1 / 34

Industrial Applications of Experimental Design

Industrial Applications of Experimental Design. John Borkowski Montana State University University of Economics and Finance HCMC, Vietnam. Outline of the Presentation. Motivation and the Experimentation Process Screening Experiments 2 k Factorial Experiments Optimization Experiments

garrison-noe
Download Presentation

Industrial Applications of Experimental Design

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Industrial Applications of Experimental Design John Borkowski Montana State University University of Economics and Finance HCMC, Vietnam

  2. Outline of the Presentation • Motivation and the Experimentation Process • Screening Experiments • 2k Factorial Experiments • Optimization Experiments • Mixture Experiments • Final Comments

  3. Motivation • In industry (such as manufacturing, pharmaceuticals, agricultural, …), a common goal is to optimize production while maintaining quality and cost of production. • To achieve these goals, successful companies routinely use designed experiments. • Properly designed experiments will provide information regarding the relationship between controllable process variables (e.g., oven temperature, process time, mixing speed) and a response of interest (e.g. strength of a fiber, thickness of a liquid, color, cost…). • The information can then be used to improve the process: making a better product more economically.

  4. Motivation The resulting economic benefits of using designed experiments include: • Improving process yield • Reducing process variability so that products more closely conform to specifications • Reducing development time for new products • Reducing overall costs • Increasing product reliability • Improving product design

  5. The Experimentation Process

  6. Defining Experimental Objectives • The first and most important step in an experimental strategy is to clearly state the objectives of the experiment. • The objective is a precise answer to the question “What do you want to know when the experiment is complete? • When researchers do not ask this question they may discover after running an experiment that the data are insufficient to meet objectives.

  7. 2. Screening Experiments • The experimenter wants to determine which process variables are important from a list of potentially important variables. • Screening experiments are economical because a large number of factors can be studied in a small number of experimental runs. • The factors that are found to be important will be used in future experiments. That is, we have “screened”the important factors from the list.

  8. 2. Screening Experiments • Common screening experiments are • Plackett-Burman designs • Two-level full-factorial (2k) designs • Two-level fractional-factorial (2k-p) designs • Example: Improve the hardness of a plastic by varying 6 important process variables. Goal: Determine which of the six variables have the greatest influences on hardness.

  9. Example 1: Screening 6 Factors Response: Plastic Hardness Factor Levels Factors -1 +1 (X1)Tension control Manual Automatic (X2)Machine #1 #2 (X3)Throughput (liters/min) 10 20 (X4)Mixing method Single Double (X5)Temperature 200o 250o (X6)Moisture level 20 % 30 %

  10. Analysis of the Screening Design Data

  11. Interpretation of Results • The most influential factor affecting plastic hardness is temperature, followed by throughput and machine type. • To increase the hardness of the plastic, a higher temperature, higher throughput, and use of Machine type #2 are recommended. • Tension control, mixing method, and moisture level appear to have little effect on hardness. Therefore, use the most economical levels of each factor in the process. • A new experiment to further study the effects of temperature, throughput and machine type on plastic hardness is recommended for further improvement.

  12. 2kFactorial Experiments • A 2k factorial design is a design such that • k factors each having two levels are studied. • Data is collected on all 2k combinations of factor levels (coded as + and - ). • The 2k experimental combinations may also be replicated if enough resources exist. • You gain information about interactions that was not possible with the Plackett-Burman design.

  13. Example 2: 23 Design with 3 Replicates(Montgomery 2005) • An engineer is interested in the effects of • cutting speed (A) (Low, High rpm) • tool geometry (B) (Layout 1 , 2 ) • cutting angle (C)(Low, High degrees) on the life (in hours) of a machine tool • Two levels of each factor were chosen • Three replicates of a 23 design were run

  14. Experimental Design with Data Factors • A : cutting speed • B : tool geometry • C : cutting angle

  15. ANOVA Results from SASA: cutting speed B: tool geometry C: cutting angle

  16. Maximize Hours at B=+1 C=+1 A= -1B: tool geometry C: cutting angle A: cutting speed Layout 2 High Low

  17. 3. Optimization Experiments • The experimenter wants to model (fit a response surface) involving a response y which depends on process input variables V1, V2, … Vk. • Because the exact functional relationship between y and V1, V2, … Vk is unknown, a low order polynomial is used as an approximating function (model). • Before fitting a model, V1, V2, … Vk are coded as x1, x2, …, xk. For example: Vi= 100 150 200 xi = -1 0 +1

  18. 4. Optimization Experiments The experimenter is interested in: • Determining values of the input variables V1, V2, … Vk. that optimize the response y (known as the optimum operating conditions). OR • Finding an operating region that satisfies product specifications for response y. • A common approximating function is the quadratic or second-order model:

  19. Example 3: Approximating Functions • The experimental goal is to maximize process yield (y). • By maximizing yield, the company can save a lot of money by reducing the amount of waste. • A two-factor 32 experiment with 2 replicates was run with: Temperature V1: Uncoded Levels 100o 150o 200o x1 Coded Levels -1 0 +1 Process time V2: Uncoded Levels 6 8 10 minutes x2 Coded Levels -1 0 +1

  20. True Function: y = 5+ e(.5x1– 1.5x2)Fitted function (from SAS)

  21. Predicted Maximum Yield (y) at x1= +1 , x2= -1(or, Temperature = 200o , Process Time = 6 minutes)

  22. Central Composite Design Box-Behnken Design(CCD) (BBD)Factorial, axial, and Centers of edges andcenter points center points

  23. Example 4: Central Composite Design (Myers 1976) • The experimenter wants to study the effects of • sealing temperature (x1) • cooling bar temperature (x2) • polethylene additive (x3) on the seal strengthin grams per inch of breadwrapper stock (y). • The uncoded and coded variable levels are - -1 0 1  . x1204.5o 225o 255o 285o 305.5o x2 39.9o 46o 55o 64o 70.1o x3.09% .5% 1.1% 1.7% 2.11%

  24. Example 4: Central Composite Design

  25. Ridge Analysisof Quadratic Model(using SAS)Predicted Maximum at x1=-1.01 x2=0.26 x3=0.68

  26. Further interpretation: • The predicted maximum occurs at coded levels of x1=-1.01 x2=0.26 x3=0.68. These correspond to sealing temperature of 225o, cool bar temperature of 57.3o, and polyethelene additive of 1.51%. • Note how flat the maximum ridge is around this maximum. That implies there are other choices of sealing temperature, cool bar temperature, and additive % that will also give excellent seal strength for the breadwrapper. • Pick that combination that minimizes cost.

  27. 5. Mixture Experiments • Goal: Find the proportions of ingredients (components) of a mixture that optimize a response of interest. 3-in-1 coffee mix has 3 components: coffee, sugar, creamer. What are the proportions of the components that optimize the taste? • Major applications: formulation of food and drink products, agricultural products (such as fertilizers), pharmaceuticals.

  28. Mixture Experiments • A mixture contains q components where xi is the proportion of the ithcomponent (i=1,2,…, q) • Two constraints exist: 0 ≤ xi ≤ 1 and Σxi = 1

  29. Mixture Experiment Models • Because the level of the final component can written as xq = 1 – (x1 + x2 + + xq-1) any response surface model used for independent factors can be reduced to a Scheffé model. Examples include:

  30. Example of a 3-Component Mixture Design

  31. Analysis of a 3-component Mixture Experiment

  32. 4-Component Mixture Experiment with Component Level Constraints (McLean & Anderson 1966)Goal: Find the mixture of Mg, NaNO3, SrNO3, and Binder that maximize brightness of the flare.

  33. 6. Final Comments • Screening experiments • 2k and 2k-p experiments • Optimization experiments • Mixture experiments • Other applications: • Path of steepest ascent (descent) to locate a process maximum (minimum). • Experiments with mixture and process variables. • Repeatability and reproducability designs for statistical quality and process control studies.

More Related