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Aug 10, 2016 5:38 PM
(3390 views)

Can a Doehlert design for 3 factors be set up in JMP?

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JMP will not create a Doehlert design automatically, but you really shouldn't be able to create one automatically. The Doehlert design is actually just a name given to the points formed when simplex optimization has found an optimum condition. Therefore, one does not really "plan" for this design. It results when the simplex has reached an optimum point and circles around the optimum. Those resulting "circling points" are called a Doehlert design with the center of the space being the optimum according to the simplex. The Doehlert design is then analyzed as if it were a planned design by using regression. This results in a model, something that you do not typically get with simplex optimization.

For three factors a typical Doehlert design would look like this:

Exp # | X1 | X2 | X3 |

1 | 0 | 0 | 0 |

2 | 1 | 0 | 0 |

3 | 0.5 | 0.866 | 0 |

4 | 0.5 | 0.2887 | 0.8165 |

5 | -1 | 0 | 0 |

6 | -0.5 | -0.866 | 0 |

7 | -0.5 | -0.2887 | -0.8165 |

8 | 0.5 | -0.866 | 0 |

9 | 0.5 | -0.2887 | -0.8165 |

10 | 0 | 0.5774 | -0.8165 |

11 | -0.5 | 0.866 | 0 |

12 | -0.5 | 0.2887 | 0.8165 |

13 | 0 | -0.5774 | 0.8165 |

You can easily just take this design and transform these coded units to your natural units. Without doing the simplex optimization though, I do not know how you would know where to place your "0" point of this design.

If your question is if JMP can analyze a Doehlert design, the answer is YES! It is just regression and you use Fit Model.

Now if your question is if JMP can do simplex optimization, the answer is not directly. A JMP script would need to be built and I believe there might even be one in the community downloads area.

I hope this helps.

Dan Obermiller

3 REPLIES

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JMP will not create a Doehlert design automatically, but you really shouldn't be able to create one automatically. The Doehlert design is actually just a name given to the points formed when simplex optimization has found an optimum condition. Therefore, one does not really "plan" for this design. It results when the simplex has reached an optimum point and circles around the optimum. Those resulting "circling points" are called a Doehlert design with the center of the space being the optimum according to the simplex. The Doehlert design is then analyzed as if it were a planned design by using regression. This results in a model, something that you do not typically get with simplex optimization.

For three factors a typical Doehlert design would look like this:

Exp # | X1 | X2 | X3 |

1 | 0 | 0 | 0 |

2 | 1 | 0 | 0 |

3 | 0.5 | 0.866 | 0 |

4 | 0.5 | 0.2887 | 0.8165 |

5 | -1 | 0 | 0 |

6 | -0.5 | -0.866 | 0 |

7 | -0.5 | -0.2887 | -0.8165 |

8 | 0.5 | -0.866 | 0 |

9 | 0.5 | -0.2887 | -0.8165 |

10 | 0 | 0.5774 | -0.8165 |

11 | -0.5 | 0.866 | 0 |

12 | -0.5 | 0.2887 | 0.8165 |

13 | 0 | -0.5774 | 0.8165 |

You can easily just take this design and transform these coded units to your natural units. Without doing the simplex optimization though, I do not know how you would know where to place your "0" point of this design.

If your question is if JMP can analyze a Doehlert design, the answer is YES! It is just regression and you use Fit Model.

Now if your question is if JMP can do simplex optimization, the answer is not directly. A JMP script would need to be built and I believe there might even be one in the community downloads area.

I hope this helps.

Dan Obermiller

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Re: Doehlert design in JMP?

Thanks DanO. That is helpful indeed.

However, I did not find the simplex optimization script in the JMP community downloads area so as to use it for generating Doehlert designs for 4 or 5 factors...

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Re: Doehlert design in JMP?

ashishnb,

I am looking to see if I can find the script for Simplex Optimization. Stay tuned. However, I feel it is very important to mention that the Doehlert design from simplex optimization is NOT a very good design. You have much better properties from a true response surface design (either I-optimal, D-optimal, Box-Behnken, or central composite). True response surface designs will have better collinearity properties, lower prediction variances, and generally higher power. They are much better at prediction.

I will continue to look for a script for simplex optimization though.

Dan Obermiller