Paint & Coatings Industry - March 2008 - (Page 62)

deSigns of the Times: Slacking Off! Property = aC + (aA – aC + aAC)A + (aB – aC + aBC)B + (aAB – aAC – aBC)AB – aACA2 – aBCB2 (5) bB = (aB – aC + aBC) bAA = – aAC bBB = – aBC (6c) (6d) (6e) If we compare Equation 5 to Equation 1 we see the following: b 0 = aC bA = (aA – aC + aAC) (6a) (6b) Equations 6a through 6e show that the effect of C on the Property is contained within the b0, bA, bB, bAA and bBB coefficients. This means that T H E Patented blending/dispersing blade design makes radical improvement over old saw tooth designs ® POLY STAINLESS Most efficient and aggressive blending/dispersing blade available. Provides proper combination of pumping action and shear/ dispersion essential for fast consistent results. Built in pumping action cuts processing time. Longer life due to heavier gauge construction. Less heat due to shorter required running time. Excellent for high or low speed and high or low viscosity. Supplied with hubs or mounting holes required to retrofit and upgrade present equipment. Pumping blades without teeth are available and are excellent for gentle blending and agitation. DESIGNERS AND MANUFACTURES OF INDUSTRIAL MIXING EQUIPMENT * * * * * * * * Equations 1 and 2 are equivalent. That is, a plot of the response surface of Equation 1 has been shown to be equivalent to that of Equation 2. In the past, when an unsophisticated researcher viewed an analysis of variance table from a slack experimental design, if the variable A showed a significant effect, the researcher would attribute the effect to a change in A as manifested by the magnitude of the bA coefficient. But, looking at Equation 6b, if the bA coefficient is significant, the researcher doesn’t know if it is due to an effect from the variable A, the variable C or their interaction, AC. Similarly for the B variable, if the bB coefficient is significant, the researcher doesn’t know if it is due to an effect from the variable B, the variable C or their interaction, BC. However, the researcher can get an idea of the magnitude of the effects of C, AC and BC, by looking at the coefficients of b0, bAA and bBB. Then the researcher can do some mental gymnastics to determine how much C, AC and BC contribute to the effect of A or B. To my mind it is easier to use the mixture equation of Equation 2. Closing Comments The only time I would recommend using a slack, factorial design would be if it is absolutely known that C has no effect on the Property. That is, if the researcher knows ahead of time that aC, aAC and a BC are all zero. Another point for why I favor mixture designs is that even for the simple example of three ingredients, the quadratic mixture design has fewer experiments than the quadratic-slack, factorial design. However, if five ingredients are to be studied, for example, the quadratic mixture model requires only 15 experiments plus replicates and lack-of-fit points, while a quadratic-slack, factorial model requires 51 experiments. 1. First published in Paint and Coatings Industry, January, 2002. 2. Published in Paint and Coatings Industry, July, 2004. Since 1948 CONN CO., L.L.C. AND www.connblade.com FAX (814) 723-8502 62 MARCH 2008 | W W W . P C I M A G . C O M Stirrers Or Complete Units For: PAINTS URETHANE FOAMS ADHESIVES SLURRIES INKS GROUTS CEMENTS ETC. . . . 11 SOUTH MARION STREET • WARREN, PENNA. 16365 • PHONE 814/723-7980 sr r TM Visit ads.pcimag.com http://www.connblade.com http://www.connblade.com http://www.connblade.com http://ads.pcimag.com http://WWW.PCIMAG.COM

Table of Contents Feed for the Digital Edition of Paint & Coatings Industry - March 2008

Viewpoint Industry News Calendar of Events Company News Mergers and Acquisitions Names in the News Marketplace Quarterly Stock Watch Reaching Strict VOC Requirements With Outstanding Durability for Industrial Maintenance and Marine Coatings A Unique Fungicide for Wood-Filled Plastic deSigns of the Times: Slacking Off! From Rocks to Nanos Shear-Free Dispersion Process Fluorinated Oxetane Oligomers as Versatile Intermediates for Polymer Modification The Effects of TPO Composition on Adhesion and Proposed Chemical Mechanism Supplier Showcase Color Management Materials Watch Products Classifieds Advertiser Index

Paint & Coatings Industry - March 2008

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