introduction to design of experiments brian cunningham jennifer horner 03-26-11 ua college of...

Introduction to Design of Experiments

Brian CunninghamJennifer Horner03-26-11

UA College of Engineering

Agenda

• Short History: Design of Experiments (DOE)• How to use DOE to optimize the

design of a spinning parachute• In-Class DOE activity with your team

DOE: A Short History

• Design of Experiments (DOE) was first introduced in the 1920s when a scientist at an agricultural research station in England, Sir Ronald Fisher, showed how valid experiments could be conducted in the presence of many naturally fluctuating conditions such as temperature, soil condition, and rainfall.

• In the past decade or two, the application of DOE has gained acceptance in the U.S. as a valuable tool for improving the quality of goods and services.

Sir Ronald Fisher

Design of Experiments Examples

A plastic molding workshop wants to reduce injection molding rejects; performs a set of experiments which change injection pressure, mix temperature and setting time. • Analysis of the results shows a combination of

temperature and setting time as the most significant factor.

• Further experiments find the optimum combination of these.

Design of Experiments Examples

A yacht design team aims to improve speed through changing the shape of the boat's sail. • Rather than try random shapes, they identify the key

sail parameters and then design and perform a set of experiments with each factor set at two levels.

• They follow this up with multi-level experiments for the two most significant factors found in the first experiment set.

• The result: a new sail that increases speed by 5%.

Why DOE?

Minimize time and cost required to obtain the most information possible at the earliest possible stage in a product’s life cycle

Cost of changesTo product design

Production Consumptiontime

$

Preliminary design

Detaileddesign

The Spinning Parachute Company

Current best-selling model:

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attach paper clip here


• The Spinning Parachute Company wants to improve this product– Better customer satisfaction ratings– Improved sales

• Goal: Improve in-flight time (fall time)


Preliminary research: 3 main factors impact the flight time

A. Blade widthB. Blade lengthC. Body length

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Blade width

Body length

Blade length


Blade widthBlade lengthBody length

Process

Increase average fall timeDecrease standard deviation of fall time

P-Diagram* to represent the design improvement of the Spinning Parachute

“Factors” “Performance characteristics”

* P-diagram is short for Parameter diagram

Noise


• Purpose of DOE in this example: Uncover statistical relationships that connect

design factors to performance characteristics Allow the design team to select the factor

settings that generate the desired performance


The company’s engineers want to test new dimensions for the three factors:

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1

21

21

212

1

2


Wider blade

Longer blade

Longer body


There are 23, or 8, possible configurations to examine:Combination A, Blade

WidthB, Blade Length

C, Body Length

1 1 1 1

2 1 1 2

3 1 2 1

4 1 2 2

5 2 1 1

6 2 1 2

7 2 2 1

8 2 2 2

This is called a “full factorial analysis.”


Rather than gather the data for all eight combinations, you can obtain valuable information from considering just four carefully chosen combinations:

A

B

C

(2, 1, 2)

(1, 1, 1)

(2, 2, 1)(1, 2, 2)

Two Orthogonal Sets of Four Combinations

Combination

A B C

1 1 1 1

2 1 2 2

3 2 1 2

4 2 2 1

Combination

A B C

1 1 1 2

2 1 2 1

3 2 1 1

4 2 2 2

Set 1

Set 2

Each set is called a “half factorial analysis.”

Orthogonal Set 1 Applied to the Spinning Parachute

Combination

A B C

1 1 1 1

2 1 2 2

3 2 1 2

4 2 2 1

Combination

ABlade width

BBlade length

CBody

length

1 narrow short short

2 narrow long long

3 wide short long

4 wide long short

Note that for each factor, each level is tested in two combinations

Gather Data for Ten Replicates

Use Set 1, the four half-factorial combinations (treatments)Combination 1 2 3 4

(A, B, C) (1, 1, 1) (1, 2, 2) (2, 1, 2) (2, 2, 1)1.22 1.69 1.63 1.781.22 1.59 1.50 1.691.12 1.53 1.56 1.841.15 1.62 1.54 1.751.25 1.60 1.59 1.751.22 1.60 1.56 1.691.28 1.63 1.56 1.751.19 1.56 1.50 1.721.38 1.63 1.50 1.751.22 1.63 1.59 1.87

Avg. fall time 1.225 1.610 1.553 1.759Stand. Dev. 0.068 0.043 0.042 0.055

Record the fall time, in seconds

Summarize Spinning Parachute Data

Depicting this data another way:

Combination(Treatment)

ABlade width

BBlade length

CBody

length

Avg. fall time

Stand. Dev.

# of Reps.

1 1 1 1 1.225 0.068 10

2 1 2 2 1.610 0.043 10

3 2 1 2 1.553 0.042 10

4 2 2 1 1.759 0.055 10

Grand Average

1.537

Analyze Results of Spinning Parachute Experiment

• Calculate the effects of each of the 3 factors on the two performance characteristics

• Example: Factor A, Blade width: There are two combinations where A is at level 1 The average fall time when factor A is at level 1 is

(1.225 + 1.610) / 2 = 1.418 seconds Now consider factor A at level 2:

(1.553 + 1.759) / 2 = 1.656 seconds So the overall effect of varying Factor A between level 1

and level 2 is |1.656 – 1.418| = .238 seconds These results also determine the level setting that leads

to the longest fall time

Analyze Results of Spinning Parachute Experiment

Now repeat this analysis for Factors B and C

ABlade width

BBlade length

CBody

length

Level 1 Avg. Fall time 1.418 1.389 1.492


Effect (difference) 0.238 0.296 0.090

Optimum level 2 2 2

Optimum configuration wide long long

Representing the Results Graphically

The steepest slope between the two factor levels indicates a greater effect on the performance characteristics

1.71.61.51.41.3

1 2 Level Factor A

Blade width

1 2 Level Factor B

Blade length

1 2 Level Factor C

Body length

Grandaverage

Develop a Prediction Equation for the Best Fall Time

Max Fall Time = 1.537 + (1.656 – 1.537) + (1.685 – 1.537) + (1.582 – 1.537) = 1.849 seconds

ABlade width

BBlade length

CBody

length



Effect (difference) 0.238 0.296 0.090

Optimum level 2 2 2

Optimum configuration wide long long

Grand average = 1.537 seconds

Final Step: Run a Verification Experiment

• Set all factors at their optimal levels• Collect data for ten replicates• Calculate the average of the ten trials• Compare with the predicted value

Your Turn!

With your team:1. Carefully cut out four parachutes according to the four

combinations from the half factorial orthogonal array

2. Conduct ten experiments for each of the four combinations (treatments)

Usually need to randomize the experiments, but time = limited here Minimize the effects of other factors, such as:

Same person always drops Perform each drop using same technique Same position of chair (minimize air current variability) Same person times the fall Same cue for start and finish of fall

Your Turn! Continued

3. Collect your data: fill in the fall times for the ten x four = 40 drops

Two team members can fill in the data – preferably using the Excel spreadsheet

4. Perform analysis on your data5. Construct your prediction equation for the longest fall

time6. Carefully cut one more parachute model to your

recommended factor levels for the longest fall time7. Run ten replicates of a verification experiment to test

your prediction Goal: within 2 standard deviations of the predicted value

Conclusion

• I ask the teams to turn in or email me their data collection and analysis form

• Additional information on DOE: http://www.moresteam.com/toolbox/t408.cfm

http://www.isixsigma.com/index.php?option=com_k2&view=itemlist&task=category&id=199:teaching-doe&Itemid=156

http://www.stat.psu.edu/online/courses/stat503/01_intro/02_intro_history.htmlhttp://www.camo.com/rt/Resources/design_of_experiment.html

http://thequalityportal.com/q_know02.htm

http://www.camo.com/rt/Resources/design_of_experiment.html











introduction to design of experiments brian cunningham jennifer horner 03-26-11 ua college of...

Documents

time slide

design factors

team slide

design improvement

set of experiments

longer body slide

yacht design team

desired performance