DOE

1. QUALITY TOOLS &
TECHNIQUES
1
TQ T
DESIGN OF EXPERIMENT
By: -
Hakeem–Ur–Rehman
Certified Six Sigma Black Belt (SQII – Singapore)
IRCA (UK) Lead Auditor ISO 9001
MS–Total Quality Management (P.U.)
MSc (Information & Operations Management) (P.U.)
IQTM–PU

2. WHAT IS EXPERIMENT?
2
 In statistics, an experiment refers to any process that
generates a set of data.
 An experiment involves a test or series of test in which
purposeful changes are made to the input variables of a
process or system so that changes in the output responses
can be observed and identified.
Noise Factors

3. OBJECTIVES OF CONDUCTING
AN EXPERIMENT
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1. Determining which variables (Input), X, are
most influential on the response (output), y,
in a study.
2. Determining where to set the influential X’s
so that ‘y’ is near the nominal requirement.
3. Determining where to set the influential x’s so
that variability in ‘y’ is small.
4. Determining where to set the influential x’s so
that the effects of uncontrollable variables ‘z’
are minimized.

4. TERMINOLOGIES
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Terms used in Design of Experiments (DOE) need to defined, these are:
 RESPONSE:
 A measurable outcome of interest, e.g.: yield, strength, etc.
 FACTORS:
 Controllable variables that are deliberately manipulated to determine their individual
and joint effects on the response(s), OR Factors are those quantities that affect the
outcome of an experiment, e.g.: temperature, time, etc.
 LEVELS:
 Levels refer to the values of factors for which the data is gathered, “values that factor
will take in an experiment”, e.g.:
Level–1 for time = 2hours
Level–2 for time = 3 hours
 TREATEMENT:
 A set of specified factor levels for an experimental run, e.g.:
Treatment–1: time = 2hrs and temperature = 1750 C
Treatment–2: time = 3hrs and temperature = 2250 C
 NOISE:
 Variables that affect product / process performance, whose values cannot be
controlled or are not controlled for economic reasons.
 REPLICATION:
 Replication is a systematic duplication of series of experimental runs. It provides the
means of measuring precision by calculating the experimental error.

5. EXAMPLES
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 EXAMPLE–1:
 In a MACHING PROCESS
 RESPONSE: Surface Finish “Y”
 FACTORS: Speed of machine “XA” & Depth of
Cut “XB”
 LEVELS: High & Low
 EXAMPLE–2:
 In a POPCORN MAKING PROCESS
 RESPONSE: Volume (ml) Yield of Popcorn “Y”
 FACTORS: Type of Popper “XA” & Grade of
corn used “XB”
 LEVELS: Air, and Oil & Budget, Regular and
luxury

6. TYPES OF EXPERIMENTS
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EXPERIMENTS
ONE-FACTOR AT A TIME
EXPRIMENTS
BEST GUESS
EXPERIMENTS
FACTORIAL
EXPERIMENTS

7. FACTORIAL EXPERIMENTS
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 Factorial experiment is the CORRECT and MOST EFFICIENT type of experiment in dealing
with several factors involved in a study; Factors are varied together instead of one at time.
The Three Basic Principles of experimental design are:
1. Replication
2. Randomization
3. Blocking
1. REPLICATION:
 It has two important properties:
 Allow us to obtain an estimate of Experimental error which provide a basic unit of
measurement for determining whether observed differences in the data are really
Statistically different.
 If sample mean is used to estimate the effect of a factor, then replication allow a more
precise estimate of the effect.
2. RANDOMIZATION:
 By randomization, both the allocation of the experimental material and the order of individual
runs or trails can be perform randomly;
 As statistical methods required observations be independent distributed, randomization made
this assumption valid.
3. BLOCKING:
 An experiment is arranging the runs of the experiment in groups “Blocks” so that runs within
each block have as much minor variation in common with each other as possible.
 e.g.: Runs using material from the same lot
 Runs carried out within a short time frame

8. 2K FACTORIAL
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 2K Factorial Designs are experiments where all
FACTORS have only TWO LEVELS
 The number of combinations (Runs) for Full
Factorial Design is denoted as n = 2k (where
k=number of Factors)
2K
Factors
Levels

9. 22 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE: Consider the manufacture of a product, for use
in the making of paint, in a batch process. Fixed amounts of raw
material are heated under pressure in rector-1 for a fixed period
of time and the product is then recovered. Currently the process
is operated at temperature 225o C and pressure 4.5 bar. As part
of Six Sigma project, aimed at increasing product yield, a 22
factorial experiment with two replications was planned. Yields
are typically around 90 Kg. It was decided after discussion
amongst the project team to use the levels 200o C and 250o C
for temperature and level 4.0 bar and 5.0 bar for pressure.
 RESPONSE: Product Yield “Y”
 FACTORS: Temperature “XA” & Pressure “XB”
 LEVELS: 200o C and 250o C & 4.0 bar and 5.0
bar

10. 22 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE (Cont…):

11. 22 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE (Cont…):
Stat > DOE > Factorial > Factorial Plots

12. 22 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE (Cont…):
The Main Effect Plot indicate that:
 On average, increasing temperature from
200o C to 250o C increases yield of
product by 8 kg.
 On average, increasing pressure from 4
bar to 5 bar decreases yield of product by
6Kg.
The parallel lines indicate no temperature–
Pressure interaction here.

13. 22 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE (Cont…):
Stat > DOE > Factorial > Analyze Factorial Design…
Factorial Fit: Yield versus Temperature, Pressure
Estimated Effects and Coefficients for Yield (coded units)
Term Effect Coef SE Coef T P
Constant 92.000 0.9354 98.35 0.000
Temperature 8.000 4.000 0.9354 4.28 0.013
Pressure -6.000 -3.000 0.9354 -3.21 0.033
Temperature*Pressure 0.000 -0.000 0.9354 -0.00 1.000
S = 2.64575 PRESS = 112
R-Sq = 87.72% R-Sq(pred) = 50.88% R-Sq(adj) = 78.51%
The P–Value indicate
that both temperature &
pressure have a real
effect on Yield.

14. 22 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE (Cont…):

15. 22 FACTORIAL
EXPERIMENTAL DESIGN
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EXERCISE:
An Engineer desire to study which is the
2 Factors determined that affect the
Defect Rate in his production line.
FACTORS:
Temperature & Pressure
LEVELS:
Temperature – 60 & 70o C &
Pressure – 3.0 & 5.5 Bar
REPLICATES: 3
DEFECT
3.93183
2.30259
0.0000
2.07944
4.33073
3.33220
2.39790
0.69315
2.19722
2.83321
1.38629
1.38629

16. 23 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE: A plastic manufacturing company had
formed a work improvement company had formed a
work improvement team consisting of engineers from
different department. The team objective is to strive to
improve the yield of a coating process. After a series of
brainstorming session, the team determined that the
following are the deciding factors and levels:
A: Temperature: 400o F and 450o F
B: Catalyst Con.: 10% and 20%
C: Processing Ramp time: 45 seconds and 90
seconds
The design is a 23 factorial and each run (treatment) is
replicated 3 times and total is 24 randomized trial.

17. 23 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE (Cont…):

18. 23 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE (Cont…):
Stat > DOE > Factorial > Factorial Plots

19. 23 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE (Cont…):

20. 23 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE (Cont…):

21. 23 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE (Cont…):
Stat > DOE > Factorial > Analyze Factorial Design…

22. 23 FACTORIAL
EXPERIMENTAL DESIGN
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EXAMPLE (Cont…):

23. GENERAL FULL
FACTORIAL DESIGN
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 A design in which at least one factor has
more than two levels.
 The experimental Runs includes all
combination of these factor levels.
Note: “Cube Plot, & Pareto Plot cannot be used in General Full
Factorial Design.”

24. GENERAL FULL
FACTORIAL DESIGN
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 Example:
 Create a General Full Factorial Experiment Where:
 FACTORS: Temperature, Operators, and Cycle Time
 LEVELS:
 Temperature: 300 & 350
 Operators: 1, 2 & 3
 Cycle Time: 40, 50 & 60
 Replicate = 3
 Response = Score

25. GENERAL FULL
FACTORIAL DESIGN
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 Stat  DOE  Factorial  Create Factorial Design…
Define Design

26. GENERAL FULL
FACTORIAL DESIGN
 CREATE THE DESIGN
Define Factors / Levels
Randomize Runs

27. GENERAL FULL
FACTORIAL DESIGN
THE PLAN:

28. GENERAL FULL
FACTORIAL DESIGN
Stat  DOE  Factorial  Analyze factorial Design

29. GENERAL FULL
FACTORIAL DESIGN
210-1-2
99
90
50
10
1
Standardized Residual
Percent
34323028
2
1
0
-1
-2
Fitted Value
StandardizedResidual
210-1-2
10.0
7.5
5.0
2.5
0.0
Standardized Residual
Frequency
50454035302520151051
2
1
0
-1
-2
Observation Order
StandardizedResidual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Score
Only temperature is a
significant factor as its P-
Value is less than 0.05

30. GENERAL FULL
FACTORIAL DESIGN
Stat  DOE  Factorial  Factorial Plots

31. GENERAL FULL
FACTORIAL DESIGN
350300
32
31
30
321
605040
32
31
30
Temperature
Mean
Operators
Cycel Time
Main Effects Plot for Score
Data Means
321 605040
32
30
28
32
30
28
T emperature
Operators
Cycel T ime
300
350
Temperature
1
2
3
Operators
Interaction Plot for Score
Data Means

32. QUESTIONS