FRACTIONAL FACTORIAL-DESIGNS FOR FACTORS WITH A PRIME NUMBER OF QUANTITATIVE LEVELS

A technique for single degree of freedom partitioning of canonical contrasts for prime level factorials with quantitative levels is reviewed. The relationship between canonical contrasts and the polynomial contrasts of response function models is discussed. Aliasing of canonical contrasts in fractional factorials is examined and alias sets from principal fractions are shown to have a particularly simple structure. Second-order response function designs built from single principal fractions or from sums of two or four different principal fractions are discussed. The accommodation of nuisance trend effects in experiments with quantitative factor effects is exemplified. Tables of fractional factorial designs for factors with three or five quantitative levels are presented.