DX7-04C-MultifactorRSM-P1.doc Rev. 4/12/06
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Multifactor RSM Tutorial (Part 1 – The Basics)
Respon Surface Design and Analysis
This tutorial shows the u of Design-Expert® software for respon surface methodology (RSM). This class of designs is aimed at process optimization. A ca study provides a real-life feel to the exerci. Due to the specific nature of the ca study, a number of features that could be helpful to you for RSM will not be exercid in this tutorial. Many of the features are ud in the General One Factor, RSM One Factor or Two-Level Factorial tutorials. If you have not completed all of the tutorials, consider doing 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, e 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 online Help system. To gain a working knowledge of RSM, we recommend you attend our Respon Surface Methods for Process Optimization workshop. Call Stat-Ea or visit our website, , for a schedule. The ca study in this tutorial involves production of a chemical. The two most important respons, designated by the letter “y”, are: • • y1 - Conversion (% of reactants converted to product) y2 - Activity.
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The experimenter cho three process factors to study. Their names and levels can be en in the following table.
Factor
A – Time B - Temperature C - Catalyst
Units
minutes degrees C percent
Low Level (-1)
40 80 2
High Level (+1)
50 90 3
Factors for respon surface study 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 compod 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 reprent axial points. How far out from the cube the 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 e Design-Expert offers a variety of options for alpha.
数学真好玩Design-Expert 7 Ur’s Guide望秦川
Multifactor RSM Tutorial – Part 1 • 1
Central Composite Design for three factors Assume that the experiments will be conducted over a two-day period, in two blocks: 1. Twelve runs: compod of eight factorial points, plus four center points. 2. Eight runs: compod 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 Click on the Respon Surface folder tab to show the designs available for RSM.
Respon surface design tab The default lection is the Central Composite design, which will be ud for this ca 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).
2 • Multifactor RSM Tutorial – Part 1懂怎么读
Design-Expert 7 Ur’s Guide
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DX7-04C-MultifactorRSM-P1.doc Rev. 4/12/06
To e alternative RSM designs for three factors, click on the choices for BoxBehnken (17 runs) and Miscellaneous designs, where you find the 3-Level Factorial option (32 runs, including 5 center points). Now go back and re-lect the Central Composite design. Before entering the factors and ranges, click the Options at the bottom of the CCD screen. Notice that it defaults to a Rotatable design with the axial (star) points t at 1.68719 coded units from the center – a conventional choice for the CCD. For Center points increa the number to the normal default of 6 and press the Tab key.
Default CCD option for alpha t so design will be rotatable 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 root of the number of factors (in this ca 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 may be the “Face Centered” (alpha equal one). Press OK to accept the rotatable value. 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 clicking to each cell and entering the details given in the introduction to this ca study.
Completed factor form
Design-Expert 7 Ur’s Guide薄刀峰
Multifactor RSM Tutorial – Part 1 • 3
You’ve now specified the cubical portion of the CCD. As you did this, Design-Expert calculated the coded distance “alpha” for placement on the star points in the central composite design. Alternatively, by clicking an option further down this screen, you could have entered values for alpha
levels and let the software figure out the rest. This 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 its default value of Full (the other option is a “small” CCD, which we do not recommend 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 lect 2.
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 cond page of the “wizard” for building a respon 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 Respons. Select 2 from the pull down list. Then enter the respon Name and Units for each respon as shown below.
Completed respon form At any time in the design-building pha, you can return to the previous page by pressing the Back button. Then you can revi your lections. Press the Continue button to get the design layout (your run order may differ due to randomization).
4 • Multifactor RSM Tutorial – Part 1
Design-Expert 7 Ur’s Guide
DX7-04C-MultifactorRSM-P1.doc Rev. 4/12/06
Design layout (only partially shown, your run order may differ due to randomization) 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.
Save the Data to a File
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 lect Save As.
博字成语Save As lection 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 in).
Design-Expert 7 Ur’s Guide
Multifactor RSM Tutorial – Part 1 • 5
