# Recipes for the Design of Experiments/Chapter 10: Taguchi Designs

The dataset under analysis includes data on vehicles collected by the Environmental Protection Agency (EPA) from 1984 to 2015. Using Taguchi design methods, the experiment tests which of 5 factors contribute significantly to the response variable, highway gas mileage. Due to the nature of Taguchi experimental designs, the predictor variables are reduced to a minimal number of levels in order to select an appropriate orthogonal array. Signal to Noise ratios are calculated, according to a higher-is-better mentality, for each experimental run in the orthogonal array in order to determine the optimal factor assignments that maximize the response. Analysis of Variance is used on both the full factorial design (as a baseline) and on the Taguchi fractionalized design to understand if the results of both designs are commensurate. ^{[1]}

This recipe for the design of experiments analyzes survey data obtained by the United States EPA regarding certain factors and their effects on vehicle gas mileage. The experimental analysis looks at five different factors and their effects on the vehicle's highway gas mileage. I use a Taguchi design approach to create an orthogonal array of a fraction design of the data set to analyze the data as well. ^{[2]}

This recipe will analyze the effects of the 5 factors on the wind speed (mph) of the storm. An ANOVA will be used to determine the main effects of the "Year," "Month," "Day," "Hour," and "Type" on a storm's wind speed. Modifications were made to the original data set to produce simplified levels for each factor. The null hypothesis is that the variation within any of these factors will have no effect on the variation in wind speed. Afterwards a parameter design will be selected to construct a Taguchi QLF and create a Taguchi orthogonal array. A second ANOVA will be run using this array to observe any differences in the statistical results. <http://rpubs.com/maxwinkelman/46969>

This recipe uses fuel economy data from the environmental protection agency. It was collected on vehicles made between 1984 and 2015 and includes things like drive type, fuel type, engine statistics and more. Aside from using a traditional ANOVA we use a Taguchi design with 5 factors and create an orthogonal array to analyze the data and the effect of the 5 factors on the response variable of highway mileage. ^{[3]}

The following analysis was completed as the result of vehicle testing done at the Environmental Protection Agency's National Vehicle and Fuel Emissions laboratory in Ann Arbor, Michigan. Five different factors were of interest: year that the car was built, fuel type, drive type, number of cylinders, and make of the car. The response variable of interest was city gas mileage (mpg). After an initial ANOVA was completed, a Taguchi design was used to find which combination of factors and levels resulted in the highest S/N ratio.
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This experiment uses a Taguchi Design to study the effect of 5 factors/independent variables on a vehicle’s city mileage.It is a 2 phase experiment in which we first analyze the effect of the factors on the response using multivariate ANOVA. In the second phase we generate an orthogonal array based on the new dataset that we create (of limited number of levels) and then perform ANOVA on the new dataset/array.The Research Question: Study the effect of 5 factors (Transmission,drive,year,fuel and make) on the city mileage of a vehicle (response variable). In order to study this problem we can formulate the null hypothesis as: ‘The variance in the type of transmission, the type of drive, the year of manufacture,the fuel type and the make of vehicle (taken separately-main effect) has no significant impact on the variance in city mileage’. The analysis can be accessed at:http://rpubs.com/Uzma_1004/47025

This analysis is from 'fueleconomy' package, using Taguchi design to study how 5 selected factors influence vehicles' city fuel economy. Selected factors are model year (year), drive train (drive), vehicle size class (class), fuel type (fuel) and number of cylinders (cyl). Before experiment design, we first categorize each factors into 3 or 4 levels, followed by exploratory analysis, initial ANOVA, Taguchi design and model adequacy checking. It turns out under conditions provided, there is one optimized combination, which also correspons our common sense. In other word, this analysis turns out to be both statistically significant and practically significant. However, I think Taguchi method still has its limitation in this case, and I mentioned it at the last part of my recipe_Hongyu Chen http://rpubs.com/chenh16/47039

This experiment is looking at the fueleconomy data set to perform a Taguchi design.This method is used to model and analyze problems to help improve quality. We are looking at how the variation in the city mileage is affected by Make, Class, Cyl, Displ, and Fuel. http://rpubs.com/tranc3/47151

This analysis uses a Taguchi Design to study the effect of 5 factors on vehicles' highway fuel economy. The experiment is conducted in two stages: in stage 1, an ANOVA is conduced to exam to effects of the five selected variables on the vehicle highway fuel economy; in stage 2, a Taguchi design is used to construct an orthogonal array, the array is then used to obtain the optimum and to replicate the estimates in stage 1. The result shows that Taguchi design method is an efficient way to find the optimum solution, however, researchers should pay attention to the significant drop in sample size, which may limit the analysis results. ^{[5]}

The following recipe is an analysis on the fuel economy dataset. Five different factors were of interest: year that the car was built, fuel type, drive type, number of cylinders, and make of the car. The response variable of interest was highway gas mileage (mpg). After an initial ANOVA was completed, a Taguchi design was used to find which combination of factors and levels resulted in the highest Signal-to-Noise ratio. - Matthew Macchi http://rpubs.com/macchm/47180

In this study that uses fuel economy data collected by the EPA from 1985-2015, a five-factor, multi-level experiment is performed to see if the make, the drive type, the fuel type, the production year, or the transmission of a vehicle (which are the five factors being considered in this analysis) has a statistically significant effect on the city fuel economy (in miles per gallon, 'mpg') of that vehicle (which is the response variable in this analysis). An analysis of variance (ANOVA) is performed as a means for determining the significance of these factors with regard to the response variable 'cty', and Taguchi Design Methods are used to create an orthogonal array that is used to further determine the significance of the factors included in this experiment.^{[6]}

In the following recipe, a dataset from the fueleconomy package is examined. Specifically, the vehicles data is used to see the effects of 5 factors, make, class, transmission, drive and fuel type of each car on the car's average highway mileage (in mpg). After initial statistical analysis is performed, an ANOVA model is created. Next, a Taguchi Design is created to find which factor-level combinations lead to the highest highway mileage, identified by the combination with the highest signal to noise ratio. Finally, the model adequacy is checked and contingencies are discussed. ^{[7]}

**Place 2016 ISYE 6020 reports here:**

**Mike D.** Following an earlier analysis on top Reddit posts from three popular subreddits (r/science, r/politics, r/news) with a 2^(6-3) fractional factorial design, this report takes the same Reddit dataset and performs a Taguchi Design using the qualityTools package in R. Exploratory analysis of the full dataset pointed to some differences between factors, however upon constructing a linear model and performing ANOVA based on an 8-run Taguchi Design it was found that none of the main effects were statistically significant. Explanations based on the limitations to highly fractional design are provided and the Taguchi method is compared to the Fractional Factorial Design method. ^{[8]}

**Mike W.** Following the fractional factorial analysis of the impact of certain factors on the number of doctors' office visits of patients, a Taguchi design is carried out on the same factors utilizing the same design style of 2^(6-3). The results of the Taguchi analysis showed more significance of factors than the FFD, indicating that all factors had some level of statistical significance in the final model. Comparisons are provided and thoughts on the Taguchi generated model are provided. ^{[9]}

**Molly R.** The experiment continues the analysis done in Project 3 (Fractional Factorial Designs) with a Taguchi experimental design. For a 2^6 experiment of health insurance data from the 'Ecdat' package, eight experimental runs were performed. A linear model was created, and an analysis of variance was performed. Unlike the fractional factorial experiment, none of the factors were significant. This could be a result of so few experimental runs, or due to the fact that the data was not normally distributed. Further analysis could be done to fit a non-linear model, or apply a different type of experimental design ^{[10]}.

**Kaan U.** Ecdat - House dataset re-analyzed in this study with Taguchi Designs and findings compared with previously conducted Fractional Factorial Designs. Two different taguchi design arrays were used. First, similar to our course examples L9_3 (three-level factors) array is used, all two level factors modified to three-levels and after during ANOVA analysis two-levels considered. Secondly: L8_2 (two level factors) array experiment conducted for observing the differences. All results of these analysis and previous FFD results compared and additionally full data.set analysis are presented. ^{[11]}

**Trilce** In this report evaluates data about air quality data from California metropolitan areas, to assess the impacts of socioeconomic and geographic characteristics on air pollution in the areas. In this follow up study, Taguchi experimental design is developed to estimate the effects of various covariates. ^{[12]}

**Alexis Z.** This experiment studies the effect of mothers smoking, baby gender, baby race, and weeks of gestation on birth weight. This study compares appropriateness of using a Taguchi Design vs. a 1/8 Fractional Factorial Design. That Taguchi Design was choosen (L8_2), and data was randomly selected from the dataset for Taguchi Analysis. The main effects were calculated, and mother smoking and weeks of gestation were chosen for the linear model. ANOVA was used to study whether explained variance > unexplained variance. The study culminated with model adequacy checking. Ultimately, it was decided that a fractional factorial design is a more appropriate design strategy for analysis of this dataset ^{[13]}.

**Yage D.** This experiment studies how blue collar workers' gender, color, age, and years of tenure in job lost affect the state unemployment rate. As factors color and gender have 2 levels, factors age and years of tenure in job lost have 3 levels. Taguchi design is used in the design of this experiment. For economic purposes, all factors are first transformed to 2-level factors. We then identified the desired effects for the design by computing exploratory main effects and ANOVA with the original data set. We can only estimate all main effects, with 8 experimental runs. As the result of ANOVA suggests, none of the main effects can explain the variations the state unemployment rate. Dataset used to conduct the experiment is from the R package "Ecdat". ^{[14]}.

**Clare D.** This recipe examines the influence of four factors on an inmate's sentence length in federal or state prison. Two of the factors have 2 levels and the other two have 3 levels. To reduce the number of experimental runs, the two 3 level factors were each decomposed into two 2 level factors. This produced an experiment with a total of 6 factors each with 2 levels. A Taguchi design was chosen for this experiment to compute the main effects of the factors and to evaluate the effectiveness of a Taguchi design in this setting. Results from the experiment were compared to an ANOVA test on the full data set of prison data as well as the results of a fractional factorial design using the same data set and the same number of runs. ^{[15]}

**Felipe O.** The recipe looks at the formulation of a Taguchi design, and comparing it to the previously formulated fractional factorial design. Using data collected to run a full factorial experiment on what factors affect the color change in clothes after being washed, a fractional factorial experiment was formed. These include type of soil, fabric, wash temperature, and whether the detergent is surfactant or not. The 3-level factors were converted into 2-level factors, and results were obtained from the new fractional design.</ref>http://rpubs.com/ortizf2/235869</ref>

**Munira S.** The recipe looks at the formulation of a Taguchi design and compares it to a previously developed fractional factorial design. The data set of interest was the Males data set from the Ecdat package in R. An L8_2 Taguchi design was utilized with 8 experimental runs. No main effects were found by utilizing the Taguchi design in contrast to the fractional factorial design. As a result, fractional factorial design was a more appropriate choice for the Males data set. ^{[16]}

**Andreas V.** Project 4 uses Taguchi Design to compare results from Project 3 (Fractional Factorial Design). In it, 8 experimental replications are used adhering to 'L8_2' design, which offers study efficiency. Main effects are calculated and plotted, and compared to the findings from Project 3. The same data-set is used, which contains factors related to traffic incident fatality rates and alcohol consumption, a well as laws prohibiting drunk driving. ^{[17]}

**Liang Z** In this project, we use Taguchi Design and compare the results with those in Project 3 (Fractional Factorial Design). The data used in this experiment is Housing dataset from Ecdat package in R. L8_2 Taguchi Design is performed in this project, and the main fact is analyzed. We do not find that main effects show significance in our experiment. However, in the full factorial design, all these factors are significant. So we need to take this risk into account when we use Taguchi Design. ^{[18]}

**Shamus W** This project uses a Taguchi design and compares the results with those from the fractional factorial design used in Project #3. The data being used in the experiment is the Cars93 dataset from the Ecdat package. For this experiment, we are interested in the effect of 4 factors, two 2-level factors and two 3-level, on the price of the vehicle. The factors observed airbags, drive train, transmission type, and origin of the vehicle. The 3-level factors were deconstructed into 2-level factors. An L8_2 Taguchi design was chosen to examine the main effects. ^{[19]}

**Bok, Joonhyuk** Among a dataset from the Ecdat R Package, we select “Mathlevel” which would be useful for expecting SAT Math Score. In Mathlevel data, ‘language’, ‘sex’, ‘physiccourse’ and ‘chemistcourse’ are selected as factors, which could explain the result of SAT Math Score and have 2 levels, 2 levels, 3 levels and 3 levels respectively. And 'sat’ is chosen as a response variable. A Taguchi design allows the reduction of the total runs, while still allowing the computation of main effects. To make the design simpler, the factors with 3 levels will be decomposed into factors with 2-level for calculating the required data needed to obtain appropriate data. For these, the sum of the variables with 2 levels will yield the value with 3 levels. After conducting the Taguchi design and comparing it with the Fractional Factorial Design, we can find out that the results of the two experiments are greatly different although they make use of the same dataset. After the results of the ANOVA test conducted on the full dataset, we learn that the Taguchi model gives a better estimate of the main effects than the Fractional Factorial Design. ^{[20]}

**Diana R** Taguchi Designs are experimental designs made to ensure desired or "optimal" performance, mainly on product and process design. This tool was explored for behavioral study developed on Depression Index for the Youth Population. The data used was part of a study entitled “Gender, Mental Illness and Crime in the United States” developed by Melissa Thompson as part of the Inter-university Consortium for Political and Social Research [2]. This database is composed of 55,602 respondents from the National Household Survey on Drug Use and Health (NSDUH) in 2004. Results of Taguchi Designed experiments were compared to Fractional Factorial Experiments and the results were compared to the general database results. ^{[21]}

**Prasanna D** Studied the effect of two 2-level factors (sex of head of household and whether the household is in urban area) and two 3-level factors (age of the head of the household and size of the household) on the total household expenditure of Vietnamese households. The dataset was obtained from Ecdat package. The study was performed using 2^6 Taguchi design by converting each of the 3-level factors into two 2-level factors. ^{[22]}

- ↑ Trevor Manzanares http://rpubs.com/manzat/46562
- ↑ http://rpubs.com/adamato/46964
- ↑ http://rpubs.com/Tothk2/Recipe10
- ↑ http://rpubs.com/braunj6/47021
- ↑ Wei Zou http://rpubs.com/serena049/47168
- ↑ http://rpubs.com/howelb/47229 - Brendan Howell
- ↑ Ali Svoboda- http://rpubs.com/svoboa/47328
- ↑ Mike D. - http://rpubs.com/deagem/taguchi
- ↑ Mike W. - http://rpubs.com/mtwassick/235326
- ↑ Molly R. http://rpubs.com/molly_ren/isye6020project4
- ↑ Kaan U - http://rpubs.com/unnuk/235404
- ↑ http://rpubs.com/trilcemarie/DoE_P04
- ↑ http://rpubs.com/ziemba/235686
- ↑ Yage D. - http://rpubs.com/dingy2/235610
- ↑ Clare D - http://rpubs.com/cadorsey/235850
- ↑ Munira S. -http://rpubs.com/mjshahir/235873
- ↑ Andreas V. http://rpubs.com/byeonb/235707
- ↑ Liang Z http://rpubs.com/zhaol11/235434
- ↑ Shamus W http://rpubs.com/shamuswheeler/project4
- ↑ Bok, Joonhyuk http://rpubs.com/bokjh3/235849
- ↑ Diana R http://rpubs.com/dgramirez82/proj4Taguchi
- ↑ Prasanna D http://rpubs.com/prasanna_date/236025