1. 2 3 1-1 The Engineering Method and Statistical Thinking Engineers solve problems of interest to society by the efficient application of scientific.

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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:– 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 columnTo 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• 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 first-principles 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

Mn = f(V,C,T)say, where the form of the function f is unknown.

where the ’s are unknown parameters.

An empirical model

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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 plotand 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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