Fractional Factorial Designs and Codes

Öz

Fractional factorial experiments with minimum aberration are commonly used in practice. In this study the characteristics of two-level fractional factorial experiments, namely word length pattern, resolution, aberration etc. are introduced. By exploring the algebraic structure of two-level fractional factorial designs, the connection between coding theory, especially Hamming codes, and fractional factorial designs is investigated. Two-level fractional factorial designs are constructed from codes (Hamming, binary linear and binary cyclic codes), and are ordered by the minimum aberration criterion. Designs and their corresponding codes are listed in a catalog.

Anahtar Kelimeler

• Minimum aberration
• Hamming codes
• Fractional factorial designs
• Coding theory

Kesirli Çok Etkenli Tasarımlar ve Kodlar

Öz

Kesirli çok etkenli en az sapma tasarımları, uygulamada yaygın olarak kullanılmaktadır. Bu çalışmada, 2-düzeyli kesirli çok etkenli tasarımların; kelime uzunluğu yapısı, çözüm, en az sapma vb. gibi özellikleri tanıtılmıştır. İki-düzeyli kesirli çok etkenli tasarımların cebirsel yapısı araştırılarak; kod teorisi, özellikle Hamming kodları, ile kesirli çok etkenli tasarımlar arasındaki ilişki incelenmiştir. 2-düzeyli kesirli çok etkenli tasarımlar, kodlardan (Hamming kodları, ikili doğrusal ve döngüsel kodlar) yararlanarak oluşturulmuş ve en az sapma ölçütüne göre sıralanmıştır. Tasarımlar ve kod olarak karşılıkları bir katalogda toplanmıştır.

Anahtar Kelimeler

• En az sapma
• Hamming kodları
• Kesirli çok etkenli tasarımlar
• Kod teorisi

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