6 - Full factorial designs

Abstract

Most commonly used experimental designs in manufacturing companies are full and fractional factorial designs at two and three levels. Factorial designs would enable an experimenter to study the joint effect of the factors on a response. A factorial design can be either full or fractional factorial. This chapter focuses on full factorial designs at two levels only. A full factorial designed experiment consists of all possible combinations of levels for all factors. The total number of experiments for studying k factors at two levels is 2 k . The 2 k full factorial design is particularly useful in the early stages of the experimental work, especially when the number of process parameters or design parameters (or factors) is less than or equal to 4. One of the assumptions one makes for factors at two levels is that the response is approximately linear over the range of the factor settings chosen. The first design in the 2 k series is one with only two factors, say, A and B, each factor to be studied at two levels. This is called a 2 2 full factorial design.