Lean Six Sigma Process Improvement Tools and Techniques: Design of Experiments

Lean Six Sigma: Process
Improvement Tools and Techniques
First Edition
Chapter 21
Design of Experiments
Copyright © 2011 Pearson Education, Inc. All Rights Reserved

Design of Experiments (1 of 32)
• Design of Experiments is a method of experimenting with
complex processes with the objective of optimizing the
process.

• Dr. Genichi Taguchi (1924- )
– Loss Function
▪ Quality, or the lack of it, is a loss to society
– Experiment Design
– Four Basic Steps to Experiments
▪ Select the process/product to be studied
▪ Identify the important variables
▪ Reduce variation on the important process
improvement
▪ Open up tolerances on unimportant variables

• Design of experiments seeks to:
– Determine which variables affect the system.
– Determine how the magnitude of the variables affects
the system.
– Determine the optimum levels for the variables.
– Determine how to manipulate the variables to control
the response.

• Methods of Experimentation
– Trial and Error
– Single Factor Experiment
▪ one change at a time
– Fractional Factorial Experiment
▪ change many things at a time
– Full Factorial Experiment
▪ change many things at a time
– Others (Box-Jenkins, Taguchi, etc.)

• Trial and Error Experiments
– Lack direction and focus
– Guesswork

• Trial and Error Experiment Example
Problem: Selecting copying settings to prepare a document
Contrast Size
7 93
6 85
5 78
• How many different permutations exist?
• What would happen if we added three settings for location
(center, left flush, right flush)?

• Single Factor Experiment
– A single factor experiment allows for the manipulation
of only one factor during an experiment.
▪ Select one factor and vary it, while holding all other
factors constant.
– The objective in a single factor experiment is to isolate
the changes in the response variable as they relate to
the single factor.

– These types of experiments are:
▪ Simple to Analyze
– Only one thing changes at a time and you can
see what affect that change has on the system.
▪ Time Consuming
– Changing only one thing at a time can result in
dozens of repeated experiments.

– In these types of experiments:
▪ Interactions between factors are not detectable.
– These experiments rarely arrive at an optimum
setup because a change in one factor frequently
requires adjustments to one or more of the other
factors to achieve the best results.
– Life isn’t this simple
▪ Single factor changes rarely occur that are not
inter-related to other factors in real life..

• Single Factor Experiment Example
Problem: What combination of factors avoids tire failure?
Speed Temperature Tire Pressure Chassis Design
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• Fractional Factorial Experiment
– Studies only a fraction or subset of all the possible
combinations.
▪ A selected and controlled multiple number of factors
are adjusted simultaneously.
– This reduces the total number of experiments.
– This reveals complex interactions between the
factors.
– This will reveal which factors are more important
than others.

• Fractional Factorial Experiment Example
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• Full Factorial Experiment
– A full-factorial design consists of all possible
combinations of all selected levels of the factors to be
investigated.
▪ Examines every possible combination of factors at
all levels.

• Full Factorial Experiment
– A full-factorial design allows the most complete
analysis
▪ Can determine main effects of the factors
manipulated on response variables
▪ Can determine effects of factor interactions on
response variables
▪ Can estimate levels at which to set factors for best
result
– Time consuming

• Full Factorial Experiment Example
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65 85 32 A
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65 85 32 B
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• Conducting an Experiment: The Process
– Plan your experiment!
▪ Successful experiments depend on how well they
are planned.
– What are you investigating?
– What is the objective of your experiment?
– What are you hoping to learn more about?
– What are the critical factors?
– Which of the factors can be controlled?
– What resources will be used?

– Setting up your experiment.
▪ Determine the factors
– How many factors will the design consider?
– How many levels (options) are there for each
factor?
– What are the settings for each level?
– What is the response factor?

– Select a study for your experiment
▪ Full Factorial
▪ Fractional Factorial
▪ Other

– Run your experiment!
▪ Complete the runs as specified by the experiment
at the levels and settings selected.
▪ Enter the results into analysis program.

– Analyze your experiment!
▪ Use statistical tools to analyze your data and
determine the optimal levels for each factor.
– Analysis of Variance
– Analysis of Means
– Regression Analysis
– Pairwise comparison
– Response Plot
– Effects Plot
– Etc.

– Apply the knowledge you gained from your experiment
to real life.

• An ANO M is an analysis of means.
– A one-way analysis of means is a control chart that
identifies subgroup averages that are detectably
different from the grand average.
▪ The purpose of a one-way ANO M is to compare
subgroup averages and separate those that
represent signals from those that do not.
– Format: a control chart for subgroup averages,
each treatment (experiment) is compared with
the grand average.

• An ANOVA is an Analysis of Variance
– Used to determine whether or not changes in factor levels
have produced significant effects upon a response variable.
▪ An ANOVA estimates the variance of the X using two-
three different methods.
– If the estimates are similar, then detectable
differences between the subgroup averages are
unlikely.
– If the differences are large, then there is a difference
between the subgroup averages that are not
attributable to background noise alone.
– ANOVA compares the between-subgroup estimate
of variance of x with the within subgroup estimate.

• Definitions:
– Factor:
▪ The variable that is changes and results observed.
– A variable which the experimenter will vary in
order to determine its effect on a response
variable.
•
(Time, temperature, operator ...)
– Level:
▪ A value assigned to change the factor.
– Temperature; Level 1:110, Level 2 :150

• Definitions:
– Effect:
▪ The change in a response variable produced by a
change in the factor level.
– Degree of Freedom:
▪ The number of levels of a factor minus 1.
– Interaction:
▪ Two or more factors that, together, produce a result
different that what the result of their separate
effects would be.

• Definitions:
– Noise factor:
▪ An uncontrollable (but measurable) source of
variation in the functional characteristics of a
product or process.
– Response variable:
▪ The variable(s) used to describe the reaction of a
process to variations in control variables (factors).
▪ The Quality characteristic under study.

• Definitions:
– Treatment:
▪ A set of conditions for an experiment
– factor x level used for a particular run.
– Run:
▪ An experimental trial. The application of one
treatment to one experimental unit.

• Definitions:
– Replicate:
▪ Repeat the treatment condition.
– Repetition:
▪ Multiple results of a treatment condition.
– Significance:
▪ The importance of a factor effect in either a
statistical sense or in a practical sense.

• Types of Errors
– Type I Error:
▪ A conclusion that a factor produces a significant
effect on a response variable when, in fact, its effect
is negligible (a false alarm).
– Type II Error:
▪ A conclusion that a factor does not produce a
significant effect on a response variable when, in
fact, its effect is meaningful.

• Experiment Errors
– lack of uniformity of the material
– inherent variability in the experimental technique

• Characteristics of a Good Experiment Design
– The experiment should provide unbiased estimates of
process variable and treatment effects (factors at
different levels).
– The experiment should provide the precision
necessary to enable the experimenter to detect
important differences.
– The experiment should plan for the analysis of the
results.

• Characteristics of a Good Experiment Design
– The experiment should generate results that are free
from ambiguity of interpretation.
– The experiment should point the experimenter in the
direction of improvement.
– The experiment should be as simple as possible.
▪ Easy to set up and carry out
▪ Simple to analyze and interpret
▪ Simple to communicate or explain to others

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Lean Six Sigma Process Improvement Tools and Techniques: Design of Experiments

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