# Design And Analysis Of Experiments Ppt

Design And Analysis Of Experiments Ppt – What is DOE? Purpose of the DOE? Select design (eg Box-Behnhen) Principle of the chosen design How does it work? How do you calculate? Conclusion

3 Design of experiments Factorial design Regression analysis Mathematical model Statistical model Response surface methodology Centrally composed Box-Behnhen design Plackett-Burmann model etc.

## Design And Analysis Of Experiments Ppt

DOE is a formal mathematical method for systematically designing and conducting scientific studies that collectively change experimental variables to determine their effect on a given response. DOE makes controlled changes to input variables to obtain maximum amounts of cause-and-effect relationship information with minimum sample size.

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DOE is more efficient than a standard approach of changing “one variable at a time” to observe the variable’s effect on a given response. The DOE generates information about the effects of various factors on a response variable and, in some cases, can determine the optimal settings for those factors.

1. The design of the experiment, 2. The collection of the data, 3. The statistical analysis of the data, and 4. The conclusions and recommendations drawn from the experiment.

9 Draw conclusions/conclusions about the results based on the results of the analysis, interpret the physical meaning of these results, determine the practical significance of the results and make recommendations for a course of action, including further experiments

10 EXAMPLE: CONCLUSIONS In statistical language, one would conclude that ob is not statistically significant at the 5% significance level since the p-value is greater than 5% (0.05).

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11 2k DESIGNS (k > 2) As the number of factors increases, the number of runs required to perform a fully factorial experiment increases dramatically. The following 2k design layout shows the number of passes required for k values ​​from 2 to 5. For example, if k = 5, then 25 = 32 trial runs are required for the full factorial experiment.

13 2k DESIGNS (k > 2) For example, if there are no significant interactions, you can estimate an answer using the following formula. (only for quantitative factors)

In order for this website to function, we log user data and pass it on to processors. To use this website, you must agree to our privacy policy, including the cookie policy.Dr. Tai-Yue Wang Department of Industrial and Information Management National Cheng Kung University Tainan, TAIWAN, ROC This is a basic course bla bla bla…

Department of Industrial and Information Management National Cheng Kung University Tainan, TAIWAN, ROC This is a basic course bla bla bla…

### Science Lab Powerpoint Presentation Slides

An experiment is a test or series of tests Experiments are commonly used in the engineering world Process characterization and optimization Evaluation of material properties Product design and development Determination of component and system tolerance “All experiments are designed experiments, some poorly designed, some well designed – designed”

Experimentation is an essential part of scientific (or engineering) methods. With each experiment, the following questions arise: Are only these methods available? Are there other factors that can influence the results? How many samples are needed for the experiment? How should the samples be assigned to the individual experiments?

In what order should the data be collected? Which method of data analysis should be used? What difference in the average observed results between method, material, machines, …?

In general, experiments are used to study the process and systems. The system or process can be represented by the following figure. The process can be the combination of operations, machines, methods, people and other resources (often materials) that convert an input into an output that has one or more observable response variables, y.

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Some process variables and material properties, x1, …, xp are adjustable. Some are not verifiable (although they may be verifiable for testing purposes).

The goals of the experiment may include: To determine which variables have the most influence on the response y To determine where to place the influential x’s so that y is almost always close to the desired nominal value. Determine where to place the influential x’s so that the variability in y is small. Determine where to place the influential x’s to minimize the effects of the uncontrollable variables z1,…,zq.

Golf example – Factor affecting score Driver – Extra large or regular ball – Balata or three-part motor skills – Walking or golf cart driving Drinking – Water or beer……

“Best Guess” Experiments Commonly Used More Successful Than You Might Think, But There Are Drawbacks… One-Factor-at-a-Time (OFAT) Experiments Sometimes Linked To The “Scientific” Or “Technical” Method By ground interaction destroyed, also very inefficient

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16 Factorial Design(1/4) In a factorial experiment, all possible combinations of factor levels are tested. The golf experiment: type of driver, type of ball that runs vs. drive type drink time of round weather type golf spike etc, etc, etc…

Improve process yield. Reduce variability and better match nominal or intended requirements. Reduce development time. Reduce overall costs. Evaluate and compare basic design configurations

Randomization Randomize the trials in an experiment Propose balancing effects of “lurking” variables Replication Sample size (improve effect estimation accuracy, estimation errors, or background noise) Replication versus replica measurements?

Replication Replication reflects sources of variability, both between runs and within runs. Examples of repeated measurements A wafer is measured three times. Four wafers are processed and measured simultaneously

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Blocking Dealing with confounders A block is a certain level of confounders. A complete repetition of the basic test is performed in each block. A block represents a constraint on randomization. All runs within a block are randomized

Identification and presentation of the problem Selecting factors, levels and ranges Selecting the response variable(s) Selecting the design Conducting the experiment Statistical analysis Drawing conclusions, recommendations

Start early with statistical thinking Your non-statistical knowledge is critical to success Pre-experimental planning (steps 1-3) critically Think and experiment sequentially (use the KISS principle (Keep it Simple, Stupid)) See Coleman & Montgomery (1993 ) Technometrics paper + additional text material

The agricultural origins, 1908-1940s W.S. Gossett and the t-test (1908) R. A. Fisher and his collaborators Profound implications for agricultural science Factorial designs, ANOVA The first industrial age, 1951 – late 1970s Box & Wilson, Response Surfaces Applications in chemical and process industries

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The second industrial era, late 1970s – 1990s Quality improvement initiatives in many companies Taguchi and robust parameter design, process robustness The modern era, starting around 1990

In order for this website to function, we log user data and pass it on to processors. To use this website, you must agree to our privacy policy, including the cookie policy. Course Objectives and Assumptions A Brief History of DOE The Strategy of Experimentation Some Basic Principles and Terminology Guidelines for Designing, Conducting, and Analyzing Experiments D. Arku DOE Course 2

Have heard a first course in STAT306, know normal distribution, know mean and variance, have performed or heard of regression analysis, know or have heard of ANOVA, have knowledge of SPSS, have not heard of designs with fractions, factorials, etc. D Arku DOE course 3

Sir Ronald A. Fisher – Pioneer invented ANOVA and used statistics in experimental design while working at Rothamsted Agricultural Experiment Station, London, England. George E. P. Box – married Fischer’s still active daughter (86 years old) developed the Response Surface methodology (1951) as well as many other contributions to s44tatistics Other Raymond Myers, J. S. Hunter, W. G. Hunter, Yates, Montgomery, Finney etc. DOE course 4

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R. A. Fisher and collaborators Profound implications for agricultural science Factorial designs, ANOVA The first industrial era, 1951 – late 1970s Box & Wilson, Response Surfaces Applications in chemical and process industries The second industrial era, late 1970s – 1990s Quality improvement initiatives in many companies Taguchi and robust parameter design, process robustness The modern era, starting around 1990 Widespread use of computer technology in DOE Extensive use of DOE in Six-Sigma and in business Use of DOE in computer experimentation D. Arku DOE course 5

6 References DG Montgomery (2008): Design and Analysis of Experiments, 7th Edition, John Wiley and Sons, one of the best books out there. Uses Design Expert software for illustrations. Uses letters for factors. Box GP, Hunter WG and Hunter JS (2005) Statistics for Experimenters: An Introduction to Design, Data Analysis and Model Building, John Wiley and Sons. 2nd Edition Classic text with many examples. No computer-aided solutions. Uses numbers for factors. Journal of Quality Technology, Technometrics, American Statistician, Technical Journals D. Arku DOE Course 6

Experiment – a test or series of tests where intentional changes are made to a system’s input variables or factors so that we can observe and identify the reasons for changes in the output response(s). Question: 5 factors and 2 answers You want to know how each factor influences the answer and how the factors can interact. You want to predict the responses for certain levels of the factors – e.g. maximize Y1 but minimize Y2. Time and budget allocated for only 30 test runs. DO course 7e

Best Gambling Approach (trial and error)

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