ISE 426-526 - Lecture 6 - 2^k Factorial Designs-b

ISE 426-526 - Lecture 6 - 2^k Factorial Designs-b - ISE...

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1 ISE 426/526 Lecture 6 - 2007 2 k Factorial Designs General Factorials Homework 3 - Correction • Problem 1 part b (Latin Square Design) – Compute the following residuals: e 133 , e 215 , d 342 using hand calculations only

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2 The 2 3 Design • 8 Treatment Combinations 1 -1 1 -1 1 -1 C B A Cube Plot The 2 3 Plus/Minus Table Run Trt Combo I A B C AB AC BC ABC 1( 1 ) 1 - 1- 1 1 1 1 2a 1 1 -1 -1 -1 -1 1 1 3b 11- 11 4a b 111- 1 5c 11 1- 6a c 1 1- 1 7b c 1 8a b c 11111111
3 Notable Properties • Signs for main effects are associated with levels of factors (+ high; - low) • Signs for interaction columns obtained by multiplying appropriate columns together • I – Identity element – associated with grand average Notable Properties – cont. • Except for I all columns have equal number of +’s and –’s • Each column sums to zero • I * any column leaves column unchanged • Product of any 2 columns yields another column in the table • Used to construct contrasts – which are used to calculate effects estimates and SS

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4 Calculating the Effects Estimates Calculating the Effects Estimates
5 Calculating the SS Example 1 A 2 3 factorial design was used to study the effect of percentage carbonation, operating pressure, and line speed on the fill height of a carbonated beverage. The data presented on the next slide shows the deviation from the target fill height.

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6 Example 1– Data RunOrder Trt Combo A B C Rep 1 Rep 2 Total 1 - 1- 3- 4 2 1 -1 -1 0 1 1 3 - 11- 10- 1 41 1 - 1 2 3 5 5 - 1 6 11213 7 - 111112 8 111651 1 Fill Height Example 1 – Cube Plot 1 -1 1 -1 1 -1 C B A 5.5 1.5 -0.5 1.0 2.5 0.5 -2.0 -0.5 Cube Plot (data means) for Fill Height
7 Effects Estimates Effects Estimates

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This note was uploaded on 11/22/2009 for the course ISE 526 taught by Professor Farrington during the Summer '07 term at University of Alabama - Huntsville.

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ISE 426-526 - Lecture 6 - 2^k Factorial Designs-b - ISE...

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