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The Inspection Report for the SN-Ratio Optimum Prediction Accuracy of Taguchi two step design
Abstract
Taguchi showed to decrease the variation. with SN-ratio on 1984.
It was called Taguchi methods in USA. However, there were many estimation problems.
So, we investigated estimation accuracy by SN ratio to compare the optimum condition(b) and the experiment best (a) for case studies. Our expectation was a<b. However 62% cases were (a>b) . Taguchi way was the very poor estimation.
Hadamard orthogonal tables correspond to interactions in linear graphs. But it only represents part of the interaction. Mixed orthogonal arrays are highly confounding to the main effects of interactions. These experimental design methods capture the main effects, but cannot grasp the interaction. About 62% of the optimal conditions for the mixed system orthogonal array are below the best experimental no. value. This chapter proposes a method for selecting optimal conditions that considers both interactions and main effects. We compared the no. best value condition (a) and the best level condition (b) of the factor effect in the orthogonal array experiment and designed it assuming that the difference level factor was strongly related to the interaction and the common level factor to the main effect. The method is described in detail as [a, b] analysis.
Researchers use their accumulated knowledge as a base to create and embody new functions, improve the efficiency of existing mechanisms, and reduce the side effects of existing technologies. There is also the problem of global warming. A researcher tries to find a feasible combination of conditions from the conditions taken up. In this case, he wants to catch the overall optimum condition by partial experiments. It is an experimental design method. As a new experimental design method, we will introduce a method of applying the design matrices to the conference C matrices and analyzing it as a coefficient graph by regression analysis of the observed values. This chapter presents experimental procedures and analysis methods using actual cases. In addition, the method for adjusting the research goals from the analysis results is also presented.
When optimizing using an orthogonal array, it is desirable to consider the various relationships between factors and assign many factors. Two-level orthogonal array can be assigned many factors. Three-level orthogonal array has the advantage of obtaining intermediate information on the level. For this reason, mixed type orthogonal arrays L18 (2137), L36 (211313), etc. are still used today (Bose and Bush in Ann Mathe Stat 23:208–524, 1952). The response of these mixed type orthogonal arrays is logarithmically converted to the SN ratio and sensitivity for optimization. This way also is called Taguchi methods (Taguchi, 1984, 1988). Parameter design with a two-step procedure for predicting the optimum conditions is performed from this SN ratio and sensitivity with factor effect graph. However, this method has two problems (1) and (2).
The number of experiments will be increased proportional to the number of layout factors in the mixed type orthogonal array.
In the first step of reducing the variation, select the combination of the levels that maximum levels the SN ratio of the factor effect graph as the optimum condition.
The confirmation value (b) had been expected as the optimum condition with minimized variation. But, there are the problems that this confirmation value (b) is worse than the best value (a) of the SN ratio of the orthogonal array used for estimation will appear for 62% of cases (Mori, 2018, 2020). So, the prediction accuracy for the optimum conditions is poor. In order to improve these problems (1) and (2), this paper report will propose a new method to apply the conference matrices to the layout and the coefficient figure to the analysis to the row data. This report provides an easy-to-understand explanation that the conference matrices reduces the number of experiments and improves prediction accuracy using the coefficient of variation, especially for researchers. We are sure our proposed ways to reduce the experimental number and the period and cost almost to 1/3–1/2 with the higher accuracy for optimizing, so we will recommend as the specific ways to solve the subjects of the Sustainable Development Goals. Especially it will contribute to create the effective countermeasures to Global Warning that has been requested immediately to take the actions to reduce the increasing temperature.
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