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DX71-04C-MultifactorRSM-P1.doc Rev. 1/24/07 Multifactor RSM Tutorial (Part 1 – The Basics)
Response Surface Design and Analysis This tutorial shows the use of Design-Expert ® software for response surface methodology (RSM). This class of designs is aimed at process optimization. A case study provides a real-life feel to the exercise.
Due to the specific nature of the case study, a number of features that could be helpful to you for RSM will not be exercised in this tutorial. Many of these features are used in the General One Factor, RSM One Factor or Two-Level Factorial tutorials. If you have not completed all of these tutorials, consider doi
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ng so before starting in on this one.
We will presume that you can handle the statistical aspects of RSM. For a good primer on the subject, see RSM Simplified (Anderson and Whitcomb, Productivity, Inc., New York). You will find overviews on RSM and how it’s done via Design-Expert in the on-line Help system. To gain a working knowledge of RSM, we recommend you attend our Response Surface Methods for Process Optimization workshop. Call Stat-Ease or visit our website, www.statease.com , for a schedule.
The case study in this tutorial involves production of a chemical. The two most important responses, designated by the lette
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r “y”, are:
• y 1 - Conversion (% of reactants converted to product)
• y 2 - Activity.
The experimenter chose three process factors to study. Their names and levels can be seen in the following table.
Factor
Units Low Level (-1) High Level (+1) A – Time
minutes 40 50 B – Temperature
degrees C 80 90 C – Catalyst percent 2 3
Factors for response surface study
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You will study the chemical process with a standard RSM design called a central
composite design (CCD). It’s well suited for fitting a quadratic surface, which usually works well for process optimization. The three-factor layout for the CCD is pictured below. It is composed of a core factorial that forms a cube with sides that are two coded units in length (from -1 to +1 as noted in the table above). The stars represent axial points. How far out from the cube these should go is a matter for much discussion between statisticians? They designate this distance “alpha” – measured in terms of
coded factor levels. As you will see Design-
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Expert offers a variety of options for alpha.

Central Composite Design for three factors


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Assume that the experiments will be conducted over a two-day period, in two blocks: 1. Twelve runs: composed of eight factorial points, plus four center points.
2. Eight runs: composed of six axial (star) points, plus two more center points.
Design the Experiment
Start the program by finding and double clicking the Design-Expert software icon. Take the quickest route to initiating a new design by clicking the blank-sheet icon on the left of the toolbar. The other route is via File, New Design (or associated Alt keys).
Main menu and tool bar
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Click on the Response Surface folder tab to show the designs available for RSM.
Response surface design tab
The default selection is the Central Composite design, which will be used for this case study. Click on the down arrow in the Numeric Factors entry box and Select 3. Ignore the option of including categoric factors in your designs (leave at default of 0
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DX71-04C-MultifactorRSM-P1.doc Rev. 1/24/07 To see alternative RSM designs for three factors, click on the choices for Box-
Behnken (17 runs) and Miscellaneous designs, where you find the 3-Level Facto option (32 runs, includ rial ing 5 center points). Now go back and re-select the Central Composite design.
oints set at
1.68719 coded units from the center – a conventional choice for the CCD.
Before entering the factors and ranges, click the Options at the bottom of the CCD screen. Notice that it defaults to a Rotatable
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design with the axial (star) p
Default CCD option for alpha set so design will be rotatable
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t of may be the “Face Centered” (alpha equal one). Press OK to accept the rotatable value. icking to each cell and entering the details given in the introduction to this case study.


Many of the options are statistical in nature, but one that produces less extreme factor ranges is the “Practical” value for alpha. This is computed by taking the fourth roo th
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e number of factors (in this case 3¼ or 1.31607). See RSM Simplified Chapter 8 “Everything You Should Know About CCDs (but dare not ask!)” for details on this practical versus other levels suggested for alpha in CCDs – the most popular of which Using the information provided in the table on page 1 of this tutorial (or on the screen capture below), type in the details for factor Name (A, B, C), Units and levels for low (-1) and high (+1), by tabbing or cl
Completed factor form
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You’ve now specified the cubical portion of the CCD. As you did this, Design-Exper calculated the coded distance “alpha” for placement on the star points in the central composite design. Alternatively, by clicking an option further down this scr t een, you could have entered values for alpha levels and let the software figure out the rest. This nd unless you must cut the number of runs to the bare minimum). You will need two blocks for this design, one for each day, so click on the Blocks field and select 2.
would be helpful if you wanted to avoid going out of operating constraints.
Now go back to the bottom of the central composite design form. Leave the Type at i
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ts default value of Full


(the other option is a “small” CCD, which we do not recomme
Selecting the number of blocks
Notice that the software displays how this CCD will be laid out in the two blocks. Click on the Continue button to reach the second page of the “wizard” for building a
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response surface design. You now have the option of identifying Block Names . Enter Day 1 and Day 2


as shown below.
Block names
Press Continue to enter Responses . Select 2 from the pull down list. Then enter the response Name and Units
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for each response as shown below.
Completed response form
At any time in the design-building phase, you can return to the previous page by pressing the Back button. Then you can revise your s
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elections. Press the Continue button to get the design layout (your run order may differ due to randomization ).
DX71-04C-MultifactorRSM-P1.doc Rev. 1/24/07
Design-Expert offers many ways to modify the design and how it’s laid out on-screen. Preceding tutorials, especially in Part 2 for the General One Factor, delved into this in detail, so go back and look this over if you haven’t already. Click the Tips button for a
refresher.

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Design layout (only partially shown, your run order may differ due to randomization)
Save the Data to Now that you’ve invested some time into your design, it would be prudent to save your work. Click on the File menu item and select Save As .
Save As selection
You can then specify the File name (we suggest tut-RSM ) to Save as type *.dx7” in the Data folder for Design-Expert (or wherever you want to Save