Analysis Of Dispersion In Quality Engineering Experiment

Quality engineering is the branch subject of technology that is used to improve the quality ojf product (or service). Robust parameter design, proposed by Taguchi Doctor, is the cote theory foundation of quality engineering. The analysis of the variation (or robustness) of produces quality performance is the key of robust parameter designing, and is the focus of experimental planning and analysis. This thesis studies the analyzing of variation from quality engineering experiments in three different aspects. Various methods are introduced and compared. And some new methods are developed.In the first chapter, some backgrounds of parameter design are introduced. And parameter design for static nominal-the-best problem is introduced too. Then we discuss some limitations of parameter, and illustrate some methods for analyzing location effects from two levers unreplicated factorial (or fractional factorial) designs. At the end of this chapter, we introduce the problems to be studied and the constitution of this thesis.In Chapter 2, we discuss the problem of identifying and estimating dispersion effects in unreplicated factorial (or fractional factorial) designs. Because these types experiments allow for simultaneous investigation of a large number of factors with relatively few experimental runs and lower cost, they have been widely employed as industrial screening experiments since seventy years ago. They were often used to identify and estimate location effects before. But stimulated by Taguchi's Methods, Box and Meyer(1986b) give a nice illustration of identifying dispersioneffects from an unreplicated 2k-p design. From then on, many statisticians have done much study on this problem. Several important methods for identifying dispersion effects are systematically illustrated in this chapter. We compare these methods base on a fundamental result about confounding of dispersion and location, and give some important relationship between these methods. For the variance log-linear model, we develop two modified methods: one is based on Score test, and the other is based on likely-hood test.Chapter 3 devotes to studying the relations between variation summary statistic and "Two Step" parameter optimization procedure. Those control factors with noise are focused in this chapter and the next chapter because they play an important role in many experiments. An exploring method based on "standard Gamma plot" is developed for analysis of cross-productdesigns. Combine this method with a theory result from Zhu, Fu and Wang(2004), we analyze for computer experiments, investigate the validity of signal-to-noise ratio and Two Step" parameter optimization procedure in these experiments. We point out the importance and the application of the theory result and the "standard Gamma plot" method.Two basic response surface methodology (RSM) approaches to parameter design evolved over 1990's: dual response surface methodology which is based on cross-product design, and response model approach which is based on combine design. In Chapter 4 we discuss some relation and difference between the two approaches. For the cross-product designed experiments, we illustrate that additional information can be get by using response model approach than by using dual response surface methodology. So the two approaches can be combined for application. And the problem of fitting response model with those control factors having noise is discussed in this chapter.In summary, This thesis studies various approaches to analyze the variation of quality characteristic. Some new methods are developed for identifying dispersion effects fnwaunreplicated 2k~p factorial (or fractional factorial ) designs. And some new results are obtained for the first, which have not been seen in the literature. In This thesis, the method of standard Gamma plot is systematically developed to select and estimate the dispersion measure. And special attention is paid to those control factors with noise. These researches in this thesis are benefit for the development of robus...