4. Process Modeling

4.4.	Data Analysis for Process Modeling

Building a Good Model

This section contains detailed discussions of the necessary steps for developing a good process model after data have been collected. A general model-building framework, applicable to multiple statistical methods, is described with method-specific points included when necessary.

Contents: Section 4

1. What are the basic steps for developing an effective process model?
2. How do I select a function to describe my process?
   1. Incorporating Scientific Knowledge into Function Selection
   2. Using the Data to Select an Appropriate Function
   3. Using Methods that Do Not Require Function Specification
3. How are estimates of the unknown parameters obtained?
   1. Least Squares
   2. Weighted Least Squares
4. How can I tell if a model fits my data?
   1. How can I assess the sufficiency of the functional part of the model?
   2. How can I detect non-constant variation across the data?
   3. How can I tell if there was drift in the measurement process?
   4. How can I assess whether the random errors are independent from one to the next?
   5. How can I test whether or not the random errors are normally distributed?
   6. How can I test whether any significant terms are missing or misspecified in the functional part of the model?
   7. How can I test whether all of the terms in the functional part of the model are necessary?
5. If my current model does not fit the data well, how can I improve it?
   1. Updating the Function Based on Residual Plots
   2. Accounting for Non-Constant Variation Across the Data
   3. Accounting for Errors with a Non-Normal Distribution