16
Steps to Improvement
A
well-run DOE method leads the
way to better products and processes.
by Ranjit K. Roy, Ph.D.
Improvement
can be achieved in one or more
of the many characteristics
of any given product or process.
In most situations, however,
improvement primarily implies
that performance is enhanced.
Experimental design is one technique
that can be learned and applied
to determine product or process
design for improved performance.
For a high-volume manufactured
part, the two statistical performance
characteristics that manufacturers
typically aim to achieve are
improving the mean (average)
and reducing the variability
around the mean. For improvement,
our goal is to move the performance
of a population of parts to
the target and minimize the
variability around it (see figures
1 and 2). No matter the application,
performance consistency is a
desirable characteristic to
achieve. Performance consistency
is achieved when the performance
is on-target most of the time.
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| Fig
1: Performance Before Experimental
Study |
Fig
2: Performance After Experimental
Study |
An effective way to improve
performance is to optimize the
engineering designs of products
or processes by experimental
means. A structured and economical
way to study projects whose
performance depends on many
factors is to apply the experimental
method known as "design
of experiments," a statistical
technique introduced in the
1920s by Ronald A. Fisher in
England. In the 1950s, Genichi
Taguchi of Japan proposed a
much-standardized version of
the technique for engineering
applications. His prescription
for experiment designs, a new
strategy to incorporate the
effects of uncontrollable factors
and ability to quantify the
performance improvement in terms
of dollars by use of a loss
function, made the DOE technique
much more attractive to the
practicing engineers and scientists
in all kinds of industries.
In January, John Wiley &
Sons Inc. published my book
on DOE/Taguchi technique. Intended
primarily for the self-learner,
the book takes the reader through
the entire application and analysis
process in 16 different steps.
One who learns the topics covered
in these 16 steps well will
be able to handle more than
99 percent of the situations
common to manufacturing and
production activities. Following
are the 16 steps you will need
to master DOE using the Taguchi
approach for your own product
and process design improvement.
Step 1: Design of experiments
and the Taguchi approach
A quick review and understanding
of the Taguchi version of DOE
is essential before diving into
the subject. The purpose here
is to gather a clear understanding
of what DOE is and understand
how Taguchi standardized the
experiment design process to
make the technique easier to
apply.
Step 2: Definition
and measurement of improvement
No experiment that lacks the
means to measure its results
is complete or useful. A clear
definition of objectives and
measurement methods allows us
to compare two individual performances,
but a separate yardstick is
needed to compare performances
of one population (multiple
products or processes) with
another. In general, individual
performance measures are different
for different projects, but
consistency is the means by
which we measure population
performance. Consistent performance
produces reduced variations
around the target (when present)
and results in reduction of
scrap, rejection and warranty.
In this step, you learn how
population performances are
measured and compared.
Step 3: Common experiments
and analyses methods
A common practice for studying
single or multiple factors is
to experiment with one factor
at a time while holding all
others fixed. This practice
is attractive, as it's simple
and supported by common sense.
However, the results are often
misleading and fail to reproduce
conclusions drawn from such
an exercise. A more effective
method for these situations
is to study their effect simultaneously
by setting up experiments following
the DOE technique. This step
should lead to some understanding
of basic DOE principles.
Step 4: Designing experiments
using orthogonal arrays
The word "design"
in "design of experiments"
implies a formal layout of the
experiments that contains information
about how many tests are to
be carried out and the combination
of factors included in the study.
Once the project is identified,
the objectives and factors and
their levels are determined
by following a recommended sequence
of discussion in a planning
meeting. There are many possible
ways to lay out the experiment;
the best method depends on the
project. A number of standard
orthogonal arrays (number tables)
have been constructed to facilitate
designs of experiments. Each
of these arrays can be used
to design experiments to suit
several experimental situations.
This step should be devoted
to learning about the different
orthogonal arrays and understanding
how easy it is to design experiments
by using them.
Step 5: Designing experiments
with two-level factors
Experiments that involve studies
of factors with two levels are
both simple and common. There
are a set of orthogonal arrays
(designated as L-4, L-8, L-12,
L-16, L-32, L-64, etc.) created
specifically for two-level factors.
Experiments of all sizes can
be easily designed using these
arrays, as long as all factors
involved are tested at two levels.
By completing this step, you
will learn how quickly experiments
involving two-level factors
can be designed and analyzed
using the standard orthogonal
arrays.
Step 6: Designing experiments
with three-level and four-level
factors
When only two levels of factors
are studied, the factors' behavior
is necessarily assumed to be
linear. When nonlinear effects
are suspected, more than two
levels of the factors are desirable.
Although many larger two-level
orthogonal arrays can be modified
to accommodate three-level and
four-level factors, a set of
standard arrays such as L-9,
L-18, L-27, modified L-16 and
modified L-32 are also available
for this purpose. This step
should help you learn the design
and analysis of these more complex
experiments.
Step 7: Analysis of
variance (ANOVA)
Calculations of result averages
and averages for factor-level
effects, which only involve
simple arithmetic operations,
produce answers to major questions
that were unconfirmed in the
earlier steps about the project.
However, questions concerning
the influence of factors on
the variation of results --in
terms of discrete proportion
--can only be obtained by performing
analysis of variance. In this
step, you'll learn how all analysis
of variance terms are calculated.
Utilize this step to review
a number of example analyses
to build your confidence in
interpreting the experimental
results.
Step 8: Designing experiments
to study interactions between
factors
Interaction among factors,
which is one factor's effect
on another, is quite common
in industrial experiments. When
experiments with factors don't
produce satisfactory results,
or when interactions among factors
are suspected, the experiment
must accommodate interaction
studies. In this step, your
objective will be learning how
to design experiments to include
interaction and how to analyze
the results to determine if
interaction is present. You
will also learn how to determine
the most desirable condition
in cases in which interaction
is found to be significant.
Although interactions among
several factors, and between
factors at three or four levels,
are also present, studies and
corrections for interaction
between two two-level factors
will suffice for most situations.
The materials in steps 1-8
prepare you for many applications
in the production floor. As
long as the factors you want
to study are all at the same
level, you're able to design
experiments using one of the
available orthogonal arrays.
You're also able to analyze
the results of such experiments
following the standard method
of analysis, which uses the
averages (means) of the multiple
sample test results of individual
experiments, and determine the
optimum design conditions. With
the knowledge you should gather
in these steps, you can indeed
apply the DOE to solve most
production problems whose solutions
lie in finding the proper combination
of the controllable factors,
instead of some special causes.
The reality, however, is that
you will often have factors
at mixed levels; some will be
at three-level, some at four-level,
and many at two-level. You also
need to learn how to analyze
the results for variability.
Recall that it's the reduction
of variability, which instills
performance consistency, that
we're after. The following additional
steps address these items and
prepare you to handle most every
type of experimental situation.
If your applications always
involve production problem solving,
you may find that your knowledge
up to this point is quite adequate
for the job. Nevertheless, you
may want to sharpen your application
skills before proceeding to
learn about the advanced concepts
in the technique described in
the eight steps that follow.
Step 9: Experiments
with mixed-level factors
Experiment designs with all
of the factors at one level
are easily handled using one
of the available standard arrays.
But these standard arrays can't
always accommodate many mixed-factor
situations that you might find
in industrial settings. Most
mixed-level designs, however,
can be accomplished by altering
the standard orthogonal arrays.
Your goal will be to learn the
procedure by which columns of
an array are modified to upgrade
and downgrade the number of
levels in creating a new column.
This way, a two-level array
can be modified to have three-level
and four-level columns. Conversely,
to accommodate a factor with
a lesser number of levels, a
four-level column can be reduced
to a three-level, and a three-level
column to two-level, by a method
known as "dummy treatment."
Step 10: Combination
designs
For some applications, the
factors and levels are such
that standard use of the orthogonal
array doesn't produce an economical
experimental strategy. In such
situations, a special experiment
design technique such as a combination
design might offer a significant
savings in number of samples.
This step will familiarize you
with the necessary assumptions
that must be made in order to
lay out experiments using combination
design. With this technique,
generally, two two-level factors
are studied by assigning them
to a three-level column.
Step 11: Robust design
strategy
Variations among parts manufactured
to the same specifications are
common even when attempts are
made to keep all factors at
their desired levels. Remember,
variation reduction is our ultimate
goal. When performance is consistently
on-target (the desired value),
the customer perceived quality
of the product is favorably
affected. Variation is most
often due to factors that are
not controllable or are too
expensive to control. These
are called the "noise factors."
In robust design methodology,
the approach is not to control
the noise factors, but to minimize
their influence by adjusting
the controllable factors that
are included in the study. This
new strategy, promoted by Taguchi,
reduces variability without
actually removing the cause
of variation.
Step 12: Analysis using
signal-to-noise (S/N) ratios
The traditional method of
calculating average factor effects
and thereby determining the
desirable factor levels (optimum
condition) is to look at the
simple averages of the results.
Although average calculation
is relatively simple, it doesn't
capture the variability of results
within a trial condition. A
better way to compare the population
behavior is to use the mean-squared
deviation, which combines effects
of both average and standard
deviation of the results. For
convenience of linearity and
to accommodate wide-ranging
data, a logarithmic transformation
of MSD (called the signal-to-noise
ratio) is recommended for analysis
of results. This step will teach
you how MSD is calculated for
different quality characteristics
and how analysis using S/N ratios
differs from the standard practice.
When the S/N ratio is used for
results analysis, the optimum
condition identified from such
analysis is more likely to produce
consistent performance.
Step 13: Results analysis
using multiple evaluation criteria
Often, a product (or process)
is expected to satisfy multiple
objectives. The result in this
case comprises multiple evaluation
criteria, which represents performance
in each of the objectives. It's
common practice, however, to
analyze only one criteria at
a time because different objectives
are likely to be evaluated by
different criteria, each of
which has different units of
measurement and relative weighting.
When the results are analyzed
separately for different criteria
and the desirable design conditions
are determined, there is no
guarantee that the factor combination
will all be alike. An objective
way to analyze the results is
to combine the multiple evaluations
into a single criterion, which
incorporates the units of measurements
and the relative weights of
the individual criterion of
evaluation. You should devote
your time during this step to
learning the principles involved
in formulation of an overall
evaluation criterion for analysis
of multiple objectives, when
present.
Step 14: Quantification
of variation reduction and performance
improvement
Most of your DOE applications
allow you to determine optimum
design that is expected to produce
an overall better performance.
The improvement of performance
often means that either the
average or the variations (or
both) have improved. When the
new design is put into practice
(i.e., the recommended design
is incorporated), it's expected
to reduce scrap and warranty
costs. In turn, this reduction
more than offsets the cost of
the new design. The expected
monetary savings from the improved
design can be calculated by
using Taguchi's loss function.
In this step, you'll learn how
to estimate the expected savings
from the improvement predicted
by the experimental results.
Further, you'll also learn how
the expected improvement in
performance from the new design
is expressed in terms of capability
improvement indexes such as
Cp and Cpk.
Step 15: Effective experiment
planning
As far as
the benefits from the technique
are concerned, experiment planning
is the most important among
the different application activities.
Therefore, it's a required first
and necessary step in the application
process. Planning for DOE/Taguchi
requires structured brainstorming
with project team members. The
nature of discussions in the
planning session is likely to
vary from project to project
and is best facilitated by one
who is well-versed in the technique.
Your effort in this step will
be to learn the structure of
proven planning sessions documented
by experienced application specialists.
Step 16: Review of example
case studies
The application knowledge
gained in steps 1-15 could be
overwhelming if you didn't have
immediate projects on which
to practice. One way to build
more confidence and extend your
application expertise is by
familiarizing yourself with
numerous types of case studies
with complete experiment design
and results analysis. In this
final step, you should seek
out and thoroughly review complete
project application reports.
Complete case studies should
contain discussions under most
of the following topics:
Now that you have an
idea about the topics and the
study sequence, one question
remains: How do you actually
go about learning them?
To get yourself comfortable
with DOE application knowledge,
you will need to understand
four phases in the application
process: (1) experiment planning,
(2) experiment design, (3) results
analysis and (4) interpretation
of results. Of these, you need
not --and may not be able to
afford the time --to be too
good with experiment design
and number crunching. These
are mundane tasks, so feel comfortable
letting a computer program do
the work for you; your focus
should be to learn the practiced
and proven discipline of how
to plan an experiment following
a structured sequence of discussion.
The experiment planning process
requires more the art of teamwork
than experimental science. Only
the experienced can describe
and share methods that have
worked. Look for references
that describe and teach the
technique through application
examples.
Both experiment planning and
interpretation analysis are
areas you'll want to gain control
over. The nature of discussions
and findings in these areas
are always project-specific.
As the experimenter, you'll
know far more about these two
areas than anyone else. Good
knowledge of the project objectives,
how objectives are evaluated,
how the factors included in
the study were selected, and
so on will help you confidently
interpret results from the routine
analysis. You will benefit most
when your reference book stresses
application rather than theory.
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