doe strategies presentation

8/12/2019 DOE Strategies Presentation

1/37

An Overview of

the Methodology & Concepts

Presented by: Larry ScottPrincipal: Process Technologies

Welcome to:

DOE Strategies:

Agenda

Intro to DOE:

Full Resolution, Two-Level Factorials

Example: Perfect Popcorn

Fractional Factorials

Regular Fraction

Irregular Fraction

Minimum Run Resolution IV & V

Overall Strategy of a Factorial DOE


2/37

Many of the most

useful designs are

extremely simple.

Sir Ronald Fisher

Father of Factorial Design

ProcessProcess

Controllable Factors (X)Controllable Factors (X)

Responses (Y)Responses (Y)

Uncontrollable Variables (Z)Uncontrollable Variables (Z)

What is DOE:What is DOE: 66--sigma enthusiast Y = f (xsigma enthusiast Y = f (x ii))

DOE is:

A series of tests,

in which purposeful changes

are made to input factors,

so that you may identify causes

for significant changes

in the output responses.


3/37

Presentation Intent

An overview of the strategy ofDOE with a focus on the concept ofresolution.

Resolution is probably the mostunder utilized opportunity in DOE,

resulting from lack of awareness.

Road Map


4/37


5/37

Experiment Requirements

System Signals

reflect the magnitude of the output

are a function of the range or spread

of the input variables.

X1: Temperature - Low = 50 deg C

High = 100 deg C

X2: Pressure - Low = 10 psi

High = 15 psi


System Signal estimates

System Noise (variance) estimates

System Power

system signal

variance level

confidence level

Resource Availability $$$$$$# of Model Coefficients

System Resolution


6/37


System Signal estimates

System Noise (variance) estimates

System Power

Resource Availability $$$$$$

# of Model Coefficients

Y = b0 + b1X1 + b2X2 + b12X1X2

System Resolution

Full Resolution, TwoLevel Design

Run high/low combos of two or more factors

Use statistics to identify the critical few

Main effects A, B

Interactions (the hidden gold!) AB

What could be simpler?


7/37

Two Level Factorial DesignAs Easy As Popping Corn!

Kitchen scientists* conducted a 23 factorial experimenton microwave popcorn. The factors are:

A. Brand of popcorn

B. Time in microwave

C. Power setting

Response 1: Taste (1-10)

Response 2: Weight (un-popped kernels - UPKs).

* For full report, see Mark and Hank Andersons' Applying DOE to MicrowavePopcorn, PI Quality 7/93, p30.

Two Level Factorial DesignFactors in coded values

13.1748

70.542++7

80.332+++660.777++5

41.280++4

50.781+3

31.671+2

23.575+1

Orderoz.ratingpercentminutesexpenseOrderStdUPKsTastePowerTimeBrandRun

R2R1CBA


8/37

Two Level Factorial DesignActual factor values

* Average scores multiplied by 10 to make the calculations easier.

13.174754Cheap8

70.5421006Cheap7

80.3321006Costly6

60.7771004Costly5

41.280756Costly4

50.7811004Cheap3

31.671756Cheap2

23.575754Costly1

Orderoz.rating*percentminutesexpenseOrderStdUPKsTastePowerTimeBrandRun

R2R1CBA

Benefits of DOE

quantify multiple variables simultaneously

identify variable interactions

independent variable analysis

identify high impact variables

improve process & product function

predictive capability within design space

extrapolation capabilityoutside design space

2

3

4

5

6

1

7


9/37

R1 - Popcorn TasteAverage A-Effect

75 74 = + 1

80 71 = + 9

77 81 = 4

32 42 = 10

42 32

7781

74 75

71 80

Pow

er

Brand

Time

A

1 9 4 10y 14

+

= =

There are four comparisons of factor A (Brand), where

levels of factors B and C (time and power) are the

same:

( )y y

Effect yn n

+

+

=

A

75 80 77 32 74 71 81 42y 1

4 4

+ + + + + + = =

42 32

7781

74 75

71 80

Pow

er

Brand

Time

R1

- Popcorn TasteAverage A-Effect


10/37

R1 - Popcorn TasteAnalysis Matrix in Standard Order

I for the intercept, i.e., average response.

A, B and C for main effects (ME's).These columns define the runs.

Remainder for factor interactions (FI's)Three 2FI's and One 3FI.

32++++++++8

42++++7

77++++6

81++++5

80++++4

71++++3

75++++2

74++++1

TasteratingABCBCACABCBAI

Std.Order

Popcorn TasteCompute the effect of C and BC

y yy

n n

+

+

= C

BC

81 77 42 32 74 75 71 80y

4 4

y4 4

+ + + + + + = =

+ + + + + + = =

-3.5-60.5-20.5-1y

32+++++++842+++777+++681+++580+++471+++375+++274+++1

ratingABCBCACABCBAOrderTasteStd.


11/37

Popcorn TasteCompute the effect of C and BC

y yy

n n

+

+

=

C

BC

81 77 42 32 74 75 71 80y 4 4

y

17

74 75 42 32 71 80 81 72

4

71.5

4

+ + + + + +

= =

+ + +

+ + +

= =

-3.5-21.5-60.5-17-20.5-1y

32+++++++842+++777+++681+++580+++471+++375+++274+++1

ratingABCBCACABCBAOrderTasteStd.

Benefits of DOE








2

3

4

5

6

1

7


12/37

Benefits of DOE






improve employee morale

2

3

4

5

6

1

Sparsity of Effects Principle

Trivial Many: the remainder that result from random variation.

These effects will be centered on zero.

Since they are based on averages,you can assume normality

by the Central Limit Theorem*.

Two types of effects:

Vital Few: the big ones we want to catch

20 % of ME's and 2FI's will be significant.


13/37

Estimating Noise

How are the trivial many effects distributed?

Hint: Since the effects are based on averagesyou can apply the Central Limit Theorem.

Hint: Since the trivial effects estimate noisethey should be centered on zero.

How are the vital few effects distributed?

No idea! Except that they are too large to bepart of the error distribution.

Half Normal Probability PaperSorting the vital few from the trivial many.

7.14

21.43

35.71

50.00

64.29

78.57

92.86

Pi

0|Effect|

BC

B

C

Significant effects:

The model terms!

Negligible effects: The error estimate!


14/37

Half-Normal Probability Paper

Significant effects(the vital few) fallabnormally high (tothe right) on theabsolute effectscale. These are

the keepers.What do you do withthe little ones?

7.14

21.43

35.71

50.00

64.29

78.57

92.86

Pi

0

|Effect|

A

B

AB

3 6 9 12 15

Analysis of Variance (taste)Sorting the vital few from the trivial many.

Source

Sum ofSquare df

MeanSquare

FValue Prob > F

Model 2343.0 3 781.0 31.5 0.001


15/37

Benefits of DOE






predictive capabilitywithin

design spaceextrapolation capabilityoutside design space

2

3

4

5

6

1

7

Benefits of DOE








2

3

4

5

6

1

7


16/37

Benefits of DOE






predictive capability within design spaceextrapolation capability outside design space

2

3

4

5

6

1

7

Popcorn Analysiswith Software

Using statistical software, lets see howwell the programming staff did on thisexercise and compare results.


17/37

Software Packages

Design-Expert 7 (Stat-Ease, Inc.)

Minitab

JMP (SAS)

Statgraphics

Statistica

Qualitek 4

Popcorn Analysis TasteHalf Normal Plot of Effects

Design-Expert SoftwareTaste

Shapiro-Wilk testW-value = 0.973p-value = 0.861A: BrandB: TimeC: Power

Positive EffectsNegative Effects

Half-Normal Plot

H

alf-Normal%P

robabilit

|Standardized Effect|

0.00 5.38 10.75 16.13 21.50

0

10

20

30

50

70

80

90

95

99

B

C

BC


18/37

Popcorn Analysis TastePareto Chart of t Effects

Pareto Chart

t-Valueof|Effect

Rank

0.00

1.53

3.06

4.58

6.11

Bonferroni Limit5.06751

t-Value Limit2.77645

1 2 3 4 5 6 7

BCB

C

( )0.05 df 42t 2.77645

= ==

( )0.052 df 4k 7

t 5.06751 = =

=

=

Popcorn Analysis TasteANOVA

Analysis of variance table [Partial sum of squares]

Sum of Mean F

Source Squares df Square Value Prob > F

Model 2343.00 3 781.00 31.56 0.0030

B-Time 840.50 1 840.50 33.96 0.0043

C-Power 578.00 1 578.00 23.35 0.0084

BC 924.50 1 924.50 37.35 0.0036

Residual 99.00 4 24.75

Cor Total 2442.00 7


19/37

Popcorn Analysis TastePredictive Equations

For process understanding, use coded values:

1. Regression coefficients tell us how the response changesrelative to the intercept. The intercept in coded values is

in the center of our design.

2. Units of measure are normalized (removed) by coding.Coefficients measure half the change from 1 to +1 for

all factors.

Actual Factors:

Taste =

-199.00

+65.00*Time

+3.62*Power

-0.86*Time*Power

Coded Factors:

Taste =

+66.50

-10.25*B

-8.50*C

-10.75*B*C

Real-World Example: BreakthroughBC Interaction!

!

"# $%

"# $&%

' &

'


20/37

Popcorn TasteBC Interaction

37.03242++

79.07781+

75.58071+

74.57574

TasteCB

B- 4 min B+ 6 min

80

70

60

50

40

30

Taste

C-75%

C+100%

Popcorn Analysis Taste

Interaction Plot (BC)Design-Expert Software

Taste

Design Points

C- 75.000C+ 100.000

X1 = B: TimeX2 = C: Power

Actual FactorA: Brand = Cheap

C: Power

4.00 4.50 5.00 5.50 6.00

Interaction

B: Time

Taste

30.0

44.0

58.0

72.0

86.0


21/37

Popcorn Analysis Taste

Contour Plot (BC)Design-Expert Software

TasteDesign Points81

32


Actual FactorA: Brand = Cheap

4.00 4.50 5.00 5.50 6.00

75.00

81.25

87.50

93.75

100.00Taste

B: Time

C:Power

40.0

45.0

50.0

55.0

60.0

65.0

70.0

75.0

75.0

Popcorn Analysis Taste3D Plot (BC)

4.00 4.50 5.00 5.50

6.0075.00

81.25

87.5093.75

100.00

37.0

47.8

58.5

69.3

80.0

Taste

B: Time

C: Power


22/37

Popcorn Analysis TasteAC Interaction Plot Comparison w/ 3D Plot

4.00 4.50 5.00 5.50 6.00

75.0081.25

87.50

93.75

100.00

37.0

47.8

58.5

69.3

80.0

Taste

B: Time

C: Power

C: Power

4.00 4.50 5.00 5.50 6.00

Interaction

B: Time

Taste

30.0

44.0

58.0

72.0

86.0

C-

C+

Popcorn Analysis UPKsYour Turn!

1. Analyze UPKs!

2. Pick the time and power

settings that maximize popcorn

taste while minimizing UPKs.


23/37

Choose factor levels to try to simultaneously satisfyall requirements. Balance desired levels of each

response against overall performance.

Popcorn: Optimization of MultipleResponses!

C: Power

4.00 4.50 5.00 5.50 6.00

Interaction

B: Time

Taste

30.0

40.0

50.0

60.0

70.0

80.0

90.0

C-

C+

C: Power

4.00 4.50 5.00 5.50 6.00

Interaction

B: Time

UPKs

0.1

1.0

1.9

2.7

3.6

C-

C+

1.At the Numerical Optimization node setthe goal for Taste to maximize with alower limit of 60 and an upper limit of90:

Popcorn Optimization


24/37

2. Set the goal for UPKs to minimize witha lower limit of 0 and an upper limit of2:


3.Optimized Solutions :

# Brand* Time Power Taste UPKs Desirability

1 Costly 4.00 100.00 79.0 0.70 0.642 Selected

2 Cheap 4.00 100.00 79.0 0.70 0.642

3 Cheap 6.00 75.00 75.5 1.40 0.394

4 Costly 6.00 75.00 75.5 1.40 0.394

*Has no effect on optimization results.



25/37

4. A quick visual for evaluating desirabilitywith: B:Time vs. C:Power -


Design-Expert Software

Desirability

Design Points

C- 75.000C+ 100.000


Actual FactorA: Brand = Costly

C: Power

4.00 4.50 5.00 5.50 6.00

Interaction

B: Time

Desirability

0.000

0.250

0.500

0.750

1.000

Prediction 0.64

5.Contour Plot


D e s i g n - E x p e r t S o f t w a re

D e s i r a b i l i t yD e s i g n P o i n ts

X 1 = B : T i m eX 2 = C : P o w e r

A c t u a l F a c t o rA : B r a n d = C h e a p

4 .0 0 4 .5 0 5 .0 0 5 .5 0 6 .0 0

7 5 . 0 0

8 1 . 2 5

8 7 . 5 0

9 3 . 7 5

1 0 0 . 0 0Des i rab i l i t y Con tour

B : T i m e

C:Power

0.100

0.100

0.200

0.200

0.300

0.300

0.400

0.500

P re d i ct i 0 .6 4


26/37

6. A 3D Surface -


D e s i g n - E x p e r t S o f t w a r e

D e s i r a b i l i t y

X 1 = B : T i m eX 2 = C : P o w e r

A c t u a l F a c t o rA : B r a n d = C h e a p

4 .00

4.50

5.00

5.50

6.00

75.0 0

81.25

87.50

93.75

100.00

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Desirability

B : T im e

C : P ow er

Benefits of DOE








2

3

4

5

6

1

7


27/37

Predictive Capability Inside Design,Extrapolation Capability Outside Design!

42 32

7781

74 75

71 80

Pow

er

Brand

Time

Benefits of DOE








improve employee moraleimprove employee morale !!!!!!!!!!!!!!!!!!!!

2

3

4

5

6

1

7

8


28/37

Road Map

Road Map


29/37

Not so Breaking News!

Full Factorial Arrays are not Efficient

Do we really need the power of a Fullfactorial design?

A 25 factorial (32 runs) provides data toevaluate:

5 ME, 10 2FI, 10 3FI, 5 4FI, 1 5FI

1

6

4

7

3

5

2

8

+

+

+

+

C

+

+

+

+

AB

+

+

+

+

AC

+

+

+

+

BC

8+++II

5+II

3++II

2++II

7+I

6+I

4++I

1I

StdABCBABlock

Fractional23 Factorial in Two Blocks


30/37

Resolution

The ability to effectively estimate acoefficient.

Full: A, B, C, AB, AC, BC, ABC

III: ME + 2FI A + BC

IV: ME + 3FI A + BCD

2FI + 2FI AB + CD

V: ME + 4FI A + BCDE

2FI + 3FI AB + CDE

Feature:Color-Coded Design Template


31/37

New!Minimum-Run Resolution IV Designs*

The minimum number of runs forresolution IV design is only two times thenumber of factors (runs = 2k). This can offerquite a savings when compared to a regularresolution IV 2k-p fraction.

!" #" $% &% '()*+

Minimum-Run Resolution IV Designs

506425303215

486424283214

466423263213

446422243212

426421223211

406420203210

38641918329

36641816*168

34641714167

32*321612166

Min2k-pkMin2k-pk

506425303215

486424283214

466423263213

446422243212

426421223211

406420203210

38641918329

36641816*168

34641714167

32*321612166

Min2k-pkMin2k-pk

, - ./


32/37

Advantages of DOE vs. OFAT

( ))

( *+ & )),

( -) $) %

( .

( ", -*+ #/ .0 *

( 1*+ -*+ 2 .0 *

( 3 .

( - )

9

8

7

6

5

4

FractionIrregular Fractionkk p

V2

3replicate 12

4

=

4replicate 16

4

=

3replicate 24

4

=

2replicate 16

4

=

3replicate 48

4

=

2replicate 32

4

=

3replicate 48

8

=

4repl icate 64

8

=

3replicate 48

16

=

4replicate 64

16

=

3replicate 96

16

=

4replicate 128

16

=

Resolution V Irregular Fractions*


33/37

Minimum Run Resolution V(MR5) Designs

Regular fractions (2k-p fractional factorials) of 2k

designs often contain considerably more runs than

necessary to estimate the coefficients in the 2FI

model.

The smallest regular resolution V design for k=7

uses 64 runs (27-1) to estimate 29 coefficients.

Balanced minimum run resolution V (MR5)

design for k=7 has 30 runs, a savings of 34 runs.

Disadvantage partial aliasing. MR5 designs

are irregular fractions.

MR5 DesignsProvide Considerable Savings

46610243010625614

3261024259225613

232512218025612212512206812811

192512195612810

17251218461289

1542561738648

1382561630647

1222561522326

MR52k-pkMR52k-pk


34/37

Resolution Summary

22VMR-5

32VI26-1 fraction

24IVSemifold

32IVFoldover

16IV26-2 screening

RunsResolutionDesign

At least consider a resolution V fraction before deciding to screenfor main effects using a resolution IV design.

Road Map


35/37

RSM: When to Apply It

Region of Operability

Region of InterestUse factorial

design to get close

to the peak. Then

RSM to climb it.

RSM vs OFATOFAT

-2 -1 0 1 2

30

45

60

75

90

Factor A

Response

-2 -1 0 1 2

60

65

70

75

80

85

90

Factor B

Response

Response

65

73

80

88

95

Response

-4-2

02

-4

-2

0

2

4

Factor A

Factor B

Response


36/37

Excuses

Claim of no interactions

OFAT is the standard

Stats are confusing

Experiments are too large

Data is too variable

Run the experiments, then evaluate the stats

Vary one factor at a time to reduce confusion

Many of the problems existing in industrytoday are not caused by people within the

workforce, but result from thesystems

within which people must work.

Author Darryl Landvater

Why Experimental Design?


37/37

Lack of Acceptance ?

Perception as Difficult

DOE Statistics

Perception of High Cost

Efficient

Focus on Short Term Solutions

Failure to solve problems permanently

Lack of Change Management Failure to focus on Doing Things Differently

If you always do what you always did;

youll always get what you always got.

- wise but unknown philosopher

Old Habits Methods Die Hard

doe strategies presentation

Documents