advantage of the performance-model approach is that it can allow fewer experiments by combining control and noise factors in a single experimental planwhich is obviously more efficient. Both process mean and variance of performance may need to be estimated simultaneously when performance-model approach is applied. So, the merit of an experimental design should also be measured from the property of both estimators of process mean and variance. However, there is no study in literature on design for estimating both mean and variance for response surface models. The difficulties lie mainly on two points: the measure of merit of a design is mult-objective; and, it is essentially a nonlinear optimal design problem since the estimator of process variance is generally a nonlinear function of the observations of performance. The study of nonlinear optimal design is still a difficult problem. This thesis considers the design for estimating both mean and variance of a specific class of quadratic response surface models. An EV design...