LO11: Predictive Modelling using Response Surface Method

Question 1

• a collection of mathematical and statistical method for modeling
• analyze a process in which the response of interest is affected by various variables
• Main goal is to optimize the process

Answer 1

Response Surface Methodology (RSM)

Question 2

Levels of measurement

Answer 2

1. Nominal = Attributes are only named; weakest
2. Ordinal = Attributes can be ordered
3. Interval = Distance is meaningful
4. Ratio = Absolute zero

Question 3

RSM Workflow

Answer 3

1. Screening
2. Characterization
3. Optimization (only if there is curvature) - RSM
4. Verification

Question 4

an experimental design that consists of two or more factors, with each factor having multiple discrete possible values or “levels” =n^K (levels raised to factors)

Answer 4

Full Factorial Design (FFD)

Question 5

Contains an imbedded factorial or
fractional factorial design with center
points that is augmented with a group
of ‘star points’ that allow estimation of
curvature

Answer 5

Central Composite Design

Question 6

An independent quadratic design in that
it does not contain an embedded
factorial or fractional factorial design.

The treatment combinations are at the
midpoints of edges of the process space
and at the center. These designs are
rotatable (or near rotatable) and require
3 levels of each factor.

Answer 6

Box-Behnken Design

Question 7

RSM Designs: CCD vs BBD

Corner points
Levels
Number of tests
Star points
Rotatable

Answer 7

Corner points = CCD - Extreme / BBD - No Extreme
Levels = CCD - 5 / BBD - 3
Number of tests = CCD - More / BBD - Less
Star points = CCD - + / BBD - -
Rotatable = CCD - Yes / BBD - Yes

Question 8

Analysis Procedure

Answer 8

1. Configure/Transform : Start with no transformation.
2. Fit Summary : Comparative statistics on polynomial models.
3. Model : Choose best (suggested) model for in-depth analysis.
   Return here for model reduction.
4. ANOVA : Check model, lack of fit values, R-square values.
5. Diagnostics : Examine diagnostic graphs to validate model.
6. Model Graphs : If model adequately represents response, generate contour
   and 3D plots.
7. Confirmation : Verify the model predictions with confirmation runs.

Question 9

It compares the variation between the actual data and the predictive value, to the
variation between the replicates.

Answer 9

Lack of Fit Test

Question 10

Diagnostics

Answer 10

❑ Normal Plot of Residuals : if residuals follow a normal distribution
: they should fall approximately along a straight line
❑ Residuals vs. Predicted : shows residual fitted against the model
: points should be randomly scattered around zero
❑ Residuals vs. Run : identify trends or patterns in the residuals
: should have no systematic pattern
❑ Predicted vs. Actual : compares predicted values vs. observed values
: points should fall along a diagonal line
❑ Box-Cox Plot : assess the need for power transformation of the response
: lambda of 1 suggests no transformation is needed

Question 11

Features of a Good DOE using RSM

Answer 11

• Provides reasonable distribution of data points throughout the region of interest.
• Allows testing model adequacy – lack of fit
• Allows experiments to be performed in blocks
• Allows designs of higher-order to be built sequentially
• Provides an internal estimate of the error
• Does not require large number of runs
• Provides reasonable robustness against outliers or missing values.

Question 12

How do you choose your experimental design

Answer 12

Depends on the objective of the experiment