W.A.A Alqraghuli - School of Mathematical Sciences, Universiti Sains Malaysia, Pulau Pinang, Malaysia
A.F.M Alkarkhi - Malaysian Institute of Chemical & Bioengineering Technology Universiti Kuala Lumpur, (UniKL, MICET), Melaka, Malaysia
Y. Yusup - School of Industrial Technology, Universiti Sains Malaysia, Pulau Pinang, Malaysia

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.

Two-level Factorial Design,Three-level Factorial Design,Four-level Factorial Design,Response Surface Models,