A simple method for dealing with aliasing in experimental design

Abstract

Purpose

The aim of this paper is to proposes a simple and unified method for generating the aliasing pattern of two‐ and three‐level fractional factorial designs be they regular or non‐regular. The paper also demonstrates how the aliasing patterns obtained using the postulated method can be used to render the main measures of aliasing severity.

Design/methodology/approach

The proposed method is based on viewing the fractional factorial designs geometrically. It entails regarding the columns of any design as vectors. On the premise that any two vectors are orthogonal if they are at right angle and bearing in mind that aliasing is a form of departure from orthogonality, the proposed method determines the degree of aliasing between any two columns by assessing the extent to which the angle between them differs from 90°.

Findings

Three examples were used to illustrate how the proposed method can be applied and to validate its results. The first dealt with a regular two‐level L₈ 2⁵⁻² design whereas the second concerned a non‐regular two‐level L₁₂ design used to study five‐factors, and the third example is based on a non‐regular L₁₈ design employed to examine three‐factors at three‐levels. For each of these, the aliasing pattern generated using the proposed method matches the one obtained using the conventional methods.

Originality/value

A recent empirical study of how experimental design is applied in certain Manufacturing Engineering journals revealed that aliasing is rarely investigated. One possible reason for this is the difficulty associated with comprehending the conventional methods of dealing with aliasing particularly in the cases where non‐regular two‐ and three‐level orthogonal arrays are used. The proposal of a simple and unified method for dealing with aliasing should encourage the researchers and practitioners to assess aliasing when performing their experiments.

Citation

Al‐Ghamdi, K.A. (2013), "A simple method for dealing with aliasing in experimental design", International Journal of Quality & Reliability Management, Vol. 30 No. 8, pp. 877-896. https://doi.org/10.1108/IJQRM-Jan-2012-0006