Design factors Taguchi

If all the factors influencing the quality characteristic can be separated into two sets - a set product design factors and a set environmental factors - then the techniques used and promoted by Taguchi can be used to derive the desired properties. However, the situation described further in this chapter does not include a clear separation of factors into two sets the product design factors are also the noise factors, which means that the product design factors can be set to a certain mean value, but a certain random variation exists around this mean. 

It was discussed above that two types of factors can influence our process or system controlled factors design factors in Taguchi s terminology) and uncontrolled factors noise factors. The latter are inherent to the experimentation and can only be estimated by replication of runs. If the variability between replications is too large, any conclusion drawn from our study may have no meaning at all. Further, their variability can be as important as the mean of the replicates. Noise factors must be identified properly and, if possible, simulated in our experimentation. Sometimes noise factors are actually uncontrolled and, in such a case, we must be able to simulate them by means of some alternative parameter controlled during the experiments. For instance, temperature inside an oven can be a noise factor, but we can measure it at different locations, and accordingly, the effect of temperature inside is simulated by a location factor. 

The analysis of the mean response and the s/n ratio can be performed employing the usual ANOVA and/or hypothesis tests to detect which factors or interactions have statistical significance. Taguchi proposed a conceptual approach based on the graphical display of the effects (they are called factor plots or marginal means followed by a qualitative evaluation. This provides objective information and a test for the significance of each design factor on the two observed responses mean and s/n ratio. 

Figure 2.7 Pareto s ANOVA table to assess the statistical significance of design factors according to Taguchi.

For the larger-the-bettef and smaller-the-bettef cases, Taguchi suggested identifying the optimal levels of the design factors or just maximising the corresponding s/n ratio. 

We now consider factorial experiments in which there is no replication of design factor combinations and no use of noise factors. The idea of identifying dispersion effects in unreplicated factorials again has roots in the work of Taguchi. It was first studied in detail by Box and Meyer (1986) and has since attracted considerable interest and research. 

Rather than rely on chance variation of the noise factors, Taguchi (1) proposes that at each point of an experimental design set up to study the control factors the noise factors are also allowed to vary following an experimental design. Suppose, for example, there are two control factors F and Fj and two noise factors, F, and F4. For each of the noise factors choose two real but extreme levels. One may then construct a factorial design 2 with the control factors and repeat each of the 4 experiments using each possible combination of levels of the noise factors, Fj, F4. We thus obtain the design of table 7.5. 

Taguchi also suggested using orthogonal array in the design of experiments to find out the influence of various factors. There are two types of factors influencing the product quality—controllable (or design) factors and uncontrollable (or noise) factors. The controllable factors can be easily identified and adjusted. On the other... 

It was discussed above that two types of factor can influence our process or system controlled factors ( design factors in Taguchi s terminology) and uncontrolled factors ( noise factors ). The latter are inherent to the... 

The performance of complex engineering systems and quality of products or processes generally depend on many factors. Taguchi separates these factors into two main groups control factors and noise factors (Ross (1988)). Control factors are those which are set by the designers or manufacturers noise factors are those over which the designers or manufacturers have no direct control but which vary in the environment of the system or product (Phadke (1989)). 

Taguchi uses fractional factorial designs to determine the first-order effects of both the control factors and the noise factors, but he separates the factors and the designs into an inner array (involving the control factors only) and an outer array (involving the noise factors only). The concept is shown geometrically in Figure 14.8 for three control factors and three noise factors. 

Thus, not only will this design estimate all of the linear and quadratic terms and interactions between the design and the environmental variables, but it will also estimate all of the two-factor interactions among the design variables and among the environmental variables. It will accomplish this in only (26 + runs, compared with the 81 runs for the Taguchi design that yields less information. 

The drawback of Taguchi designs is the relatively large number of experiments to perform. No case studies that optimize factors and at the same time test their ruggedness towards noise factors in the field of analytical chemistry are known to us. 

The Taguchi method uses a particular experimental design, the goal of which is to select those settings of the design variables, which give optimal results for the performance of a product. More over, those settings of the noise factors are selected, that have minimal effects on the performance of the product. 

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