When there are numerous treatment factors to be examined but a limited budget, it may only be possible to observe a small proportion of the treatment combinations. Some main-effect and interaction contrasts cannot then be distinguished and are said to be aliased. Such fractional factorial experiments form the topic of in this chapter 15, where two methods of design construction are discussed to enable minimum aliasing between important contrasts. The first method is to select one block from a single-replicate block design. The second method uses the concept of an orthogonal array. Saturated designs, supersaturated designs, and definitive screening designs are introduced for searching for influential factors among a large number of potentially important factors. The concepts introduced in this chapter are illustrated through a real experiment and with the use of SAS and R software