Process modeling.pdf
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4. Process Modeling
4.
Process Modeling
The goal of this chapter is to present the background and specific analysis techniques
needed to construct a statistical model that describes a particular scientific or
engineering process. The types of models discussed in this are limited to those based on
an explicit mathematical function. These types of models can be used for prediction of
process outputs, for calibration or for process optimization.
1.
Introduction
Definition
2.
Assumptions
Assumptions
2.
Terminology
3.
Uses
4.
Methods
3.
Design
Definition
4.
Analysis
Modeling Steps
2.
Importance
2.
Model Selection
3.
Design Principles
3.
Model Fitting
4.
Optimal Designs
4.
Model Validation
5.
Assessment
5.
Model Improvement
5.
Interpretation & Use
Prediction
6.
Case Studies
Load Cell Output
2.
Calibration
2.
Alaska Pipeline
3.
Optimization
3.
Ultrasonic Reference Block
4.
Thermal Expansion of Copper
Detailed Table of Contents: Process Modeling
References: Process Modeling
Appendix: Some Useful Functions for Process Modeling
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1.
1.
1.
1.
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4. Process Modeling
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4. Process Modeling
4.
Process Modeling - Detailed Table of
Contents [4.]
The goal of this chapter is to present the background and specific analysis techniques needed to
construct a statistical model that describes a particular scientific or engineering process. The types
of models discussed in this are limited to those based on an explicit mathematical function. These
types of models can be used for prediction of process outputs, for calibration or for process
optimization.
Introduction to Process Modeling
[4.1.]
What is process modeling?
[4.1.1.]
1.
2.
What terminology do statisticians use to describe process models?
[4.1.2.]
3.
What are process models used for?
[4.1.3.]
Prediction
[4.1.3.1.]
1.
2.
Calibration
[4.1.3.2.]
3.
Optimization
[4.1.3.3.]
4.
What are the some of the different statistical methods for model building?
[4.1.4.]
Linear Least Sum of Squares Regression
[4.1.4.1.]
1.
2.
Nonlinear Least Sum of Squares Regression
[4.1.4.2.]
3.
Weighted Least Sum of Squares Regression
[4.1.4.3.]
4.
LOESS (aka LOWESS)
[4.1.4.4.]
2.
Underlying Assumptions for Process Modeling
[4.2.]
What are the typical underlying assumptions in process modeling?
[4.2.1.]
The process is a
statistical
process.
[4.2.1.1.]
1.
1.
2.
The means of the random errors are zero.
[4.2.1.2.]
3.
The random errors have constant standard deviation.
[4.2.1.3.]
4.
The random errors follow a normal distribution.
[4.2.1.4.]
5.
The data are randomly sampled from the process.
[4.2.1.5.]
6.
The explanatory variables are observed without error.
[4.2.1.6.]
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4. Process Modeling
3.
Data Collection for Process Modeling
[4.3.]
What is design of experiments (aka DEX or DOE)?
[4.3.1.]
1.
2.
Why is experiment design important for process modeling?
[4.3.2.]
3.
What are some general design principles for process modeling?
[4.3.3.]
4.
I've heard some people refer to "optimal" designs, shouldn't I use those?
[4.3.4.]
5.
How can I tell if a particular experiment design is good for my application?
[4.3.5.]
4.
Data Analysis for Process Modeling
[4.4.]
What are the basic steps for developing an effective process model?
[4.4.1.]
1.
2.
How do I select a function to describe my process?
[4.4.2.]
Incorporating Scientific Knowledge into Function Selection
[4.4.2.1.]
1.
2.
Using the Data to Select an Appropriate Function
[4.4.2.2.]
3.
Using Methods that Do Not Require Function Specification
[4.4.2.3.]
3.
How are estimates of the unknown parameters obtained?
[4.4.3.]
Least Sum of Squares
[4.4.3.1.]
1.
2.
Weighted Least Sum of Squares
[4.4.3.2.]
4.
How can I tell if a model fits my data?
[4.4.4.]
How can I assess the sufficiency of the functional part of the model?
[4.4.4.1.]
1.
2.
How can I detect non-constant of variation across the data?
[4.4.4.2.]
3.
How can I tell if there was drift in the measurement process?
[4.4.4.3.]
4.
How can I assess whether the random errors are independent from one to the
next?
[4.4.4.4.]
5.
How can I test whether or not the random errors are distributed
normally?
[4.4.4.5.]
6.
How can I test whether any significant terms are missing or misspecified in the
functional part of the model?
[4.4.4.6.]
7.
How can I test whether all of the terms in the functional part of the model are
necessary?
[4.4.4.7.]
5.
If my current model does not fit the data well, how can I improve it?
[4.4.5.]
Updating the Function Based on Residual Plots
[4.4.5.1.]
1.
2.
Accounting for Non-Constant Variation Across the Data
[4.4.5.2.]
3.
Accounting for Errors with a Non-Normal Distribution
[4.4.5.3.]
5.
Use and Interpretation of Process Models
[4.5.]
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4. Process Modeling
1.
What types of predictions can I make using the model?
[4.5.1.]
How do I predict the average response for a particular set of predictor variable
values?
[4.5.1.1.]
1.
2.
How can I estimate the value and uncertainty of a single observable
response?
[4.5.1.2.]
2.
How can I use my process model for calibration?
[4.5.2.]
Single Use Calibration Intervals
[4.5.2.1.]
1.
3.
How can I optimize my process using the process model?
[4.5.3.]
6.
Case Studies in Process Modeling
[4.6.]
Load Cell Calibration
[4.6.1.]
Background & Data
[4.6.1.1.]
1.
1.
2.
Selection of Initial Model
[4.6.1.2.]
3.
Model Fitting - Initial Model
[4.6.1.3.]
4.
Graphical Residual Analysis - Initial Model
[4.6.1.4.]
5.
Interpretation of Numerical Output - Initial Model
[4.6.1.5.]
6.
Model Refinement
[4.6.1.6.]
7.
Model Fitting - Model #2
[4.6.1.7.]
8.
Graphical Residual Analysis - Model #2
[4.6.1.8.]
9.
Interpretation of Numerical Output - Model #2
[4.6.1.9.]
10.
Use of the Model for Calibration
[4.6.1.10.]
11.
Work This Example Yourself
[4.6.1.11.]
2.
Alaska Pipeline
[4.6.2.]
Background and Data
[4.6.2.1.]
1.
2.
Check for Batch Effect
[4.6.2.2.]
3.
Initial Linear Fit
[4.6.2.3.]
4.
Transformations to Improve Fit
[4.6.2.4.]
5.
Weighting to Improve Fit
[4.6.2.5.]
6.
Compare the Fits
[4.6.2.6.]
7.
Work This Example Yourself
[4.6.2.7.]
3.
Ultrasonic Reference Block Study
[4.6.3.]
Background and Data
[4.6.3.1.]
1.
2.
Initial Non-Linear Fit
[4.6.3.2.]
3.
Transformations to Improve Fit
[4.6.3.3.]
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