Resolution III Design Example - Revision history

Lisa Hacker at 21:07, 18 September 2023

2023-09-18T21:07:12Z

← Older revision		Revision as of 21:07, 18 September 2023
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	<noinclude>{{Banner DOE Examples}}		<noinclude>{{Banner DOE Examples}}
	''This example appears in the [~~[Two_Level_Factorial_Experiments#Resolution_III_Designs\|Experiment Design and Analysis Reference book]~~]''. </noinclude>		''This example appears in the [https://help.reliasoft.com/reference/experiment_design_and_analysis DOE reference]''. </noinclude>

Richard House at 17:45, 10 August 2017

2017-08-10T17:45:09Z

← Older revision		Revision as of 17:45, 10 August 2017
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	Using the alias relations, the effects obtained from DOE++ for the present design can be expressed as:		Using the alias relations, the effects obtained from the DOE folio for the present design can be expressed as:


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	The fold-over design for the experiment is obtained by reversing the signs of the columns <math>D\,\!</math>, <math>E\,\!</math>, and <math>F\,\!</math>. In DOE++, you can fold over a design using the following window.		The fold-over design for the experiment is obtained by reversing the signs of the columns <math>D\,\!</math>, <math>E\,\!</math>, and <math>F\,\!</math>. In a DOE folio, you can fold over a design using the following window.

	[[Image:doe7_48_1.png\|center\|311px\|Fold-over design window\|link=]]		[[Image:doe7_48_1.png\|center\|311px\|Fold-over design window\|link=]]

Richard House at 21:28, 21 April 2016

2016-04-21T21:28:48Z

← Older revision		Revision as of 21:28, 21 April 2016
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	[[Image:doe7_44.png\|center\|~~838px~~\|Design properties for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]		[[Image:doe7_44.png\|center\|800px\|Design properties for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].\|link=]]


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	[[Image:doe7_45.png\|center\|~~654px~~\|Experiment design for the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]		[[Image:doe7_45.png\|center\|700px\|Experiment design for the [[Two_Level_Factorial_Experiments#Example_8\| example]].\|link=]]


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	[[Image:doe7_46.png\|center\|~~599px~~\|Normal probability plot of effects for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]		[[Image:doe7_46.png\|center\|650px\|Normal probability plot of effects for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].\|link=]]


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	[[Image:doe7_47.png\|center\|~~617px~~\|Effect values for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]		[[Image:doe7_47.png\|center\|612px\|Effect values for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].\|link=]]


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	The fold-over design for the experiment is obtained by reversing the signs of the columns <math>D\,\!</math>, <math>E\,\!</math>, and <math>F\,\!</math>. In DOE++, you can fold over a design using the following window.		The fold-over design for the experiment is obtained by reversing the signs of the columns <math>D\,\!</math>, <math>E\,\!</math>, and <math>F\,\!</math>. In DOE++, you can fold over a design using the following window.

	[[Image:doe7_48_1.png\|center\|~~350px~~\|Fold-over design window]]		[[Image:doe7_48_1.png\|center\|311px\|Fold-over design window\|link=]]

	The resulting design and the corresponding response values obtained are shown in the following figures.		The resulting design and the corresponding response values obtained are shown in the following figures.

	[[Image:doe7_48.png\|center\|~~650px~~\|Fold-over design for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]		[[Image:doe7_48.png\|center\|722px\|Fold-over design for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].\|link=]]

	[[Image:doe7_49_1.png\|center\|~~644px~~\|Effect values for the fold-over design in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]
			[[Image:doe7_49_1.png\|center\|700px\|Effect values for the fold-over design in the [[Two_Level_Factorial_Experiments#Example_8\| example]].\|link=]]


	Comparing the absolute values of the effects, the active effects are <math>B\,\!</math>, <math>C\,\!</math>, <math>D\,\!</math> and the interaction <math>CD\,\!</math>. Therefore, the most important factors affecting the taste of the cakes in the present case are sugar quantity, egg quantity and their interaction.		Comparing the absolute values of the effects, the active effects are <math>B\,\!</math>, <math>C\,\!</math>, <math>D\,\!</math> and the interaction <math>CD\,\!</math>. Therefore, the most important factors affecting the taste of the cakes in the present case are sugar quantity, egg quantity and their interaction.

Richard House at 22:29, 6 January 2016

2016-01-06T22:29:58Z

← Older revision		Revision as of 22:29, 6 January 2016
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	[[Image:doe7_44.png~~\|thumb~~\|center\|838px\|Design properties for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]		[[Image:doe7_44.png\|center\|838px\|Design properties for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]


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	[[Image:doe7_45.png~~\|thumb~~\|center\|654px\|Experiment design for the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]		[[Image:doe7_45.png\|center\|654px\|Experiment design for the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]


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	[[Image:doe7_46.png~~\|thumb~~\|center\|599px\|Normal probability plot of effects for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]		[[Image:doe7_46.png\|center\|599px\|Normal probability plot of effects for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]


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	[[Image:doe7_47.png~~\|thumb~~\|center\|617px\|Effect values for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]		[[Image:doe7_47.png\|center\|617px\|Effect values for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]


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	The fold-over design for the experiment is obtained by reversing the signs of the columns <math>D\,\!</math>, <math>E\,\!</math>, and <math>F\,\!</math>. In DOE++, you can fold over a design using the following window.		The fold-over design for the experiment is obtained by reversing the signs of the columns <math>D\,\!</math>, <math>E\,\!</math>, and <math>F\,\!</math>. In DOE++, you can fold over a design using the following window.

	[[Image:doe7_48_1.png~~\|thumb~~\|center\|~~650px~~\|Fold-over design window]]		[[Image:doe7_48_1.png\|center\|350px\|Fold-over design window]]

	The resulting design and the corresponding response values obtained are shown in the following figures.		The resulting design and the corresponding response values obtained are shown in the following figures.

	[[Image:doe7_48.png~~\|thumb~~\|center\|650px\|Fold-over design for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]		[[Image:doe7_48.png\|center\|650px\|Fold-over design for the experiment in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]

	[[Image:doe7_49_1.png~~\|thumb~~\|center\|644px\|Effect values for the fold-over design in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]		[[Image:doe7_49_1.png\|center\|644px\|Effect values for the fold-over design in the [[Two_Level_Factorial_Experiments#Example_8\| example]].]]


	Comparing the absolute values of the effects, the active effects are <math>B\,\!</math>, <math>C\,\!</math>, <math>D\,\!</math> and the interaction <math>CD\,\!</math>. Therefore, the most important factors affecting the taste of the cakes in the present case are sugar quantity, egg quantity and their interaction.		Comparing the absolute values of the effects, the active effects are <math>B\,\!</math>, <math>C\,\!</math>, <math>D\,\!</math> and the interaction <math>CD\,\!</math>. Therefore, the most important factors affecting the taste of the cakes in the present case are sugar quantity, egg quantity and their interaction.

Kate Racaza at 23:18, 1 April 2014

2014-04-01T23:18:32Z

← Older revision		Revision as of 23:18, 1 April 2014
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	<noinclude>{{Banner DOE Examples}}		<noinclude>{{Banner DOE Examples}}
	''This example appears in the [~~http://reliawiki.org/index.php/~~Two_Level_Factorial_Experiments#Resolution_III_Designs\|Experiment Design and Analysis Reference book]''. </noinclude>		''This example appears in the [[Two_Level_Factorial_Experiments#Resolution_III_Designs\|Experiment Design and Analysis Reference book]]''. </noinclude>

Kate Racaza: Created page with '{{Banner DOE Examples}} ''This example appears in the [http://reliawiki.org/index.php/Two_Level_Factorial_Experiments#Resolution_III_Designs|Experiment Design and Anal…'

2014-04-01T22:51:47Z

Created page with '<noinclude>{{Banner DOE Examples}} ''This example appears in the [http://reliawiki.org/index.php/Two_Level_Factorial_Experiments#Resolution_III_Designs|Experiment Design and Anal…'

New page

<noinclude>{{Banner DOE Examples}}
''This example appears in the [http://reliawiki.org/index.php/Two_Level_Factorial_Experiments#Resolution_III_Designs|Experiment Design and Analysis Reference book]''. </noinclude>

A baker wants to investigate the factors that most affect the taste of the cakes made in his bakery. He chooses to investigate seven factors, each at two levels: flour type (factor <math>A\,\!</math>), conditioner type (factor <math>B\,\!</math>), sugar quantity (factor <math>C\,\!</math>), egg quantity (factor <math>D\,\!</math>), preservative type (factor <math>E\,\!</math>), bake time (factor <math>F\,\!</math>) and bake temperature (factor <math>G\,\!</math>). The baker expects most of these factors and all higher order interactions to be inactive. On the basis of this, he decides to run a screening experiment using a 2 <math>_{\text{III}}^{7-4}\,\!</math> design that requires just 8 runs. The cakes are rated on a scale of 1 to 10. The design properties for the 2 <math>_{\text{III}}^{7-4}\,\!</math> design (with generators <math>D=AB\,\!</math>, <math>E=AC\,\!</math>, <math>F=BC\,\!</math> and <math>G=ABC\,\!</math>) are shown in the following figure.

[[Image:doe7_44.png|thumb|center|838px|Design properties for the experiment in the [[Two_Level_Factorial_Experiments#Example_8| example]].]]

The resulting design along with the rating of the cakes corresponding to each run is shown in the following figure.

[[Image:doe7_45.png|thumb|center|654px|Experiment design for the [[Two_Level_Factorial_Experiments#Example_8| example]].]]

The normal probability plot of effects for the unreplicated design shows main effects <math>B\,\!</math>, <math>C\,\!</math>, <math>D\,\!</math> and <math>G\,\!</math> to be significant, as shown in the next figure.

[[Image:doe7_46.png|thumb|center|599px|Normal probability plot of effects for the experiment in the [[Two_Level_Factorial_Experiments#Example_8| example]].]]

However, for this design, the following alias relations exist for the main effects:

<center><math>\begin{align}
& A= & A+BD+CE+FG \\
& B= & B+AD+CF+EG \\
& C= & C+AE+BF+DG \\
& D= & D+AB+CG+EF \\
& E= & E+AC+BG+DF \\
& F= & F+BC+AG+DE \\
& G= & G+CD+BE+AF
\end{align}\,\!</math></center>

Based on the alias structure, three separate possible conclusions can be drawn. It can be concluded that effect <math>CD\,\!</math> is active instead of <math>G\,\!</math> so that effects <math>C\,\!</math>, <math>D\,\!</math> and their interaction, <math>CD\,\!</math>, are the significant effects. Another conclusion can be that effect <math>DG\,\!</math> is active instead of <math>C\,\!</math> so that effects <math>D\,\!</math>, <math>G\,\!</math> and their interaction, <math>DG\,\!</math>, are significant. Yet another conclusion can be that effects <math>C\,\!</math>, <math>G\,\!</math> and their interaction, <math>CG\,\!</math>, are significant. To accurately discover the active effects, the baker decides to a run a fold-over of the present design and base his conclusions on the effect values calculated once results from both the designs are available.

The present design is shown next.

[[Image:doe7_47.png|thumb|center|617px|Effect values for the experiment in the [[Two_Level_Factorial_Experiments#Example_8| example]].]]

Using the alias relations, the effects obtained from DOE++ for the present design can be expressed as:

<center><math>\begin{align}
& Effec{{t}_{A}}= & 0.025=A+BD+CE+FG \\
& Effec{{t}_{B}}= & -0.225=B+AD+CF+EG \\
& Effec{{t}_{C}}= & 2.075=C+AE+BF+DG \\
& Effec{{t}_{D}}= & 2.875=D+AB+CG+EF \\
& Effec{{t}_{E}}= & -0.025=E+AC+BG+DF \\
& Effec{{t}_{F}}= & -0.075=F+BC+AG+DE \\
& Effec{{t}_{G}}= & 3.825=G+CD+BE+AF
\end{align}\,\!</math></center>

The fold-over design for the experiment is obtained by reversing the signs of the columns <math>D\,\!</math>, <math>E\,\!</math>, and <math>F\,\!</math>. In DOE++, you can fold over a design using the following window.

[[Image:doe7_48_1.png|thumb|center|650px|Fold-over design window]]

The resulting design and the corresponding response values obtained are shown in the following figures.

[[Image:doe7_48.png|thumb|center|650px|Fold-over design for the experiment in the [[Two_Level_Factorial_Experiments#Example_8| example]].]]

[[Image:doe7_49_1.png|thumb|center|644px|Effect values for the fold-over design in the [[Two_Level_Factorial_Experiments#Example_8| example]].]]

Comparing the absolute values of the effects, the active effects are <math>B\,\!</math>, <math>C\,\!</math>, <math>D\,\!</math> and the interaction <math>CD\,\!</math>. Therefore, the most important factors affecting the taste of the cakes in the present case are sugar quantity, egg quantity and their interaction.