1. Using an Add-In Based on a JMP Script to Analyze
an Unreplicated Fractional Split-Plot Experiment
Tony Cooper and Sam Edgemon of the SAS Institute
Why
“Add-Ins?”
Why
“Fractional Split Plot Designs?”
FFSP
Add-In
Add-ins, in general, add to JMP’s ability: for example, JMP will not provide a Singular Value Decomposition, but this math can easily be added and surfaced via JSL
Two experimental techniques; (1) Fractionation and (2) Split plot. Powerful techniques that must be used simultaneously.
This add-in determines which degrees of freedom are estimated with whole plot precision and which with split plot precision.
It reports this information and then uses regression analysis and normal probability plots to analyze the experiments.
Follow the analysis in the following steps:
Invoking the Macro
Analysis Overview: Description
Analysis Part 1: Identity
Analysis Part 2(a) - Whole Plot Confounding
Analysis Part 2(b) - Split Plot Confounding
Output 3(a) - Whole Plot Significance
Output 3(b) - Split Plot Significance
Conclusion
Fractional factorials allow an experimenter to efficiently get information on many factors and important interactions.
Split plot experiments are run to save resources; time and money
And, Add-ins automate a series of JMP dialog boxes – for example,
When should use this technique?
How to learn about using this technique?

2. When to use this technique?
In Design
Factor Relationship Diagram
Whole-plot factors define the design and builds a set of prototypes, split-plot factors vary the noise seen by the prototypes giving robustness.
In Manufacturing
Experiment run to scale-up whereby an upstream process generates large batches that are finished in more flexible downstream processing. Whole-plot factors on upstream process reduces cost.
Bingham, D. and Sitter, R. R. (1999). “Minimum Aberration Two-Level Fractional Factorial Split-Plot Designs”. Technometrics 41, pp. 62–70.
Bisgaard, S. (2000). “The Design and Analysis of 2k−p ° 2q−r Split-Plot Experiments”. Journal of Quality Technology 32, pp. 39–56
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3. How to learn this technique?
Analysis
Needs to be particular to surface the multiple error structure
Confounding – what is aliased, and is it aliased at the whole-plot or split plot level
Significance – comparison of effect to the correct noise component
Goos, Peter and Gilmour, Steven G. (2012) A general strategy for analyzing data from split-plot and multistratum experimental designs. Technometrics, 54, (4), 
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4. Invoking the Macro Return Next
The Add-in asks which factors are changed at the whole-plot level; those changed less frequently.
The add-in requires that all factors are coded ±1
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5. Analysis Overview
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6. Analysis Part 1: Identity
The first section of output is the overall identities.
Identity: 2^{(3-1)+(3-0)} or
A*B*C
A*p*q*r*s
B*C*p*q*r*s
Identity =
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7. Return Prev Next Analysis Part 2(a) – Whole Plot Confounding
Column Names
Aliasing
A=B*C
B=A*C
C=A*B
A=B*C
B=A*C
C=A*B
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8. Analysis Part 2(b) – Split Plot Confounding
Column Names
Aliasing p q r
A*p=B*C*p
A*q=B*C*q
A*r=B*C*r
B*p=A*C*p
C*p*q_Plus
C*p*r_Plus
C*q*r_Plus
p*q*r
A*p*q*r_Plus
B*p*q*r_Plus
C*p*q*r_Plus
p=A*B*C*p
q=A*B*C*q
r=A*B*C*r
A*p=B*C*p
A*q=B*C*q
A*r=B*C*r
B*p=A*C*p
B*q=A*C*q
B*r=A*C*r
C*p=A*B*p
C*q=A*B*q
C*r=A*B*r
p*q=A*B*C*p*q
p*r=A*B*C*p*r
q*r
A*p*q_Plus
A*p*r_Plus
A*q*r_Plus
B*p*q_Plus
B*p*r_Plus
B*q*r_Plus
C*p*q=A*B*p*q
C*p*r=A*B*p*r
C*q*r=A*B*q*r
p*q*r=A*B*C*p*q*r
A*p*q*r=B*C*p*q*r
B*p*q*r=A*C*p*q*r
C*p*q*r=A*B*p*q*r
B*q=A*C*q
B*r=A*C*r
C*p=A*B*p
C*q=A*B*q
C*r=A*B*r
p*q
p*r
q*r=A*B*C*q*r
A*p*q=B*C*p*q
A*p*r=B*C*p*r
A*q*r=B*C*q*r
B*p*q=A*C*p*q
B*p*r=A*C*p*r
B*q*r=A*C*q*r
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9. Output 3(a) – Whole Plot Significance
Whole Plot Normal Probability Plot
Lenth's PSE
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10. Output 3(b) – Split Plot Significance
Split Plot Normal Probability Plot
Lenth's PSE =
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11. Conclusion Return Prev
Fractional factorials, unreplicated designs and split-plot experiments are all commonly used in industry. Experience with Designed Experiments (DoE) suggests making unreplicated fractional split-plots accessible to engineers, scientists and other technicians makes sense. Split-plot experiments have at least two error structures. In a fractional split-plot, a first task is to determine the appropriate error term associated with each aliased term in the model. Normal probability plots can then be used to assess statistical significance in unreplicated designs. Manipulating matrices in a JMP script can efficiently determine and evaluate the aliasing for a split-plot experiment, calculate their effects, draw multiple normal probability plots and evaluate the significance of the effects.
JMP Add-ins are a straightforward method to deploy strings of JMP work. This can be linking a series of existing JMP output or modifying and creating additional output using JMP scripting.
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