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Doe Taguchi Design

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9/25/2015
9/25/2015
Priyanka Palamuru
SCSU
Priyanka Palamuru
SCSU
Design of Experiment on a Catapult

Taguchi Design
Design of Experiment on a Catapult

Taguchi Design

Objective
The objective of this project is to analyze the effect of various factors controlling the catapult model using Design of experiments (DOE).
Design : Taguchi
Software : Minitab17

Introduction Design of experiments (DOE) is a method of finding the important and less important factors involved in an experiment through a number of steps such as information gathering and mathematical calculations either manually or using a software. It is considered as one of the accurate techniques and widely used in various fields such as engineering, healthcare, education, etc. It is also known for its quality improvement, efficiency, cost and effectiveness. Catapult experiment is generally used to demonstrate DOE as it has the simplest setup and meets the requirements for this method.

Taguchi Design 1. Define the process objective i.e. whether we need the output to be maximum or nominal or smaller. In this experiment, it is given as nominal the best. 2. Determine the factors which affect the outcome and number of levels the factors can vary for performing the experiment. Here, the factors are Start angle, Stop position, Cup Position and Peg position and has three levels each. 3. Select the suitable orthogonal array based on number of factors and levels, prepare a table with number of experiments and conditions to perform the experiment. 4. Conduct the experiments by changing the conditions as in the completed table above to collect the data, noting a minimum of 3 readings for each row. 5. Calculate SNR, ANOM and ANOVA to determine the effect of different factors on performance.
Minitab
Minitab is a statistics package used to implement many quality improvement methods. These days, Minitab is used in conjunction with the implementation of Six sigma, CMMI and other statistics-based process improvement methods.
Source: Wiki

Data Collection

Factors in the catapult experiment are 1. Start angle 2. Stop position 3. Cup position 4. Peg position

Levels to be considered are FACTOR | LEVEL 1 | LEVEL 2 | LEVEL 3 | Start angle | 140 | 160 | 180 | Stop position | 3 | 4 | 6 | Cup position | 1 | 3 | 2 | Peg position | 1 | 2 | 3 |

To select the suitable orthogonal array, degrees of freedom needs to be calculated. DOF = No of factors × (No of levels -1) + 1 = 4 (3-1) + 1 = 9 L9 will be the best option from above table for 4 factors at 3 levels. However, if we want to perform more experiments, L18 and above rows can be chosen.

L9 orthogonal array:

Substituting the values to be used in the experiment:

Start angle | Stop position | Cup position | Peg position | 140 | 3 | 1 | 1 | 140 | 4 | 3 | 2 | 140 | 6 | 2 | 3 | 160 | 3 | 3 | 3 | 160 | 4 | 2 | 1 | 160 | 6 | 1 | 2 | 180 | 3 | 2 | 2 | 180 | 4 | 1 | 3 | 180 | 6 | 3 | 1 |

Each row conditions are setup, experiment is carried out 3 times and yields are noted. Start angle | Stop position | Cup position | Peg position | Yield1 | Yield2 | Yield3 | 140 | 3 | 1 | 1 | 41 | 36 | 39 | 140 | 4 | 3 | 2 | 37 | 36 | 37 | 140 | 6 | 2 | 3 | 28 | 27 | 27.5 | 160 | 3 | 3 | 3 | 38 | 37.5 | 39 | 160 | 4 | 2 | 1 | 67 | 67 | 62 | 160 | 6 | 1 | 2 | 47 | 46 | 46 | 180 | 3 | 2 | 2 | 81 | 77 | 79 | 180 | 4 | 1 | 3 | 72 | 71.5 | 69 | 180 | 6 | 3 | 1 | 68 | 62 | 65 |

Now, the experimental results are entered in the Minitab software and Taguchi design is selected for obtaining SNR, Means, Standard deviation, ANOVA, contour plots, surface plots, interaction plots etc.

Results from Minitab Start angle | Stop position | Cup position | Peg position | Yield1 | Yield2 | Yield3 | SNRA1 | STDE1 | MEAN1 | 140 | 3 | 1 | 1 | 41 | 36 | 39 | 23.730 | 2.5166 | 38.667 | 140 | 4 | 3 | 2 | 37 | 36 | 37 | 36.057 | 0.5774 | 36.667 | 140 | 6 | 2 | 3 | 28 | 27 | 27.5 | 34.807 | 0.5000 | 27.500 | 160 | 3 | 3 | 3 | 38 | 37.5 | 39 | 33.975 | 0.7638 | 38.167 | 160 | 4 | 2 | 1 | 67 | 67 | 62 | 27.095 | 2.8868 | 65.333 | 160 | 6 | 1 | 2 | 47 | 46 | 46 | 38.089 | 0.5774 | 46.333 | 180 | 3 | 2 | 2 | 81 | 77 | 79 | 31.932 | 2.0000 | 79.000 | 180 | 4 | 1 | 3 | 72 | 71.5 | 69 | 32.883 | 1.6073 | 70.833 | 180 | 6 | 3 | 1 | 68 | 62 | 65 | 26.716 | 3.0000 | 65.000 |

ANOM:
Taguchi Analysis: Yield 1, Yield 2, ... versus Start Angle, Stop Positio, ...

Response Table for Signal to Noise Ratios
Nominal is best (10×Log10(Ybar^2/s^2))

Start Stop Cup Peg
Level Angle Position Position Position
1 31.53 29.88 31.57 25.85
2 33.05 32.01 31.28 35.36
3 30.51 33.20 32.25 33.89
Delta 2.54 3.33 0.97 9.51
Rank 3 2 4 1

Response Table for Means

Start Stop Cup Peg
Level Angle Position Position Position
1 34.28 51.94 51.94 56.33
2 49.94 57.61 57.28 54.00
3 71.61 46.28 46.61 45.50
Delta 37.33 11.33 10.67 10.83
Rank 1 2 4 3

Response Table for Standard Deviations

Start Stop Cup Peg
Level Angle Position Position Position
1 1.1980 1.7601 1.5671 2.8011
2 1.4093 1.6905 1.7956 1.0516
3 2.2024 1.3591 1.4470 0.9570
Delta 1.0044 0.4010 0.3485 1.8441
Rank 2 3 4 1

Main effects plot for SNRs, Means and Standard deviations

From the Main effects plot for SNRs graph, ideal conditions for nominal the best objective are observed as
Start angle 160
Stop position 6
Cup position 3
Peg position 2

ANOVA
General Linear Model: SNRA1 versus Start Angle, Stop Position, Cup Position, Peg Position

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value Start Angle 2 9.821 4.9106 * * Stop Position 2 17.026 8.5130 * * Cup Position 2 1.491 0.7457 * * Peg Position 2 157.310 78.6552 * *
Error 0 * *
Total 8 185.649

As cup position and start angle can be considered as noise, above table from Minitab can be modified as below Factor | Degrees of Freedom | Sum of squares | Mean squares | F | Start angle | 2 | 9.821 | 4.911 | 1.737 | Stop position | 2 | 17.026 | 8.513 | 3.010 | Cup position | 2 | 1.491 | 0.746 | 0.264 | Peg position | 2 | 157.310 | 78.655 | 27.892 | Error | 0 | 0 | | | Total | 8 | 185.649 | | | (Error) | (4) | (11.312) | (2.828) | |
Interpretation of F value in Taguchi
F < 1, Factor effect is smaller
F > 2, Factor is not quite small
F > 4, Factor effect is quite large

Contour plot

Surface plot

Interaction plot

Predicted Taguchi results
The best conditions for our objective drawn from the graphs above are substituted in the Predict Taguchi results option available in Minitab. PSNRA1 | PMEAN1 | PSTDE1 | PLSTD1 | 38.7706 | 41 | 0.457309 | -0.738753 |

Conclusion
Design of Experiment on a Catapult is conducted and results are obtained using Taguchi method.

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...UNIVERSITAS INDONESIA SIX SIGMA MAKALAH diajukan sebagai salah satu tugas mata kuliah Manajemen Kualitas Terpadu yang diampu oleh Bapak Dr. Ir. Rahmat Nurcahyo, M.Eng.Sc. NAMA : TRISNA YUNIARTI NPM : 1406507114 FAKULTAS TEKNIK DEPARTEMEN TEKNIK INDUSTRI UNIVERSITAS INDONESIA 2014 KATA PENGANTAR Alhamdulillah atas kehadirat Allah SWT karena berkat segala rahmat dan hidayah-Nya sehingga penulis dapat menyelesaikan tugas makalah ini dengan baik. Makalah ini merupakan salah satu tugas mata kuliah Manajemen Kualitas Terpadu yang membahas mengenai Six Sigma baik itu sejarahnya, konsep Six Sigma, tahapan, tools yang digunakan dalam six sigma, serta contoh studi kasus. Akhir kata semoga makalah ini bisa bermanfaat bagi pembaca pada umumnya dan penulis pada khususnya. Penulis menyadari bahwa dalam pembuatan makalah ini masih ada kekurangan untuk itu penulis menerima saran dan kritik yang bersifat membangun demi perbaikan kearah kesempurnaan. Akhir kata penulis sampaikan terima kasih. Penulis, Trisna Yuniarti ABSTRAK Metodologi Six sigma untuk peningkatan kualitas adalah sebuah sistem yang banyak konsep, tools, dan prinsip-prinsip yang dapat membantu perusahaan fokus pada pengembangan dan membuat produk dan layanan yang mendekati sangat sempurna. Hal itu berdasarkan pekerjaan statistik Joseph Juran, seorang Rumania yang lahir di US sebagai perintis manajemen mutu. Kata Sigma adalah huruf Yunani yang digunakan untuk area statistik yang mengukur...

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Total Quality Management

...part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Marina Jozipovic Typesetting InTech Prepress, Novi Sad Cover InTech Design Team First published July, 2012 Printed in Croatia A free online edition of...

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