IJE TRANSACTIONS A: Basics Vol. 31, No. 1 (January 2018) 12-18   

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W. A. A. Alqraghuli, A. F. M. Alkarkhi and Y. Yusup
( Received: October 24, 2017 – Accepted in Revised Form: November 30, 2017 )

Abstract    Three-factor interaction for the two-level, three-level, and four-level factorial designs was studied. A new technique and formula based on the coefficients of orthogonal polynomial contrast were proposed to calculate the effect of the three-factor interaction The results show that the proposed technique was in agreement with the least squares method. The advantages of the new technique are 1) it is fixed, 2) it is simple and 3) it is easy to apply without the complicated matrix formula of the least squares method. This new technique will also enhance the use of the coefficients of orthogonal contrast when analyzing other experimental designs.


Keywords    Two-level factorial design, Three-level factorial design, Four-level factorial design, Response surface models


چکیده    تعامل سه عامل برای طرح های فاکتوریل دو سطح، سه سطح و چهار سطح مورد مطالعه قرار گرفت. یک روش و فرمول جدید مبتنی بر ضرایب کنتراست چندجمله ای متعامد برای محاسبه اثر متقابل سه عامل پیشنهاد شده است. نتایج نشان می دهد که روش پیشنهادی با روش کوچکترین مربع مطابقت دارد. مزایای روش جدید عبارتند از: 1) آن تثبیت شده است، 2) ساده است و 3) استفاده از آن بدون فرمول ماتریس پیچیده روش کوچکترین مربع آسان است.همچنین، این روش جدید استفاده از ضرایب کنتراست متعادل را هنگام تحلیل سایر طرح های تجربی افزایش می دهد.


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