Figure 1-8 The dot diagram illustrates variation but does not identify the problem.
1-2 Observing Processes Over Time
1-2 Observing Processes Over Time
Figure 1-14 Enumerative versus analytic study.
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 + ε
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.
1-3 Mechanistic and Empirical Models
Example
Suppose we are interested in the number average molecular weight (Mn) of a polymer. Now we know that Mn is related to the viscosity 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 β’s are unknown parameters.
1-3 Mechanistic and Empirical Models
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
Figure 1-15 Three-dimensional plot of the wire and pull strength data.
Figure 1-16 Plot of the predicted values of pull strength from the empirical model.
1-4 Probability and Probability Models
1-4 Probability and Probability Models
- Probability models help quantify the risks involved in statistical inference, that is, risks involved in decisions made every day.
- Probability provides the framework for the study and application of statistics.
Chia sẻ với bạn bè của bạn: |
