DOE Design Of Experiments - Engineering - My LIUC
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Engineering
DOE
Design Of
Experiments
(notes)
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 1DOE - Design Of
Engineering
Experiments - introduction – purpose of the lecture notes (1)
Purpose of these notes on DOE is:
▪ both to get the students familiar with some
problems - summed up by the concepts of “internal
validity” and “external validity” - related to the
results of tests on some suitable subjects
▪ … and to show to the students themselves some
tests patterns related to the above concepts
As additional information it’s also to say that what shown in
the following must be meant as preliminary to DOE subject,
so the achievement of a professional sound knowledge would
require a thorough further study in depth.
Most of this document’s content is extracted from:
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 2DOE - Design Of
Engineering
Experiments - introduction – meaning (1)
Design of experiments (DOE) is a systematic, rigorous
approach to engineering problem-solving that applies
principles and techniques at the data collection stage so as to
ensure the generation of valid, defensible, and supportable
engineering conclusions. In addition, all of this is carried out
under the constraint of a minimal expenditure of engineering
runs, time, and money.
[https://www.itl.nist.gov - US National Institute of Standards and Technology
Design of Experiments (DOE) is a method to find out the relation between
factors affecting a process and the output of the process. It tries to build a
cause & effect relationship so that the outcome of a process can be predicted
under given pre-conditions. It is also called a quasi-experiment. To establish
the relationship, a set of experiments are conducted and then the value of
the output parameter is analyzed and interpreted.
[https://www.itl.nist.gov - US National Institute of Standards and Technology
DOE is defined ad “… branch of applied statistics deals with planning,
conducting, analyzing and interpreting controlled tests to evaluate the factors
that control the value of a parameter or group of parameters.
[https://asq.org/ ASQ Quality resources
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 3DOE
Resistenza
Resistenza
- Design
dei
dei
Of
Engineering
Experiments
materiali
materiali - introduction – meaning (2) – additional note (i)
The meaning of DOE is conceptually linked to the one of «research»
Research designs are the
plans and the procedures
for research that span the
decisions from broad
assumptions to detailed
methods of data collection
[J. Cresswell – Research Design ]
and analysis. It involves
the intersection of
philosophical assumptions,
strategies of inquiry, and
specific methods
[J. Cresswell – Research Design –
SAGE]
Scientific method is that process by
which deductive and inductive
reasoning methods are employed to
empirically develop knowledge
Modern engineering investigations would be tipically referred to «scientific
method» whose itsown concept includes quantitative research
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 4DOE - Design Of
Engineering
Experiments - introduction – meaning (2) – additional note (ii)
Quantitative research is a mean for
testing objective theories and by
examining the relationship among
variables. These variables can be
measured, typically on instruments, so
that numbered data can be analyzed
using statistical procedures. The final
written report has a set structure
consisting of introduction, literature and
theory, methods, results and
discussions
[J. Cresswell – Research Design]
after due considerations, one could say
that quantitative research reflects the
content of modern scientific method
which combines the deductive and
inductive reasoning processes, and
adds the use of appropriate and
advanced experimental design
conditions to yield a comprehensive,
complex and highly disciplined method
[J. T. Luftig, V. S. Jordan - Design of Experiments in Quality
of inquiry.
Engineering]
references before “modern scientific method” have been “trial and error” (beginning of
20th century) and “empirical method” which combined with empirical methods.
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 5DOE - Design Of
Engineering
Experiments - design process – plan phase (1)
• the plan phase includes:
✓ refine and develop statements of the
problem
Now, apart from the first
✓ define the research study
three issues (about which
framework
following pages propose an
✓ write the research exercise), the other ones
question(s)/hypothesis are related to internal
validity and to external
✓ define/select the dependent
validity, that’s possible
variable(s)and criterion measures
threats that could impact
✓ identify and classify treatment, the design itself. Such
independent and nuisance variables threats are related to the
way of the development,
✓ create the most appropriate and
design and to the ability to
efficient experimental design
generalize its results.
available as possible
Following that some
✓ design the sampling plan typical test patterns able
✓ assess the data collection to cause or to protect
instrumentsDOE - Design Of
Engineering
Experiments - design process – plan phase (2) – exercise (i)
➢ the following exercize is referred at the first three items of the plan
phase.
Imagine that we have created a background data base for the deployment of activties
oriented toward the urgent needs for cost reduction in a particular manufacturing facility.
Financial impact data and cost-benefits analyses have revealed that one of the major cost in
this facility correspond to the purchase of knives for use on a machine that skits material.
These knives are used until they are worn and are replaced on a regular base. Not only are
the knives themselves expensive, but the downtime associated with their replacement is
significant (mean replacement time has been calculated to be 32,5 minutes). As a result of
an appeal to common sense based upon previous experience, some of the plant’s line
personnel have indicated that the mean time between failures (MTBF) varies for knives
purchased from the three current suppliers. These data have never been assessed on a
formal basis. However, a permanent record has been maintained by the production
organization for the last three years as related to both (1) time to failure and (2) time to
replacement. A decision has been made to review the data base and seek out potetial
opportunities.
Your assignment as related to this problem decision is:
1. Classify the type of research study most likely to be conducted.
2. Write a statement of the problem.
3. Write an appropriate set of research questions or hypothesis based upon your statement
of the problem
[J. T. Luftig, V. S. Jordan - Design of Experiments in Quality
Engineering]
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 7DOE - Design Of
Engineering
Experiments - design process – plan phase (3) – exercise (ii)
The classification of analytical research, whose meaning is linked to the extraction of
relationships from a deductive system, is opposing to other types of research, that’s:
• Descriptive ---> aimed to determine what something is,
• Relational ---> focused on possible relationships between variables,
• Experimental ---> finalized to discover casual relationships.
1. Classification of the type of research
Since we’re evaluating historical data (three years history of time to failure and time for
replacement) to compare MTBF for the three current suppliers, the type of research used
is analytical research (historical).
2. Statement of the problem.
The purpose of this study is to determine whether the life of slitter knives varies for
knives purchased from our three current suppliers. The knives of interest for this study
are all knivs used on this machine for the last three years. Life will be based on the basis
of time to failure and time to replacement.
3. Research hypothesis
There are no significant difference in slitter knife life (as measured by time to failure and
time to replacement) for our three current suppliers.
[J. T. Luftig, V. S. Jordan - Design of Experiments in Quality
Engineering]
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 8DOE - Design
Engineering
Of Experiments - design process
and external validities (i)
– plan phase (4) – internal
About the subsequent items of the plan plan phase, it’s important to take
into account the threats that could impact on the test’s outcome. Such threats
are represented by the concept of internal and external validity.
✓ internal validity: internal validity is a function of the degree to which the
design is technically correct , as well as the successful elimination and
control of systematic errors (Spector, 1982). Experimental research that is
internally valid usually allows us to generalize the sample results to the
equivalent effects for the research’s population.
✓ external validity: external validity refers to the overall ability to
generalize, or used the results of a study. Specifically, a study is said to be
externally valid if it is (1) internally valid, or technically sound, and (2) the
result of the study associated with the research’s population can be
generalized to the target population or universe.
Such validities’ definition are linked to the more known Type I and Type II errors (or α and
β errors) that’s:
▪ Type I: the incorrect decision to reject the null hypothesis (in other words to say that a
treatment, meant as independent variable, doesn’t affect the subject, meant as
dependent variable, while it’s influenced) internal validity
▪ Type II: the incorrect decision to accept the null hypothesis (to say that a treatment
affects the subject while it doesn’t) external validity
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 9DOE - Design Of
Engineering
Experiments - design process
and external validities (ii)
– plan phase (5) – internal
[J. T. Luftig, V. S. Jordan - Design of Experiments in Quality Engineering]
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 10DOE - Design Of
Engineering
Experiments - design process
and external validities (iii)
– plan phase (5) – internal
➢ The validity of of a test’s outcome is often invalidated by the effects of
an extraneous or unknown variables intermingled with the treatment’s
ones. About it some tests’ patterns have been generated in order to
protect by not validities occurrence.
➢ Such patterns use a characterictic simbology, that’s:
• R which stanf for the applicaton of randomization criteria,
• O that is about observations or measurements of variables,
• X which means the application of the tretment.
About R: lackness of randomization is the most useful cause of error.
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 11DOE - Design Of
Engineering
Experiments - design process
and external validities (iv)
– plan phase (5) – internal
Examples of designs typically impacting on Type I error
are:
✓ once-shot case study X O
• in the absence of comparative data an inference of improvement can
not be justified
✓ one-group pretest-posttest design O X O
• how do we know that something else (during the treatment
application) did not change?
✓ static group comparison design X O
O
• … the second O represents a control group
• … absence of randomization assurance (represented by the dashed
line).
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 12DOE - Design Of
Engineering
Experiments - design process
and external validities (v)
– plan phase (6) – internal
More in general … factors jeopardizing the internal validity:
▪ history events affecting the experimental units (dependent variables)
and arising between subsequent measurements.
▪ maturation phenomena arising into the experimental units not related to
the the treatment (fatigue, wear etc.)
▪ selection (biases) inappropriate randomization ways are employed (sampling,
assignment etc.) resulting in differences between comparative
groups attributed to the treatment effect
▪ mortality loss of experimental units or subjects during the conduction of
the experiment,
▪ testing effects detectable after first obeservations.
▪ instrumentation results confounded with the treatment but due to changes in
observations’ processes.
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 13DOE - Design Of
Engineering
Experiments - design process
and external validities (vi)
– plan phase (7) – internal
Examples of designs typically protecting on Type I error are:
✓ pretest-posttest control group design
R O X O
R O X O
✓ posttest-only control group design
R X O
R X O
No pretest is considered because, in specific cases, one could be
concerned as whether pretested experimental units respond to the
treatment effect in the same way the experimental units not pretested
will respond
✓ Solomon four groups design
R O X O
R O X O
R O X O
R O X O
… it combines the strengths of the two above groups
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 14DOE - Design Of
Engineering
Experiments - design process – plan phase (8) – internal
and external validities (vii)
factors typically impacting on Type II error are:
✓ an extraneous manipulable independent variable is confounded
with the denominator (*)
such mistake results in an addition of the experimental error with the
variability proper of each observed group
✓ the selected experimental design lacks sensitivity
sensitivity refers to the precision or power of an experiment to detect
treatment effects
✓ external variables are confounded with the numerator (*) or the
other threats to internal validity
the issue is the effect of a confounded variable masking the effect of a
treatment which truly does exist
(*) the words «numerator» and «denominator» are respectively referred
to the differences detected after the treatment and to experimental
errors, that in some statistical inference tools (for instance the t of
Students) are just on the numerator and denominator of such tools.
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 15DOE - Design Of
Engineering
Experiments - design process – study phase (1)
Just as (very)
preliminary on on the
data one got (ref. to
the study phase of the
Research Process,
page 5), in this and in
the following pages
you can find some
references on suitable
statistical tools about.
[M. Davies, N. Hughes – Research Project - \Palgrave Mc. Millan 2014]
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 16DOE - Design Of
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Experiments - design process – study phase (2)
[M. Davies, N. Hughes – Research Project - \Palgrave Mc. Millan 2014]
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 17DOE - Design Of
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Experiments - design process – study phase (3)
[M. Davies, N. Hughes – Research Project - \Palgrave Mc. Millan 2014]
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 18Engineering
D. Sorrenti – Corso di “Industrial Design” – Università C. Cattaneo LIUC – A.A. 2017-2018 19You can also read
