Dx8 Factorials

7/31/2019 Dx8 Factorials

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DOE made easy with Design-Expertsoftware by Stat-Ease 1

Design of Experiments (DOE) Made Easy

and More Powerful via Design-Expert SoftwarePart 1 Factorials for Screening, Characterization and Verification*

By Mark J. Anderson, PE, CQE

Stat-Ease, Inc., Minneapolis, MN

[email protected]

Rank12345 7 9 12 16

D

AD

A

To avoid cross talk please put your microphone on mute except when you

need to ask a question or weigh in with a comment (feel free!).

Timer by Hank Anderson

*Posted at www.statease.com/webinar.html
http://www.statease.com/webinar.htmlhttp://www.statease.com/webinar.html


2/29

Mission and Agenda for this Webinar Series

Objective:

Show-and-tell what DOE can do with the aid of dedicated software

from Stat-Ease and support of its experts.

Approach:

Span factorials from simple to sublime

Spare on methods (get this from DOE Simplified, 2ndEd.)

Not an exhaustive presentation of features. For a complete list,

see www.statease.com/dx8descr.html.

Agenda of Webinars:

1. Factorials for screening, characterization and verification

2. Response surface methods (RSM) for process optimization

3. Mixture design for optimal formulation


"Theory guides, experiment decides."

-- I. M. Kolthoff
http://www.statease.com/dx8descr.htmlhttp://www.statease.com/dx8descr.html


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Strategy of Experimentation: Factorials


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ReferencesA Trilogy of Primers

Now in 2ndedition*!

* Productivity Press, New York, 2007.

Co-authors Mark & Pat

A free intro to Formulation Simplifiedbook (under development):

A Primer on Mixture Design: Whats In It for Formulators?

www.statease.com/pubs/MIXprimer.pdf
http://www.statease.com/pubs/MIXprimer.pdfhttp://www.statease.com/pubs/MIXprimer.pdfhttp://www.statease.com/patwhit.htmlhttp://www.statease.com/markand.html


5/29


Real-World Factorial* Headlines

John Deere Saves $500K Annually

Scitech Journal

Kodak Saves Thousands Metal Forming

Cover-Wrap Process Optimized IE Solutions

Solvent Pop Prevented Paint & Coatings

Wafer Transport Jams Cleared Micro

3.5x More to Web Site

Harvard Business Review(2x3x2x3)

Cheese Sauce More Enticing

Food Product Design (4x2)

Yield Increased 65% Quality

Immunoreagent Kit Validated (2x3x3x2)

Scrap Reduced 90% Rubber & Plastics

Welding Defects Eliminated Quality

Tape Line UnstuckAdhesives & Sealants

Enzymatic Assay Optimized

Biomolecular Sciences (2x3x3x4x6)

Wafer Defects Reduced Semiconductor Mfg

Purple Paper Brightened Up TAPPI

$180K Saved in Wafer Production Micro

Polycarbonate Lined Out Paint & Coatings

Bread No Longer Falls Flat Quality Progress

Faster ExtractionAmerican Laboratory

Breakthrough in Hardcoat Paint & Coatings

Capper Process Optimized Packaging World

Telemarketing Made More Effective

Three-Fold Less Variability Paint & Coatings

Foundry Saves $50k /Year Job Shop

Technology

Heat Therapy Made Rugged

Medical Device & Diagnostic Industry

Contact [email protected] for these and other pubs likely some relevant for you.

* Two-level factorials unless noted.
mailto:[email protected]:[email protected]


6/29

New Features for Factorials (1stbatch)Simple Stuff (but very useful!)

F1 Help now context sensitive: Heads-up on how to navigate

screen currently on view (also see more detail in Screen Tips).

Design layout column widths now adjust automatically by

double-clicking column-header boundaries: Multiple

columns adjust simultaneously!

Attach row comments by right-clicking on row headers:Ahandy way to record important observations.

Many new, high-visibility tools: Optional views, such as

Model Graphs, are now easily seen.

Better defaults and tick marks: Nicely rounded values

provide presentable graphs straight away. More-interactive cube plots: Click on design points to see

factor levels and response predictions on graph legends.


Popcorn


7/29

New Features for Factorials (2ndbatch)More Sophisticated

Tolerance interval (TI) estimates on point prediction:

This is important for verification studies to ensure your process

stays within manufacturing specifications.

Improved curvature testing for factorials with center points:All design points are now fitted to the polynomial model used

for predictions. This provides a more realistic impact of

significant non-linear response behavior.


Stent -CPa


8/29

New Features for Factorials (3rd Batch)For General Factorials

DOE made easy with Design-Expert

software by Stat-Ease 8

Design-Expert Software

wood failureError estimates

Shapiro-Wilk testW-value = 0.887p-value = 0.159A: WoodB: AdhesiveC: ApplicatorD: ClampE: Pressure

Half-Normal Plot

Half-Normal%

Probability

|Normal Effect|

0.00 2.67 5.35 8.02 10.69

0102030

50

70

80

90

95

99

A

B

C

D

ABBCHalf-normal selection ofimportant effects on all

factorial designs, not just

two-level.*

For example, for 5 woods glued

with 5 adhesives, using 2applicators with 4 clamps at 2

pressures. The vital effects

become apparent at a glance!

*(Detailed in Graphical Selection of Effects in General Factorialswinner of

the Shewell Award for best presentation at the 2007 Fall Technical Conference.)


9/29

A Handy V8 Feature for Categorical Factors

Provides far easier main effects plotting and makes interactions

more meaningful. Previously, the only option to average factors

came via a hidden drop-list. The screen-shot series above showsthe result of simply pressing the Avg for 5 woods glued with 5

adhesives using 2 applicators at 2 pressures. This causes the least

significant difference (LSD) bars to shrink, revealing an important

difference between two particular clamps.DOE made easy with Design-Expert


Push-button averaging on

the factors tool:


10/29

A High-Level General Factorial Case Study

This case study demonstrates the use of Design-Expert to

design and analyze an experiment with categorical factors that

incorporate many treatments each. It comes from the life-

science industry, involving application of an enzyme linked

immunosorbent assay (ELISA), the basis of most diagnostic

testing in humans, for example to detect West Nile Virus.

The design, facilitated by the use of a multiplexed 96-well

microplate, incorporates three key factors at two levels each,plus all pairs of ten polyclonal antibodies. This is a 2x2x2x10x10

general factorial.




11/29

Factorial Design Planning ProcessSpecifics for the ELISA case

1. State objective in terms of measurable responses. For each:a. Define the effect (response difference Dy) that is important to detect for

each response. (This is the signal, at a minimum, you are listening for.)

A change of 2500 in median fluorescent intensity (MFI) is of interest.

b. Estimate experimental error (variations) for each response. (The noise.)

Historical data leads to an estimated standard deviation of 1500 MFI.2. Select the input factors to study and establish their ranges. (Wider the better.)

3. Select a design and evaluate it for:

Resolution of effects (beware of aliasing).

Not an issue -- this will be a full factorial.

Power based on signal-to-noise ratios (D/s). (> 80 %, 90 % verification.)

Normally done for main effects, but in this case also the DE interactionbecause the primary purpose of the design is to find the best antibody pair.

Examine all runs for unsafe factor combinations. (Pre-test the extremes.)

11DOE made easy with Design-Expert

software by Stat-Ease


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ELISA CaseBuild a General Factorial Design (page 1 of 3)

1. Choose General Factorial on the Factorial tab, enter 5

for the number of categoric factors and click on Vertical:




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2. Enter factors and levels and then Continue>>:




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3. Accept the default of 1 replicate and click Continue>>.

4. Enter the response MFI, Delta of2500 and Sigma of1500.

5. Click on the Edit model for power button. Add the DE

interaction to the Main effects model. Click OK and then

Continue>>.




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Fluorescent units: D = 2500, s = 1500, D/s = 1.67

Power of only 44.7% for the capture/detect antibody pair;

want power of at least 80% for effects of interest!



ELISA CaseEvaluating Power: One Replicate, 80 wells

15


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Background on PowerNo Factor Effect; H0: D = 0

Power = (1 )*100%

Power is the probability

of revealing an activeeffect of size delta (D)

relative to the noise (s)

as measured by signal to

noise ratio (D/s).

It should be high (atleast 80%) for the effect

size of interest.

16

Truth is

No effect

Effect

ANOVA says

Retain H0 Reject H0

OK

OK

Type I error

(alpha rate)

False alarm

Type II error

(beta rate)

Failure to

detect


17/29

Power Calculation Pictured

The noncentral F-distribution is a function ofD and s. For detail see

Sizing Fixed Effects for Computing Power in Experimental Designs by

Oehlert and Whitcomb posted at www.statease.com/pubs/power.pdf.DOE made easy with Design-Expert


Central F-distribution (H0) F-critical Noncentral F-distribution (HA)

beta (type II error) alpha (type I error) power (44.7 %)
http://www.statease.com/pubs/power.pdfhttp://www.statease.com/pubs/power.pdf


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ELISA CaseAdd a Replicate

1. Click and name the blocks Plate 1 and

Plate 2.

Click Continue>> twice.




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Two replicates achieve adequate power!



ELISA CaseEvaluating Power: Two Plates

19


20/29

ELISA Case AnalysisHalf-Normal Plot of Effects Reveal a Vital Few



Note: To plot

multiple contrastson a comparative

scale, the effects

are normalized.*

*(Detailed in Graphical Selection of Effects in General Factorials by Whitcomb & Oehlert.)

Design-Expert SoftwareMFI

Error estimates

Shapiro-Wilk testW-value = 0.824p-value = 0.001A: BufferB: pHC: NaClD: DetectE: Capture

Half-Normal Plot

Half-Normal%Probability

|Normal Effect|

0.00 9.00 18.00 27.00 36.00

0.0

10.020.030.0

50.0

70.0

80.0

90.095.0

99.0

99.9

A

BDE

AB

BD BE

DE


21/29

ELISA CaseDE Interaction at Best Combination of A & B



Top fluorescing pairs of antibodies circled.

3,8

5,3 6,5

8,421407

Design-Expert SoftwareMFI

X1 = D: DetectX2 = E: Capture

Actual FactorsA: Buffer = TrisB: pH = 7.6C: NaCl = Average

E1 c1E2 c2E3 c3E4 c4

E5 c5E6 c6E7 c7E8 c8E9 c9E10 c10

E: Capture

d1 d2 d3 d4 d5 d6 d7 d8 d9 d10

Interaction

D: Detect

MFI

0

5000

10000

15000

20000

25000


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ELISA Case Demo

See how this general factorial is built with power calculated

(DE interaction included), analyzed, and optimized for

maximum MFI (18,000 minimum).



ELISA

Demonstrate reference lines on plots,

a new feature in V8 (horizontal at 18000).


23/29

General Factorial Case Study #2:Hydraulic Gear Pump* (experiment design only)



Hydraulic gear pumps are vital for many

machines including vehicles and airplanes.

However, they tend to lose efficiency due to

internal leakage. OEM engineers must verify

that one such device will remain within aspecified range of performance regardless of

normal production variations. They settle on

nine factors, primarily categorical -- shown

at right with number of levels each.

*(Loosely based on Experiments for derived factors with

application to hydraulic gear pumps, by C. J. Sexton , S. M. Lewis

& C. P. Please,Journal of the Royal Statistical Society: Series C

(Applied Statistics), 2002, V50, Part 2, pp 155-170)

A. Flange (3)

B. Cover (3)

C. Float (3)

D. Bearing (2)

E. Involute (2)

F. Lead edge (2)

G. Side Gap (2)H. Pressure (3)

I. Speed (3)


24/29

Pump Case

Specifying the Experiment Design



Based on subject-matter knowledge, the engineers are mostconcerned about interactions involving the float (factor C).

Customized pumps are costly, so a minimal-run design is desired.

Choose a d-optimal design for a reduced 2FI model: intercept, 9

main effects and 8 two-factor interactions (those involving C).

39 model points (builds) must be picked from the 3888

(3x3x3x2x2x2x2x3x3) possible combinations, in other words,

approximately a 1/10thfraction.

To estimate lack-of-fit pick 5 more unique combinations

From these 44 builds, select 4 to replicated for pure error. 48 pumps will be built in total.

Differences in leak-back of 4 units are of interest.

This normally varies by a standard deviation of 1 unit.


25/29

Pump Case

Will the design provided proper power?

1.Define the change (Dy) that is important. (Signal)

2.Estimate experimental error (s). (Noise)

3.From signal-to-noise ratio (Dy/s) estimate power.

If runs suffice, the averaging provided by the matrixwill cut noise to reveal the signal.



25

Yes, for this signal/noise ratio (3) the power

exceeds the 80% guideline, but for some

interactions short of the 90% that may be

needed for verification testing.

Hydraulic Pump


26/29

New Features for RSM & MixturesSneak Preview

Smoother color gradations on 2D contours: More

impressive for presentations. Rounded contour values: More presentable

defaults requiring less fiddling.

Plant flags on 3D surfaces: Previously, you could

only put flags on 2D contour plots.

New and fully configurable mesh option thatreflects smooth, lighted colors off your 3D surface:

Dazzle your customers and colleagues.

3D graphs that you can spin with your mouse:

Simply grab and rotate!

IV-optimal design: Ideal for optimizing constrained

process or mixture experiments. Direct setting of discrete (fixed) numeric levels in

for response surface method designs.

Discrete factor levels adhered to in numeric

optimization.DOE made easy with Design-Expert


To be continued!


27/29

How to Get Free Help

Search publications posted at www.statease.com.

In Stat-Ease software press for Screen Tips, view reports in

annotated mode, look for context-sensitive Help (right-click)

or search the main Help system.

Explore Experiment Design Forum http://forum.statease.com

and post your question (if not previously answered).

E-mail [email protected] for answers from Stat-Eases

staff of statistical consultants.

Call 612.378.9449 and ask for statistical help.

27DOE made easy with Design-Expert

http://www.statease.com/http://forum.statease.com/mailto:[email protected]:[email protected]://forum.statease.com/http://www.statease.com/


28/29



Stat-Ease Training:

Computer-Intensive Statistical Workshops

Shari Kraber,

Workshop Manager

& Master [email protected]

Statistics for

Technical Professionals

PreDOEWeb-Based (optional)

www.statease.net

Experiment Design

Made Easy

Response Surface

Methods for

Process Optimization

Mixture Design

for

Optimal Formulations

Robust Design and

Tolerance Analysis

Designed Experiments

for Life Sciences

Advanced Formulations:

Combining Mixture &

Process Variables
mailto:*[email protected]://www.statease.net/http://www.statease.net/mailto:*[email protected]


29/29

Statistics Made Easy

Best of luck for your

experimenting!

Thanks for listening!

-- Mark



Mark J. Anderson, PE, CQE

Stat-Ease, Inc.

[email protected]

*Pdf of this Powerpoint presentation posted atwww.statease.com/webinar.html.

For future webinars, subscribe to DOE FAQ Alert atwww.statease.com/doealert.html.
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Dx8 Factorials