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?

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 Return

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), 340-354 Return

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 Return Next

Analysis Overview Return Prev Next

Analysis Part 1: Identity The first section of output is the overall identities. Identity: 2^{(3-1)+(3-0)} or 3.3.1.0 A*B*C A*p*q*r*s B*C*p*q*r*s Identity = Return Prev Next

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 Return Prev Next

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 Return Prev Next

Output 3(a) – Whole Plot Significance Whole Plot Normal Probability Plot Lenth's PSE 3.1361718 Return Prev Next

Output 3(b) – Split Plot Significance Split Plot Normal Probability Plot Lenth's PSE = 0.1075782 Return Prev Next

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.   Return Prev