Design of Experiments - iqcWoodyiqcwoody.weebly.com/uploads/1/6/2/2/1622879/doe_handout.pdf · Design of Experiments Industrial Quality Consultants LLC page 2 Doing a DOX / DOE Steps

Design of Experiments

Industrial Quality Consultants LLC page 1

How People Learn Lessons from the 20 Questions exercise o o The two elements in any learning process o o The Iterative learning process 1. 3. 2. 4.

Knowledge

Experience

1.

1. 1.

2. 2. 2.

3.

3. 3.

4. 4.



Doing a DOX / DOE

Steps for Doing a DOX determine problem and extent fishbone process flow

brainstorming KT determine response variables determine factors and levels determine organizational opportunities let computer help you design experiment perform "envelope test" run experiment using data sheet collect data analyze results determine important factors optimize for cost or stability the unimportant factors follow up



The Fishbone Example

Fishbone Chart (cause and effect)

Source of problem Response variables

General Category

General Category

General Category

General Category

General Category

(Method) (Operator) (Measurement)

(Machine) (Material)

Sub group

Factors, variables

Sub sub group

levels



The Fishbone

Factor Name - (low) level + (high) level A _______________ _______________ _______________ B _______________ _______________ _______________ C _______________ _______________ _______________



Full Factorial 23 Work Sheet

FACTOR LEVELS NAMES - (low) + (high)

A _____________ _______________ _______________

B _____________ _______________ _______________

C _____________ _______________ _______________

Table of Signs EXPERIMENT

Factor levels Factors listed by name Responses

A

B

C STD (0bs)

order Run

order

A

B

C

Y 1

Y 2

- - - 1 ____ ______ ______ ______ ______ ______

+ - - 2 ____ ______ ______ ______ ______ ______

- + - 3 ____ ______ ______ ______ ______ ______

+ + - 4 ____ ______ ______ ______ ______ ______

- - + 5 ____ ______ ______ ______ ______ ______

+ - + 6 ____ ______ ______ ______ ______ ______

- + + 7 ____ ______ ______ ______ ______ ______

+ + + 8 ____ ______ ______ ______ ______ ______



Envelope Test

The Envelope Test gets its name from the recommended procedure that after the tally is made, the sheet is put in an envelope and put away until the experiment is run and results analyzed. THE PURPOSE: The purpose of the envelope test is to document that learning has occurred. What is listed is the belief of those involved prior to the running of the experiment. It is not intended to point fingers, place blame or anything negative. Names should not be used, only marks to indicate the pretest guess of the important factors. THE PROCEDURE: If there is only one response variable, then only use the Y1 column. If there is more than one response, use additional columns. Ask each person to guess (predict, conjecture, etc.) the factor, factors, or interactions that they think are important. This is equivalent to declaring which effects they think will fall off of the line in the Normal and/or Half Normal Probability Plot. Each person votes for each of the response variables. If they think that a factor will be important, make a tally mark beside that factor ( no names ). Try to get everyone to vote (all those involved in the Fishbone should vote). If someone does not vote, when the experiment is all over and analysis made, they will say "I knew that!".

Envelope Test 23

Factor

Y1 Y2 Y3

A B C

AB AC BC

ABC



Full Factorial 23 Work Sheet -- Main Effects

MAIN EFFECTS

- A + - B +

- C +

MAIN EFFECTS

- A + - B + - C +

- A + - B + - C +

1,3,5,7 2,4,6,8 1,2,5,6 3,4,7,8

1,2,3,4 5,6,7,8



Full Factorial 23 Work Sheet -- Interactions

AB Interaction AB Interaction AB Interaction

- A + - A + - B +

B

-

+ ++

-

- A

B

AC Interaction AC Interaction AC Interaction

- A + - A + - C +

C

-

+ ++

-

- A

C

BC Interaction BC Interaction BC Interaction

- B + - B + - C +

C

-

+ ++

-

- B

C

5,7 6,8

1,3 2,4

1,5

4,8

2,6

3,7

5,6 7,8

1,2 3,4



Full Factorial 23 No Interactions - examples

P - +

Q-

Q+

Neither P nor Q are important

P - +

Q-

Q+

Q are important, P not

P - +

Q-

Q+

P important, Q not

P - +

Q-

Q+

Both P and Q are important

P - +

Q-

Q+

P - +

Q-

Q+



Full Factorial 23 Interactions - examples

Interaction plotsgraphical display and course of action

Y

- Q +

P+

Y

- Q +

Y

- Q +

Y

- Q +

P- P-

P+

P+

P-

for max or min response, use P+and set Q to appropriate level

for consistant response, use P-

and either Q level

P+

P-

P+

P-

for max or min response, use Q+and set P to appropriate level

for consistant response, use Q-

and either P level

P+

P-

for max or min response, bothmust be considered

P-P+

P+

P-for max , avoid P+Q-

for min, use P+Q-

for consistant response, useand either P level

and either Q level

Q+

P-or

P+

P- P-

P+

P+

P+

P-

P-



Full Factorial 23 Cube Plot & Conclusions

Observations / Conclusions

o

o

o

o

2A-B-C- A+B-C-

A-B+C- A+B+C-

A-B-C+ A+B-C+

A-B+C+ A+B+C+

The number in corner of the cube is the standard order number.

A - +

B

C

+

+

- -

6

1

5

3 4

7 8



Two Variables - a Geometric View

Two Variable Plot in cube form

P+

P -

Q - Q+

P+

P -Q - Q+

P+

P -Q - Q+

P+

P -Q - Q+

P+

P -Q - Q+

P+

P -

Q - Q+

P+

P -Q - Q+

P+

P -Q - Q+

P no P yes

Q no

Q yes

INT no

INT yes

Any two factors, say P and Q, can be plotted with the response Y on the ordinate axis. Each of these factors can either be important ( significant... fall off of the Normal Probability Plot line) or not be important. Additionally, the interaction between the two can be important or not. This shows a possible result under the eight potential situations



Steps in the Analysis



Full Factorial 23 Work Sheet calculate EFFECTS

Table of signs for Treatment assignments 23 Standard Order

Avg A B C AB AC BC ABC Response

+ - - - + + + - __________

+ + - - - - + + __________

+ - + - - + - + __________

+ + + - + - - - __________

+ - - + + - - + __________

+ + - + - + - - __________

+ - + + - - + - __________

+ + + + + + + + __________

divisor 8 4 4 4 4 4 4 4

EFFECT ID EFFECT Value

Avg A B C

AB AC BC

ABC



Full Factorial 23Work Sheet

7.1

21.435.750.064.378.6

92.9

dotplot

standard form for an 8 run factorial experiment

Normal Probability Plot

7.1

21.435.750.064.378.6

92.9

dotplot

standard form for an 8 run factorial experiment

Half-Normal Probability Plot



Helpful Hints for Interpretation

Pareto Chart: Look for groups or patterns of long and short bars. Remember “effect sparcity” - more should be unimportant than important.

Normal Probability Plot: Fat dots and wide lines. Again “effect sparcity”, most of the dots make up the line. Important (big players, significant factors) will be off the line - below and to the right or above and to the left. Caution- sometimes the only reason is it off the line is because it is the only negative value - its size(magnitude may be small).

For both probability plots, when the point is far off the line, it is obvious. If it is not far off the line, then there is not much evidence to say the factor associated with that effect has a strong influence.

Half Normal Probability Plot: (used more often for factor selection - especially 8 run designs.) Fat dots and wide lines. Again “effect sparcity”, most of the dots make up the line. Important (big players, significant factors) will be off the line - only below and to the right. It looks only at the magnitude of the effect.

For designed experiments with centerpoints and replicates, a p-value is available to provide statistical evidence of influential factors and interactions.

The List of Calculated Effects: Three factor interactions rarely exist - most of the time it is more an indication of the variation (noise) of the process. If it is one of the points off the line, most of the time you should conclude that none of the factors are important.



DOX Decision Tree A DOX Decision Tree is a tool used when there are multiple response variables for an experiment. The responses are analyzed one at time. A decision is made as to which factor(s) ,if any, are important and then a decision is made about which level of those factors is the preferred operating level.

For the three factor example at the left, there are five response variables (Y1,Y2,Y3,Y4 and Y5). Each was analyzed separately,. • For response Y3 and Y5, nothing was important (fell off of the NP or HNP line). These can be placed on either side of the NONE. • For Y1, factor B was the only important factor and the preferred operating level is the high (+) level. So Y1 is listed beside the B on the + level side. • For Y2, C was the only important factor and the low ( - ) level is preferred. • For Y4, the AC interaction is important so the label is placed on either side of AC and marked with an asterisk. Y4 is also placed beside C low and A high indicating the preferred level for each.

An additional situation that could arise is a type of interaction I call an AVOID. There is an interaction that is important, but there is only one situation that must be avoided. Had the above

three factor example had an AVOID rather than an INT, it would have said to avoid the A at the high ( + ) level and C at the low ( - ) level. Then, because Y2 want to be at the low level, A must also be set to the low ( - ) to avoid the A+C- setting. This form can be used for a test with up to eight factors. With all of the interactions that are possible (28), an alternative procedure can be used to identify the interactions. On either side of the INT (or AVOID) line, list the response with the name of the interaction beside it in parenthesis, labeling the preferred ( or AVOID) setting. For the example above, on either side of the INT line, enter Y4*(A+C-).

ABC

ABACBC

ABC

DOX Decision Tree

- level + level

INT *Avoid #NONE

Three factor example

Y1Y2

Y3

Y4*

Y5

Y4*

Y4*

ABCDEFG

DOX Decision Tree

- level + level

INT *Avoid #NONE

H



The Advantages and Disadvantages

The Advantages and Disadvantages of DOX / DOE over OAATS

Advantages of DOX / DOE over OAATS

•

•

•

•

• Disadvantages of DOX / DOE over OAATS

•

•

•

•



Full Factorial 23 Centerpoints

Definition of Centerpoint Design o Advantages of Centerpoint vs no Centerpoint o o o o

A- +

B

C+

+

- -



Full Factorial 23 Centerpoints

FACTOR LEVELS NAMES - (low) 0 (mid) + (high)

A ___________ ____________ ____________ ____________

B ___________ ____________ ____________ ____________

C ___________ _____________ ____________ ____________

Table of Signs CENTERPOINT EXPERIMENT

Factor levels Factors listed by name Responses

A

B

C STD (0bs)

order Run

order

A

B

C

Y 1

Y 2

- - - 1 ____ ______ ______ ______ ______ ______

+ - - 2 ____ ______ ______ ______ ______ ______

- + - 3 ____ ______ ______ ______ ______ ______

+ + - 4 ____ ______ ______ ______ ______ ______

- - + 5 ____ ______ ______ ______ ______ ______

+ - + 6 ____ ______ ______ ______ ______ ______

- + + 7 ____ ______ ______ ______ ______ ______

+ + + 8 ____ ______ ______ ______ ______ ______

0 0 0 9 ____ ______ ______ ______ ______ ______

0 0 0 10 ____ ______ ______ ______ ______ ______

0 0 0 11 ____ ______ ______ ______ ______ ______

0 0 0 12 ____ ______ ______ ______ ______ ______



Full Factorial 24

Definition of Full Factorial 4 factor design

std orde

r

A B C D AB AC AD BC BD CD ABC ABD ACD BCD ABCD

1 - - - - + + + + + + - - - - + 2 + - - - - - - + + + + + + - - 3 - + - - - + + - - + + + - + - 4 + + - - + - - - - + - - + + + 5 - - + - + - + - + - + - + + - 6 + - + - - + - - + - - + - + + 7 - + + - - - + + - - - + + - + 8 + + + - + + - + - - + - - - - 9 - - - + + + - + - - - + + + -

10 + - - + - - + + - - + - - + + 11 - + - + - + - - + - + - + - + 12 + + - + + - + - + - - + - - - 13 - - + + + - - - - + + + - - + 14 + - + + - + + - - + - - + - - 15 - + + + - - - + + + - - - + - 16 + + + + + + + + + + + + + + +

Advantages o o o o o o



Fractional Factorial Experiments RESOLUTION

A full factorial designed experiment is a design where the high (+) and the low (-) level of each factor is tested in combination with each level of all the other factors. When the number of factors gets large (more than five ) , the number of tests (runs) required starts to become large (32 or more). Through proper selection of a subset of tests, good risk management can be used to balance the number of tests and the information that is lost by not testing all combinations. Judicious selection of the subset is the key to minimizing the loss of information. The information lost is measured as the RESOLUTION of the test. RESOLUTION Resolution is a roman numeral (subscripted) that identifies the level of confounding. Strict definition (BHH p.385): The length of the shortest word in the defining relation. Resolution V means 2 factor interactions (2fi) are confounded (mixed) with 3 factor interactions (3fi) , and main effects are confounded with 4fi. Because we discount 3fi and higher, we deem 2fi and main effects clear. examples: 25-1 The best, most efficient Fractional designs are Resolution V designs. Resolution IV means 2fi are confounded (mixed) with other 2fi, and main effects confounded with 3fi. Main effects are clear. examples: 24-1 , 26-2 , 27-3 , 28-4 Resolution IV designs are pretty good designs. They don't tell you directly which 2fi is important, but they do tell you which MAIN Effects are and some of the 2fi that are not. They work well as screening designs. Resolution III means 2fi are confounded with main effects. Use only for screening test or when you think only main effects may be important. examples: 23-1 , 25-2 , 26-3 , 27-4 , 29-5 , 210-6 , 211-7 Use with caution. One possible use is for problem resolution, where you only want to solve a problem and not understand it at all.



RECOMMENDED DESIGNS Column Assignments and Resolution

Number of variables (factors) 3 4 5 6 7 8

4 23-1 1/2 F C=AB

III

RUNS

8 23 FULL

24-1 1/2 F

D=ABC IV

25-2 1/4 F D=AB E=AC

III

26-3 1/8 F D=AB E=AC F=BC

III

27-4 1/16 F D=AB E=AC F=BC

G=ABC III

16 23 FULL 2Xs

24 FULL

25-1 1/2 F

E=ABCD V

26-2 1/4 F

E=ABC F=BCD

IV

27-3 1/8 F

E=ABC F=BCD G=ACD

IV

28-4 1/16 F E=BCD F=ACD G=ABC H=ABD

IV

Table layout: 26-2

1/4 F E=ABC F=BCD

IV

design name fractionalization column substitutions resolution

Be careful using resolution III designs. Main Effects are mixed with 2fi.

Detailed information is available for the following designs: Design page 24-1 6-6 25-1 6-6 26-2 6-6 27-3 6-7 28-4 6-7



Fractional Factorial column of signs demo

Fractional Factorial Design Generators Resolution k III IV V 3 C=AB (Full) 4 D=ABC (Full) 5 D=AB

E=AC E=ABCD

6 F=BC E=ABC F=ABD

F=ABCDE

7 G=ABC G=ACD G=ABCDEF 8 H=BCD G=ABCD

H=ABEF 9 E=ABC

F=ABD G=ACD H=BCD I=ABCD

F=ABC G=ABD H=ABE I=ACDE

H=ABCDE I=ABCFG

10 J=AB J=BCDE J=ADEF 11 K=AC F=ABC

G=ABD H=ABE I=ACD J=ACE K=ADE

K=BDFG

12 L=AD L=BCD 13 M=BC M=BCE 14 N=BD N=BDE 15 O=CD O=CDE Note: k is the number of factors Resolution III – no main effects are aliased with other main effects, although they may be aliased with a 2 factor interaction (2fi) Resolution IV – no main effects are aliased with any other main effect or 2fi, although a 2fi may be aliased with another 2fi Resolution V – no main effects or 2fi effects are aliased with one another. The number in the black box is the number of runs – i.e means 16 runs.

4

8 8

81616

16

16 32

32

6464

128

256

16

32



Table of signs of a 24-1 -- full table with confounding Generator is D=ABC std

order

A B C (D) AB AC (AD) BC (BD) (CD) ABC (ABD) (ACD) (BCD) (ABCD)

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



Graphical Display of Fractional Factorial

Graphical representation of 25-1

A

BC CA

B

A

BCCA

B

D- +

+

-

E

Each cube shows a representation of ABC 3fi. One is the +ABC the other is the -ABC. The +DE 2fi (D-E- and D+E+) always sees the +ABC while the -DE (D-E+ and D+E-) always sees the -ABC. If the +ABC were assigned to the left two cubes (or the right two) , then the ABC 3fi would be mixed with the D Main Effect. You might also be able to see how a full factorial is formed by dropping out any factor.



Miscellaneous

Blocking

Definition of Blocking A block is a portion of the experimental material that is expected to be more homogeneous than the aggregate. (BHH) Removing a source of variation from the analysis (not the test program) , which is not of interest in testing. Most of the time it you block because you have to , not because you want to. Examples : Batches of raw material which you will be subjecting to test. ( It is best to run your test all from the same batch. If you cannot, you can use blocking to remove differences between batches from the analysis.) Shifts There may be a difference between 1st and 2nd shift and all of the tests cannot be run on the same shift, but we don't want the differences between shifts to pollute the experiment. Operators To remove the difference between operators from the experiment when all runs cannot be made by the same operator, use the operator as a blocking factor. Benefits of blocking

An experiment can produce good results in spite of a known ( or potential ) source of variation. SORTING is not the same as BLOCKING. Sorting is when you want to not randomize one or more of the test factors for economic or connivance reasons. The statistically correct procedure is to completely randomize, however sometimes the economic decision is made not to randomize all factors. As we have said, randomizing is like and insurance policy. You can choose not to take the insurance with increased risk. Good blocking experiments use higher order interactions to set up the blocking schemes. Sorting is using one of the MAIN EFFECTS to set up the blocking scheme. Block what you can and randomize what you cannot !



Miscellaneous

Blocking Setup

Factorial Experiment Layout in Standard Order 24

OBS

ORDER A B C D AB AC AD BC BD CD ABC ABD ACD BCD ABCD 1 - - - - + + + + + + - - - - + 2 + - - - - - - + + + + + + - - 3 - + - - - + + - - + + + - + - 4 + + - - + - - - - + - - + + + 5 - - + - + - + - + - + - + + - 6 + - + - - + - - + - - + - + + 7 - + + - - - + + - - - + + - + 8 + + + - + + - + - - + - - - - 9 - - - + + + - + - - - + + + -

10 + - - + - - + + - - + - - + + 11 - + - + - + - - + - + - + - + 12 + + - + + - + - + - - + - - - 13 - - + + + - - - - + + + - - + 14 + - + + - + + - - + - - + - - 15 - + + + - - - + + + - - - + - 16 + + + + + + + + + + + + + + +

Blocked Factorial Experiment

Block #1

Blocking std ID order 1 1 - - - - + + + + + + - - - - + 2 10 + - - + - - + + - - + - - + + 3 11 - + - + - + - - + - + - + - + 4 4 + + - - + - - - - + - - + + + 5 13 - - + + + - - - - + + + - - + 6 6 + - + - - + - - + - - + - + + 7 7 - + + - - - + + - - - + + - + 8 16 + + + + + + + + + + + + + + +

Block #2

9 9 - - - + + + - + - - - + + + -

10 2 + - - - - - - + + + + + + - - 11 3 - + - - - + + - - + + + - + - 12 12 + + - + + - + - + - - + - - - 13 5 - - + - + - + - + - + - + + - 14 14 + - + + - + + - - + - - + - - 15 15 - + + + - - - + + + - - - + - 16 8 + + + - + + - + - - + - - - -



Miscellaneous

Transformations

Handling Skewed Distributions Another data characteristic that is often encountered in the analysis of process variation studies is the skewed distribution. Such situations are often present when: 1. There is a positive relationship between the sample standard deviation (S) and average ( X ). 2. The standard deviation is more than 20 to 30 percent of the average.

3. The data range over more than an order of magnitude (i.e. XX

maxmin

is greater than 10).

4. The response must always be positive but can take on small values close to zero as well as

much larger values. Variance components are most frequently used to construct sampling plans that assume the

random variation in the data can be described by a normal distribution. It is, therefore, generally recommended that when a skewed distribution is encountered, the observations be transformed to another scale (e.g., log or square root) so that the variation can be more closely approximated by a normal distribution.

The power transformation is very useful in modeling skewed distributions because it contains

many well-known transformations as special cases. The transformation is given by: Y = XP where X is the original measurement scale and Y is the transformed scale. The parameter P

defines the transformation. Some examples follow: P Transformation 1 none 0.5 square root 0 log -1 reciprocal The value of P can be estimated from the data using either the procedure of Box and Cox (1964), also see Box, Hunter, and Hunter (1978), or by studying the relationship between the average and the standard deviation (Box, Hunter, and Hunter [1978]).



2k

2-LevelOptimizationcenterpoints

Ascent/DescentMethod

3-LevelOptimization DOE

Increased local information

2k-pScreening DOE

Fractional Factorial

Full Factorial

The Simplex method

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-1.5

-0.7

5

0

0.75

1.5

- 1 . 5

- 0 . 2 5

1- 2

- 1

0

1

2

3

Y

AB

P r e d i c t e d V a l u e s

2 - 31 - 20 - 1- 1 - 0- 2 - - 1

-1.5

-0.7

5

0

0.75

1.5

- 1 . 5

- 0 . 2 5

1- 2

- 1

0

1

2

3

Y

AB

P r e d i c t e d V a l u e s

2 - 31 - 20 - 1- 1 - 0- 2 - - 1

-1.5

-0.7

5

0

0.75

1.5

- 1 . 5

- 0 . 2 5

1- 8- 6- 4- 202468

Y

AB

P r e d i c t e d V a l u e s6 - 84 - 62 - 40 - 2- 2 - 0- 4 - - 2- 6 - - 4- 8 - - 6

When using a centerpoint design, it will not distinguish which factor is not linear. You cannot determine from a centerpointdesign which of the three response surfaces shown on the left is the appropriate one.

Further testing is required.These types of designs are most often classified as Response Surface Methodology.

Two conditions make these type of designs most effective:

a non-linear response is indicated (from subject matter knowledge or a centerpoint test)

the levels for both factors are continuous (can take on a range of values)

Factor A is non-linear, B is linear or not important

Factor B is non-linear, A is linear or not important

Both Factor A and B are non-linear

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Taking Advantage of Curvature:Variation Transformation

The principle of heteroscedasticity states that a variable is heteroscedastic if variances are unequal for different settings.

We can shift the mean and reduce the variation!!!

Having a good understanding of process capability will help us to change designs to be robust to manufacturing processes.

X1 X2

Y2

Y1

Optimization



Bibliography & References

• ASQC & Marcel Dekker, Quality Tree, Quality Engineering, ASQC Press, Vol. 5, Num 1. • Barker, TB., Quality By Experimental Design, Marcel Dekker, Inc, New York 1985. • Box, Hunter, Hunter, Statistics For Experiments, First Edition John Wiley & Sons, New York. • The learning process - pages 1-13. • One-at-a-time - pages 12-17. • Full Factorial - pages 306-334. • Fractional factorial - pages 374 - 400. • Box, Hunter, Hunter, Statistics For Experiments, 2nd Edition John Wiley & Sons, New York. • Box, G.E.P. Teaching Engineers Experimental Design with Paper Helicopter, Quality

Engineering, 1992 Vol. 4 Num 2. • Design-Ease Software, by Stat-Ease , Statistics Made Easy , (800-325-9816). • Finn, Lynda, Kramer, Tim, Raynard, Sue, Design of Experiments,: Shifting Quality

Improvement Into High Gear. Joiner Associates, Inc, Quality Progress Magazine by ASQC, 1987

• Gunter, Bert - Idea for the Funnel Test, @ John Deere & Company. 1990. • Gunter, Bert, Statistically Designed Experiments (5 part series), Quality Progress, Dec 1989,

Feb 1990, April 1990, June 1990, Aug 1990. • Hladik, Lori J., Experimental Design Fringe Benefits, Quality Magazine by ASQC, April 1990. • Hendrix, D.C., Sixteen Ways to Mess Up An Experiment, ChemTech Magazine, April 1985. • Kerber, M.W., An analysis of the Catapult, Final Report, EM499, Spring 1990. • Knowtton, Jeff, Kepplinger, Ren, The Exerpimentation Process, Quality Progress by ASQC,

February 1993. • Nybeck, William, Design For Quality, John Deere Dubuque Works, 1990. • Schubert, Kerber, Schmidt, The Catapult Problem: Enhanced Engineering Modeling Using

Experimental Design, Quality Engineering, ASQC Press, Vol. 4 Number 4, 1992.

Documents

Design of Experiments - iqcWoodyiqcwoody.weebly.com/uploads/1/6/2/2/1622879/doe_handout.pdf · Design of Experiments Industrial Quality Consultants LLC page 2 Doing a DOX / DOE Steps