2016-Sustainable Industrial Processing Summit
SIPS 2016 Volume 4: Santilli Intl. Symp. / Mathematics Applications
| Editors: | Kongoli F, Gaines G, Georgiev S, Bhalekar A |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2016 |
| Pages: | 320 pages |
| ISBN: | 978-1-987820-42-3 |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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The use of symmetric Latin squares in experimental designs on sustainable engineering
Raul Falcon1;1UNIVERSITY OF SEVILLE, Seville, Spain;
Type of Paper: Regular
Id Paper: 232
Topic: 38
Abstract:
Latin square design is commonly used to eliminate the effect of two nuisance factors on an experiment for which the efficiency of some treatments is required to be tested. Thus, for instance, the fuel consumption of distinct brands of petrol by distinct types of vehicles and drivers can be analyzed by means of Latin square design. Both nuisance factors are respectively regarded as rows and columns of a Latin square whose symbols represent the treatments under consideration. This is randomly selected from a predetermined set of Latin squares of a given order. The respective assignment of both factors and treatments to the different rows, columns and symbols of this Latin square is also randomly carried out. The analysis of the effects of both nuisance factors and treatments, which are usually tested by means of ANOVA and $F$ tests, depends directly on which Latin square is chosen. Particularly, it depends on its autotopism group, because the more symmetric is the Latin square, the less distinct designs can be considered. This work focuses in particular on the influence that right-multiplication autotopisms have in the analysis of variance of distinct types of problems on sustainable engineering. To this end, we simulate experimental designs based on an additive model for Latin square design.