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# Design of experiments

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Implementing Taguchi screening designs in product development …

Implementing Taguchi screening designs in product development

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• 1. Design of Experiments – Screening Designs Implementing Taguchi screening designs in product development Beth Pavlik 12.18.12Farm Design, Inc. Experimental Design
• 2. Keywords • Experimental Design (also known as Design of Experiments or often just DOE): purposeful changes of the inputs to a process in order to observe the corresponding changes in the outputs • Screening Design: A preliminary experiment (usually on the order of tens of tests) to determine the main factors (variables) affecting the mean • Taguchi method: A set of screening designs used to identify factors that affect mean and variation in the outputs Experimental Design Fractional Factorial Screening Designs Full Factorial Taguchi MethodFarm Design, Inc. Experimental Design Page 2
• 3. Comparison between common methods Full Factorial Taguchi Screening Design All combinations of variables and levels tested A fraction of full factorial tests run, usually either 8, 18, or 27 configurations Variables: Design factors, inputs into the test matrix Levels: Variations of each variable, ex. Variable is mass, levels are 2g and 10g. Advantages: Advantages: • No aliasing concerns: all main factors and all • Identifies robust design (when noise variables interactions can be evaluated are identified) • Always orthogonal • Usually orthogonal • Obtains a large amount of data using a minimum number of resources Disadvantages: Disadvantages: • Cost • Confounding variables / Aliasing: lose • Time information on some or all interactions • Resources Helpful if you want to completely characterize Helpful if you want to identify factors that the performance maximize/minimize performanceFarm Design, Inc. Experimental Design Page 3
• 4. Screening Design Types – Why Taguchi? Purpose: Help you identify the main factors affecting the output using minimal resources Most screening designs are of Resolution III: Resolution III is a type of fractional factorial that is typically used when screening a large number of factors to find only the most important factors for future experimentation. Very little interaction information exists, if any. Some examples are: Plackett-Burnam Taguchi 1. Stresses only a few basic designs most commonly used in industry 2. Provides a table of these designs 3. Avoids needing a PhD in statistics by providing a cookbook approach to analysis Good candidates for screening designs tend to be projects where a full factorial would work well if you had unlimited resourcesFarm Design, Inc. Experimental Design Page 4
• 5. What are the main advantages and disadvantages? • Disadvantage: Screening design: Aliasing/confounding variables: • 3 variables (A,B,C) at 2 levels (1,-1) – Full factorial = 8 runs (as shown) – Taguchi L4 screening = yellow rows only, 4 configurations with 4 runs each = 16 runs – Minimal data for two-way interactions (AB, AC, BC) – Incomplete data for three-way interactions (ABC) 2 data points for 1 data point for less data points each level each level than levels Run A B AB C AC BC ABC x- x+ y- y+ 1 -1 -1 1 -1 1 1 -1 -1 1 -1 1 2 -1 -1 1 1 -1 -1 1 3 -1 1 -1 -1 1 -1 1 4 -1 1 -1 1 -1 1 -1 -1 1 -1 1 5 1 -1 -1 -1 -1 1 1 6 1 -1 -1 1 1 -1 -1 -1 1 -1 1 7 1 1 1 -1 -1 -1 -1 -1 1 -1 1 8 1 1 1 1 1 1 1 Design variables Noise variables • Advantage: Screening design: Noise data • The full factorial is 8 separate configurations • The screening design is 4 separate configurations that are run 4 times for each noise variable • Depending on your noise variables, this usually results in more data for less timeFarm Design, Inc. Experimental Design Page 5
• 6. Basic Steps 1. Take a close look at variables. Separate design variables (inner array) from noise variables (outer array). – Design variables are controllable aspects of your design that you will change depending on the outputs (ie geometry, spring rate, applied force). – Noise variables are variables that you have no control over and will vary similarly in a real scenario (ie ambient temperature, manufacturing tolerances, sample size tolerances). – Get historical data if necessary: If you don’t have an understanding of how variables will affect the testing, run a few tests to get a better idea of which variables are important. Also try to understand the physics of relationships to determine critical variables. 2. Determine the number of levels (ie max/min, # of materials) for each design variable. To simplify the design, choose the same number of all levels, but if this is not possible (ie a mix of qualitative and quantitative variables) try to stick to a mixture of 2 and 3. Choose meaningful levels. Too extreme of a difference can lead to misleading data for other variables. 3. Select the appropriate sized screening design based on the number of design variables and the levels of each. General guidelines: # design variables < 5, # levels = 2  full factorial # design variables < 8, # levels = 2  L8 # design variables < 13, # levels is 2,3 or a mix  L18 # design variables 8 < 13, # levels is 3  L27 4. Set up the test matrix. Sort columns based on how well you understand each variable. Sort rows by how time consuming it is to change test setups. Randomization is not generally necessary, but it’s always good practice.Farm Design, Inc. Experimental Design Page 6
• 7. Basic Steps 5. Test! 6. Analyze the data. Calculate the output for each level of each factor and graph on one chart: Main Effects Plot. Determine the expected performance for the optimized variables. 7. Do enough confirmation experiments that you’re confident in the results. Make sure that your actual performance matches your expected performance.Farm Design, Inc. Experimental Design Page 7
• 8. Output: Main Effects Plot Compare variable levels against overall mean Measure output for each level of input • Maximizing tissue denuded is desired, so variable levels in green indicate optimized input levels. Large slope: Small slope: more critical less critical Page 8Farm Design, Inc. Experimental Design
• 9. Output: Expected Performance Expected performance is the performance we should see if we run tests using the optimized variables. This means that if we set all the variables to the levels indicated in the table above, the mean performance will be 73%, which is an increase of about 11%. Expected Performance* = M + (Speed – M) + (Mass – M) + (Geom – M) + (Temp – M) + (Size– M) = 62 + (65 – 62) + (63 – 62) + (66 – 62) + (62 – 62) + (65– 62) = 73% * This equation assumes the variables are independentFarm Design, Inc. Experimental Design Page 9
• 10. When to Use a Taguchi Screening Design Cheat Sheet Keep in mind there are exceptions to each guideline below. There are no cut and dry rules for when to use and when not to use Taguchi, so get in touch with an experienced colleague or take a look at one of the resources on the next slide. GENERALLY… When to use: • Output / response is defined and quantitative • Main factors / variables are clearly independent of one another • # main factors > 5 Good candidates for screening designs tend to be projects where a full factorial would work well if you had unlimited resources When NOT to use: • No noise variables (unless you are just screening for variables to pare down for more testing) • Main factors or noise variables are not clearly identifiable • If your output is a “normal” value rather than maximizing/minimizing • If you know the output is nonlinear Poor candidates for screening designs tend to be projects where there are interactions between variables, ie variables effect on one another.Farm Design, Inc. Experimental Design Page 10
• 11. Resources • Stephen R. Schmidt and Robert G. Launsby. 2005. Understanding Industrial Designed Experiments (4th Ed.). Air Academy Press, Colorado Springs, CO, USA. • Engineering Statistics Handbook. Ed. Carroll Croarkin and Paul Tobias. 1 June 2003. National Institute of Standards and Technology Information Technology Laboratory SEMATECH. 10 December 2012 <http://www.itl.nist.gov/div898/handbook/index.htm>.Farm Design, Inc. Experimental Design Page 11