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1-1 The Engineering Method and
Statistical Thinking
• Engineers solve problems of interest to society by the
efficient application of scientific principles
• The engineering or scientific method is the approach to
formulating and solving these problems.
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1-1 The Engineering Method and
Statistical Thinking
The Field of Probability
• Used to quantify likelihood or chance
• Used to represent risk or uncertainty in engineering
applications
• Can be interpreted as our degree of belief or relative
frequency
The Field of Statistics
• Deals with the collection, presentation, analysis, and
use of data to make decisions and solve problems.
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1-1 The Engineering Method and
Statistical Thinking
The field of statistics deals with the collection,
presentation, analysis, and use of data to
• Make decisions
• Solve problems
• Design products and processes
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1-1 The Engineering Method and
Statistical Thinking
• Statistical techniques are useful for describing and
understanding variability.
• By variability, we mean successive observations of a
system or phenomenon do not produce exactly the same
result.
• Statistics gives us a framework for describing this
variability and for learning about potential sources of
variability.
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1-1 The Engineering Method and
Statistical Thinking
Engineering Example
Suppose that an engineer is developing a rubber
compound for use in O-rings. The O-rings are to be
employed as seals in plasma etching tools used in the
semiconductor industry, so their resistance to acids
and other corrosive substances is an important
characteristic.
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1-1 The Engineering Method and
Statistical Thinking
Engineering Example
The engineer uses the standard rubber compound to
produce eight O-rings in a development laboratory
and measures the tensile strength of each specimen
after immersion in a nitric acid solution at 30°C for 25
minutes.
The tensile strengths (in psi) of the eight O-rings are
1030, 1035, 1020, 1049, 1028, 1026, 1019, and 1010.
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1-1 The Engineering Method and
Statistical Thinking
Engineering Example
• The dot diagram is a very useful plot for displaying a
small body of data - say up to about 20 observations.
• This plot allows us to see easily two features of the
data; the location, or the middle, and the scatter or
variability.
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1-1 The Engineering Method and
Statistical Thinking
Engineering Example
• Since tensile strength varies or exhibits variability, it is
a random variable.
• A random variable, X, can be model by
X=+
where  is a constant and  a random disturbance.
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1-1 The Engineering Method and
Statistical Thinking
Engineering Example
• The dot diagram is also very useful for comparing
sets of data.
Adding Teflon
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1-1 The Engineering Method and
Statistical Thinking
Some obvious questions to ask:
• How do we know that another set of the modified
compounds will not give different results?
•Is that adding teflon will increase the tensile strength is a
reliable conclusion based on the test results obtained so
far?
•Is it possible that adding teflon has no effect on increasing
strength? It is only due to the inherent variability.
Statistical thinking can help answer these questions.
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1-1 The Engineering Method and
Statistical Thinking
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1-1 The Engineering Method and
Statistical Thinking
Engineers are interested in comparing two different
conditions (treatments) to determine whether either
condition produces a significant effect on the
response that is observed.
Example: Rubber compounds – O-rings.
• We can think of each sample of eight O-rings as a
random and representative sample of all parts that
will ultimately be manufactured.
•Completely randomized designed experiment!
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1-1 The Engineering Method and
Statistical Thinking
• When statistical significance is observed in a
randomized experiment, we can be confident in the
conclusion that it was the difference in treatments
that resulted in the difference in response.
• Sometimes, we may not choose an object at
random.
Example: a study linking high iron level in the body
with increased risk of heart attack.
• The researchers tracked the subjects over time.
Called Observational Study!
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1-2 Collecting Engineering Data
In the engineering environment, the data are a
sample that has been selected from some
population.
Three basic methods for collecting data:
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A retrospective study using historical data
An observational study
A designed experiment
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1-2 Collecting Engineering Data
Acetone-butyl alcohol distillation column
丙酮-丁基
Will use the distillation column
To illustrate the three methods.
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1-2 Collecting Engineering Data
1-2.1 Retrospective Study
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1-2 Collecting Engineering Data
1-2.2 Observational Study
An observational study simply observes
the process of population during a period
of routine operation.
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1-2 Collecting Engineering Data
1-2.3 Designed Experiments
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Factorial experiment
Replicates
Interaction
Fractional factorial experiment
One-half fraction
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1-2 Collecting Engineering Data
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1-2 Collecting Engineering Data
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1-2 Collecting Engineering Data
k factors  2k runs
How about k=5,6,…, or 100?
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1-2 Collecting Engineering Data
k factors  2k runs
Not necessary to do all runs for k>4. (infeasible!)
To design such a fractional factorial experiment
is a topic in this course.
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1-2 Collecting Engineering Data
1-2.4 Random Samples
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1-2 Collecting Engineering Data
1-2.4 Random Samples
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1-3 Mechanistic and Empirical Models
Models play an important role in the analysis of nearly
all engineering problems.
Much of the formal education of engineers involves
learning about the models relevant to specific fields and
the techniques for applying these models in problem
formulation and solution.
• Mechanistic models
• Empirical models
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1-3 Mechanistic and Empirical Models
A mechanistic model is built from our underlying
knowledge of the basic physical mechanism that relates
several variables.
Example: Ohm’s Law
Current = voltage/resistance
I = E/R
I = E/R + 
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1-3 Mechanistic and Empirical Models
An empirical model is built from our engineering and
scientific knowledge of the phenomenon, but is not
directly developed from our theoretical or firstprinciples understanding of the underlying mechanism.
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1-3 Mechanistic and Empirical Models
Example of an Empirical Model
Suppose we are interested in the number average
molecular weight (Mn) of a polymer. Now we know that Mn
is related to the viscosity (黏性) of the material (V), and it
also depends on the amount of catalyst (C) and the
temperature (T ) in the polymerization reactor when the
material is manufactured. The relationship between Mn and
these variables is
An empirical model
say, where the form of the function f is unknown.
Mn = f(V,C,T)
where the b’s are unknown parameters.
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1-3 Mechanistic and Empirical Models
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1-3 Mechanistic and Empirical Models
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1-3 Mechanistic and Empirical Models
In general, this type of empirical model is called a
regression model.
The estimated regression line is given by
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1-3 Mechanistic and Empirical Models
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1-3 Mechanistic and Empirical Models
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1-4 Observing Processes Over Time
Whenever data are collected over time it is important to plot
the data over time. Phenomena that might affect the system
or process often become more visible in a time-oriented plot
and the concept of stability can be better judged.
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1-4 Observing Processes Over Time
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1-4 Observing Processes Over Time
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1-4 Observing Processes Over Time
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1-4 Observing Processes Over Time
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1-4 Observing Processes Over Time
Average of the first 20 samples
Statistical process control!
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