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Fun

ctio

n> Planning for a Successful Design of

Experiment

Jim Akers SIU ASQ Spring Conference 2013

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Topics we will cover

This presentation will provide a process for planning a successful design of experiment.

We will cover• the basics of DOE• creating a charter• choosing an appropriate design

The participants will take away a DOE charter template and a flowchart for simple design selection. The major focus is asking and answering the right questions to create an appropriate experiment.

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THE BASICS OF DOE

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• Will help you gain knowledge in:– Improving performance characteristics– Understand relationships between process variables– Reducing costs– Understand how to optimize processes

• Creates the ultimate process knowledge to make your product/process

Better

Faster

Cheaper

Objectives in Using DOE

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Let’s Start with an Example:

Plot a histogram and calculate the average and standard deviation

Data

18 16 30 29 28 21 17 41 8 1732 26 16 24 27 17 17 33 19 1831 27 23 38 33 14 13 26 11 2821 19 25 22 17 12 21 21 25 2623 20 22 19 21 14 45 15 24 34

Fuel Economy of 50 automobiles (in mpg)

Fuel Economy

0

2

4

6

8

10

12

14

16

0 to <6 6 to <12 12 to <18 18 to <24 24 to <30 30 to <36 36 to <42 42 to <48 48 to <54 54 to <=60mgp

Nu

mb

er

of

Ca

rs

7266.7

88.22

S

X

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What Might Explain the Variation?

• DOE is about discovering and quantifying the magnitude of cause and effect relationships.

• We need DOE because intuition can be misleading.... but we’ll get to that in a minute.

• Regression can be used to explain how we can model data experimentally.

METHOD

MEASUREMENT

MANPOWER

EffectEFFECT

MACHINE

MATERIALMOTHERNATURE

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Mileage Data with Vehicle Weight:

• Let’s take a look at the mileage data and see if there’s a factor that might explain some of the variation.

• Draw a scatter diagram for the following data:

X - Weight (lbs) Y - Mileage(mpg)3000 182800 212100 322900 172400 313300 142700 213500 122500 233200 14

Observation1

10

6789

2345

Y=f(X)X Y

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• Plot the data on a scatter chart and draw a best fit line

• Determine the equation for that line,– you now have a ‘model’ for the data

Regression Analysis

y = -0.0152x + 63.507R² = 0.9191

05

101520253035

1900 2400 2900 3400 3900

mpg

Weight

Scatter Chart (Weight vs mpg)

Y=f(X)

2800

~21We have now

experimented with one factor, but that does not explain all

of the variation.

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There are a few basic ways to understand a process you are working on. We will talk about two of them.

• Classical 1FAT experiments – One factor at a time (1FAT) focuses on one variable at two or

three levels and attempts to hold everything else constant (which is impossible to do in a complicated process).

• DOE– When properly constructed, it can focus on a wide range of

key input factors and will determine the optimum levels of each of the factors.

Each have their advantages and disadvantages.

Experimenting with a System

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• Let’s consider how two known (based on years of experience) factors affect gas mileage, tire size (T) and fuel type (F).

1FAT Example

Fuel Type Tire size

F1 T1

F2 T2

Y=f(X)T(1,2) YF(1,2)

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Step 1:

Select two levels of tire size and two kinds of fuels.

Step 2:

Holding fuel type constant (and everything else), test the car at both tire sizes.

1FAT Design

Fuel Type Tire size Mpg

F1 T1 20

F1 T2 30

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Since we want to maximize mpg the more desirable response happened with T2

Step 3: Holding tire size at T2, test the car at both fuel types.

1FAT Design

Fuel Type Tire size Mpg

F1 T2 30

F2 T2 40

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• Looks like the ideal setting is F2 and T2 at 40mpg.

• This is a common experimental method.

1FAT Design

Fuel Type Tire size Mpg

F1 T2 30

F2 T2 40

What about the possible interaction effect of tire size and fuel type? F2T1

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• Suppose that the untested combination F2T1 would produce the results below.

• There is a different slope so there appears to be an interaction. A more appropriate design would be to test all four combinations.– That is called a full factorial

1FAT Design

0

10

20

30

40

50

60

70

T1 T2

Tire Size

mpg

F2

F1

14

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• We need a way to – investigate the relationship(s) between variables– distinguish the effects of variables from each other (and maybe tell if

they interact with each other)– quantify the effects...

...So we can predict, control, and optimize processes.

What About Other Factors – and Noise?

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DOE to the Rescue!! Y=f(X)

Run X1 X2 X3 X4 Y1 Y2 Y3 Y-bar SY

1 - - - -2 - - + +3 - + - +4 - + + -5 + - - +6 + - + -7 + + - -8 + + + +

DOE uses purposeful changes of the inputs (factors) in order to observe corresponding changes to the outputs (response).

Remember the IPO’s we did – they are real important here.

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• To ‘design’ an experiment, means to pick the points that you’ll use to understand the design space.

The Basics

Run A B1 - -2 - +3 + -4 + +

In tabular form, it would look like:

High (+)

Low (-)

Fa

cto

r B

Se

ttin

gs

Factor A Settings High (+)Low (-)

(-,+)

(+,-)

(+,+)

(-,-)

YAB

X1

X2

Design Space

AB+

+

--

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• A full factorial is an experimental design which contains all levels of all factors. No possible treatments are omitted. – The preferred (ultimate) design– Best for modeling (Response Surface Methods)

• A fractional factorial is a balanced experimental design which contains fewer than all combinations of all levels of all factors.– The preferred design when a full factorial cannot be

performed due to lack of resources– Okay for some modeling – Good for screening

Full vs. Fractional Factorial

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• Full factorial– 2 level– 3 factors– 8 runs– Balanced (orthogonal)

• Fractional factorial– 2 level– 3 factors– 4 runs - half fraction– Balanced (orthogonal)

2 Level Designs

runs 823

runs 42 13

19

factors ofnumber

2

k

runsrk

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• Full factorial– 3 level– 3 factors– 27 runs– Balanced (orthogonal)– Used when it is expected the response is non-linear

3 Level Designs

runs 2733

factors ofnumber

3

k

runsrk

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Average Y when A was set ‘high’

Average Y when A was set ‘low’R

esp

on

se

- Y

Factor ALow High

• The difference in the average Y when A was ‘high’ from the average Y when A was ‘low’ is the ‘factor effect’

• The differences are calculated for every factor in the experiment

Measuring An “Effect”

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When the effect of one factor changes due to the effect of another factor, the two factors are said to ‘interact.’

more than two factors can interact at the same time, but it is rare outside of chemical reactions.

Res

pons

e -

Y

Factor ALow High

B = High

B = Low

SlightRes

pons

e -

Y

Factor ALow High

B = High B = Low

Strong

Looking For InteractionsR

espo

nse

- Y

Low High

B = High

B = LowNone

Factor A

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• Too much variation in the response• Measurement error• Poor experimental discipline• Aliases (confounded) effects• Inadequate model• Something changed

- And: -

Reasons Why a Model Might Not Confirm:

There may not be a true cause-and-effect relationship.

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Proof – Storks do bring babies!

• A plot of the population of Oldenburg, Germany at the end of each year against the number of storks observed in that year, 1930-1936.

Source: “Statistics for Experimenters” by Box, Hunter, and Hunter. (1978)

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• Useful to see how factors effect the response and to determine what other settings provide the same response

Response Surface Method - 2D Contour Plot

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• Helpful in reaching the optimal result

Response Surface Method- 3D Response Surface Plot

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CREATING A CHARTER

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Planning - DOE Steps

• Set objectives - create a Charter– Comparative

• Determine what factor is significant

– Screening• Determine what factors will be studied

– Model – Response Surface Method• Determine interactions and optimize

• Select factors (process variables from C&E) and levels you will test• Select an experimental design• Execute the experiment• CONFIRM the model!! Verify the data is consistent with the

experimental assumptions• Analyze and interpret the results• Use/present the results

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• I. STATEMENT OF THE PROBLEM: ____________________________________________________________________________________

(During this step you should estimate your current level of quality by way of Cpk, dpm, or total loss. This estimate will then be compared with improvements found after Step XII.)

• II. OBJECTIVE OF THE EXPERIMENT: ____________________________________________________________________________________

• III. START DATE: ________ END DATE: ________

Planning - Charter

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• IV. SELECT MEASUREABLE QUALITY CHARACTERISTICS (also known as responses, dependent variables, or output variables). These characteristics should be related to customer needs and expectations.

Planning - Charter

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• V. COMPLETE A LITERATURE REVIEW, PROCESS FLOW DIAGRAM, AND CAUSE & EFFECT DIAGRAM. FROM THE CAUSE & EFFECT DIAGRAM SELECT FACTORS (also known as parameters or input variables) which are anticipated to have an effect on the response. Write Standard Operating Procedures for all variables that are to be held constant.

Planning - Charter

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• VI. DETERMINE THE NUMBER OF RESOURCES TO BE USED IN THE EXPERIMENT. Consider the desired number, the cost per resource, time per experimental trial, the maximum allowable number of resources.

• VII. WHICH DESIGN TYPES AND ANALYSIS STRATEGIES ARE APPROPRIATE? Discuss advantages and disadvantages of each.

• VIII. SELECT THE BEST DESIGN TYPE AND ANALYSIS STRATEGY TO SUIT YOUR NEEDS.

Planning - Charter

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• IX. CAN ALL THE RUNS BE RANDOMIZED? ____________________________________________________________________________________

WHICH FACTORS ARE MOST DIFFICULT TO RANDOMIZE?________________________________________________________________________

• X. CONDUCT THE EXPERIMENT AND RECORD THE DATA. (Monitor both of these events for accuracy.)

• XI. ANALYZE THE DATA, DRAW CONCLUSIONS, MAKE PREDICTIONS, AND PERFORM CONFIRMATION TESTS.

Planning - Charter

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• XII. ASSESS RESULTS, MAKE DECISIONS, AND DOCUMENT YOUR RESULTS.

(Evaluate your new state of quality and compare with the quality level prior to the improvement effort. Estimate your return on investment. If necessary, conduct more experimentation.)

Planning - Charter

MS Word Template available at: http://jimakers.com/downloads/DOE_Setup.docx

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CHOOSING AN APPROPRIATE DESIGN

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Choosing an Appropriate Design

Source: Understanding Industrial Designed Experiments – ISBN 1-880156-03-2

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2-Level Design Summary

Source: Understanding Industrial Designed Experiments – ISBN 1-880156-03-2

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Thank you

Jim Akers