Using Taguchi methods for industrial process optimization.

Author:Sutterfield, J.S.
 
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  1. INTRODUCTION

    Statistical experimental methods have emerged as a powerful method for analyzing cause and effect relationships among factors over the past 75 years. Design of Experiments (DoE) methods are used in industry for process improvement; and optimization purposes (Singh et al., 2006; Huang and Lin, 2004. Taguchi (1986) introduced a simplified and modified DoE approach, which has been widely adopted in industry. More recently, the power of Taguchi's approach is that it is quite generally applicable to a broad range of experimental situations in which the components of variation, including those of interaction, are desired. It has been used for such diverse applications as bearing deflections, diesel engine nozzle design, cloth quality evaluation, the design of clothing, bank and insurance contracting and electrical power consumption (Taguchi, 1988b) as well as engineering and science in general (Wright, 2002). One limitation of the method is the actual process tends to cause disruption in the plant, and may be uneconomical (Sukthomya and Tannock, 2005). In recent years, researchers have developed approaches (Neural Networks (Guh and Tannock, 1999); and Evolutionary Operations (Box 1957)) to test process parameters, without production interruptions. However, in this study, classical experimental analysis and Taguchi Methods, without actual experimentation, are used to investigate process parameter effects.

    The chief purpose of experimental analysis is to determine cause and effect relationships among control factors, factors that can be varied, and response factors, the (un)desirable effect(s) resulting from the variation. It is often important from the standpoint of production efficiency and economy to establish the maximum response that may result from variation of the control factors. Establishing the extent of the response to incremental changes in numerous control factors may be problematical because of interactions between control factors. The term interaction is used to indicate that control factors react with each other to produce a greater effect than that which would be caused if the individual effects of the factors were merely combined. Such interactions may even occur among three or more control factors. The usual approach is to estimate the magnitude of any interaction(s).

    In employing experimental methods, the factors which might affect a given outcome are incrementally varied to examine the degree to which a given factor, or combination of factors, may affect a given result. Control factors may also be incremented simply to determine whether a given response factor is absent or present, viz, whether or not the given occurs. More often, though, the purpose of an experiment is aimed at establishing change in the response factor that occurs from incremental changes in the levels of the control factors. Taguchi points out that, strictly speaking, there is always some interaction between (among) control factors, (Taguchi, 1988a) even though such interactions may be minute. However, when interactions are not small, they will cause the response variable to react in a non-linear fashion. As a consequence, interactions among two or more control variables may cause a response variable to increase (or decrease) over a certain part of an interval, and then decrease (or increase) as the control factors are varied over another part of their intervals. Often, this is an extremely important consideration for production applications, for if a response factor of interest is maximized (or minimized, or perhaps eliminated entirely), it is futile to increase the factor, or combination of factors, beyond the point at which the response factor of interest is optimized. Taguchi's method of experimentation is particularly powerful in such analyses because of its ability to identify not only principal effects of control variables, but interactions among them.

    This paper presents two alternative ways to investigate process variable effects, using classical experimental analysis and Taguchi methods. A detailed case study examines the application of poison antidotes to animals for survival times, using factorial experiments.

  2. LITERATURE REVIEW

    The work of Sir Ronald A. Fisher of England (Fisher, 1942) is credited with the immense contribution to experimentation over several decades ago (Kempthorne, 1967). Up to the time that Fisher began his important work, estimation of population parameters and tests of hypotheses were performed by making assumptions as to the distribution of the unknown population parameters. Fisher argued that this approach was completely wrongheaded, and that the population parameters should be estimated from samples taken from the population (Kempthorne, 1942). This insight revolutionized the entire field of experimental analysis As a matter of fact, it was Fisher who originated most of the ideas used in modern experimental method (Box, Hunter and Hunter, 1978).

    In the late 1940s and early 1950s experimentation received another very large benefit when it began to merge with the quality movement that began taking root in Japan in this period. During this period the ideas of Deming had been largely rejected by American industrialists. However, Deming found that his ideas concerning quality were readily accepted by the Japanese, who were attempting to rebuild their industrial base after WW II and were interested in reducing costs to the greatest extent possible. Moreover, Japan did not have extensive natural resources, and was solicitous of eliminating as much waste as possible. With this situation prevailing, Deming's ideas readily took hold. At the time Deming began work with the Japanese, he had been using statistical methods to improve quality (Sutterfield and Kelly, 2005), and soon began teaching them Statistical Quality Control. The Japanese had already discovered that statistical methods could be employed for much more than monitoring and improving quality (Montgomery, 1991). At about the same time, such pioneers as Ishikawa (1952), Masuyama (1955, 1956) and Taguchi(1956a, 1956b) had begun to use such methods to facilitate scientific experimentation.

    In a third 1956 work, Taguchi published the original version of his monumental work on experimental method. Although many other Japanese scientists have made many substantial contributions to the field of experimental method, it is Taguchi, more than any other, who has advanced this area of science, and after whom the field has been named as "Taguchi Methods." Considering the immense success achieved by the Japanese using designed experiments, it is to be regretted that they have not been more widely used in the West (Montgomery, 1991).

    Although there are very significant differences between the classical approach to Design and Analysis of Experiments and the methods developed and practiced by Taguchi, it is not the purpose of this paper to discuss all of these. However, one chief difference is that Taguchi's method conceives of the data of an experimental arrangement as being related by some function. Although the function will probably be unknown, it nonetheless relates the data in some way and can therefore be described by a polynomial expansion about each of the experimental data points. The polynomials used are an orthogonal set, discovered by Chebyshev (Taguchi, 1988ab). These polynomials make it possible to evaluate first, second, third, etc., order components of variation in a given experimental factor. They also make it possible to evaluate interactions of factors at these levels. These same polynomials may also be used to form contrasts for comparing the effects of varying levels of...

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